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Simulation Modeling for
Staff Optimization of the
Toronto Emergency Medical
Services Call Centre
Gillian Chin & Jason Coke
A thesis submitted in partial fulfilment
of the requirements for the degree of
BACHELOR OF APPLIED SCIENCE
Supervisor: Professor M.W. Carter
Department of Mechanical and Industrial Engineering
University of Toronto
March 2008
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Abstract
The Toronto Emergency Medical Service (EMS) Call Centre is responsible for receiving 911
calls from the public and dispatching ambulances should they be required. The Call Centre faces
the issue of how many call takers to staff on the four 12-hour shifts. The purpose of this thesis is
to determine the effectiveness of the current staffing routine as well as calculating the optimal
number of call takers for any given hour of the week. There must be a balance between having
excess capacity for unexpected demand spikes, and keeping the number of call takers minimal to
save resources.
This analysis was performed by assessing approximately three years of historical data on calls to
EMS. A simulation model was built with Simul8 software to gauge the effects of different
combinations of call takers, across the standard shift patterns. Since historical demand for EMS
calls is rising, an increase in call volume was also simulated to determine if current EMS staffing
levels are suitable for the future. Finally, an Excel spreadsheet was built as a model to validate the
results found in Simul8.
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Acknowledgements
We would like to extend our gratitude to the following for their time, efforts and expertise in
supporting us for the duration of this thesis.
Professor Michael Carter
Dave Lyons, Manager of the Toronto EMS System Control Centre Design Project
Dan Cottom, Coordinator, Control Centre Design Project, Toronto EMS
Adrian, Data Analyst, Toronto EMS
Wallace Law, Indy 0T7+PEY and Visual8 Consultant
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Table of Contents
ACKNOWLEDGEMENTS ..............................................................................................................................I
TABLE OF CONTENTS ................................................................................................................................II
LIST OF FIGURES ...................................................................................................................................... V
LIST OF TABLES ....................................................................................................................................... VI
1.0 INTRODUCTION .................................................................................................................................. 1
1.1 PURPOSE ................................................................................................................................................. 1 1.2 BACKGROUND .......................................................................................................................................... 1 1.3 MOTIVATION ............................................................................................................................................ 2 1.4 OBJECTIVES .............................................................................................................................................. 3
2.0 LITERATURE REVIEW ........................................................................................................................... 5
2.1 THE USE OF SIMULATION FOR MODELING/ANALYSIS........................................................................................ 5 2.2 QUEUING THEORY AS A VIABLE METHODOLOGY OF DATA REPRESENTATION ......................................................... 7 2.3 SIMULATION AND QUEUING THEORY IN RELATION TO CALL CENTRES ................................................................... 8 2.4 SIMULATION AND QUEUING THEORY IN RELATION TO EMERGENCY SERVICES ...................................................... 10
3.0 METHODOLOGY ................................................................................................................................ 12
3.1 DESCRIPTION OF CALL RECEIVING SYSTEM .................................................................................................... 12 3.1.1 Description of General System for Call Receiving: ...................................................................... 12 3.1.2 Description of ACD Specific Call Receiving System ..................................................................... 14
3.2 DATA ANALYSIS ...................................................................................................................................... 15 3.2.1 Incoming Call Distributions/Inter-arrival Rates .......................................................................... 15 3.2.2 Call Durations ............................................................................................................................. 19 3.2.3 Call Duration Distribution ........................................................................................................... 20
3.3 ENTERING DATA INTO THE SIMULATION MODEL ............................................................................................ 22 3.3.1 Incoming Call Distributions/Inter-arrival Rates .......................................................................... 22 3.3.2 Call Duration Distribution ........................................................................................................... 22
4.0 THE SIMULATION MODEL ................................................................................................................. 23
4.1 DATA DEVELOPMENT: LEARNING THE SYSTEM .............................................................................................. 23 4.2 PHYSICAL STRUCTURE OF THE SIMULATION ................................................................................................... 24
4.2.1 Call Arrivals ................................................................................................................................. 24 4.2.2 Queue for Incoming Calls ........................................................................................................... 24 4.2.3 Call Stations ................................................................................................................................ 25
4.3 VISUAL LOGIC COMMANDS ....................................................................................................................... 25 4.3.1 Inter-Arrival Rate Parameter Reset ............................................................................................ 25 4.3.2 Call Durations ............................................................................................................................. 26 4.3.3 Pre-emptive Call Priorities .......................................................................................................... 26 4.3.4 Incorporating Shift Patterns ....................................................................................................... 27
5.0 THE EXCEL MODEL ............................................................................................................................ 30
5.1 RATIONALE FOR THE NEED OF AN EXCEL MODEL ............................................................................................ 30 5.2 METHODOLOGY FOR CONSTRUCTING THE EXCEL MODEL ................................................................................ 30
5.2.1 The Numerical Representation ................................................................................................... 31 5.2.2 The Graphical Representation .................................................................................................... 31
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5.3 FUNCTIONALITY ...................................................................................................................................... 32 5.3.1 Parameter Changes .................................................................................................................... 32
5.3.1.1 Desired Busy Rate ................................................................................................................................ 32 5.3.1.2 Probability............................................................................................................................................ 32 5.3.1.3 Total Call Volume ................................................................................................................................. 33
5.3.2 Two Methods of Adjusting Call Volume ..................................................................................... 33 5.3.2.1 Adjusting by Total Call Volume ............................................................................................................ 33 5.3.2.2 Adjusting Call Volume by Hour of the Week ........................................................................................ 33
6.0 ANALYSIS OF RESULTS ...................................................................................................................... 37
6.1 – ANALYSIS OVERVIEW ............................................................................................................................. 37 6.2 – VARIABLES .......................................................................................................................................... 38
6.2.1 – Time of Day.............................................................................................................................. 38 6.2.2 – Call Takers per Shift ................................................................................................................. 40 6.2.3 – Call Volume .............................................................................................................................. 41
6.3 KEY PERFORMANCE INDICATORS ................................................................................................................ 41 6.4 DISCUSSION OF RESULTS ........................................................................................................................... 43
6.4.1 Example of Results Obtained ...................................................................................................... 43 6.4.1.1 Example of Use of Results .................................................................................................................... 44
6.4.2 Results by Time Window at 100% Call Volume .......................................................................... 45 6.4.3 Results by Time Window at 115% Call Volume .......................................................................... 51 6.4.4 Summary of Results .................................................................................................................... 54
6.5 COMPARISON OF TIME WINDOW RESULTS TO 24/7 RESULTS .......................................................................... 56 6.5.1 Weekends ................................................................................................................................... 59
6.6 QUESTIONS ANSWERED ............................................................................................................................ 60 6.6.1 Current Sufficiency of Staffing Levels ......................................................................................... 60 6.6.2 Overstaffing and Understaffing.................................................................................................. 60 6.6.3 Sufficiency of Current Staffing levels in the Future ..................................................................... 60 6.6.4 Required Staffing Levels ............................................................................................................. 61
7.0 VALIDATION ..................................................................................................................................... 62
7.1 VALIDATION BY AN EXPERT ........................................................................................................................ 62 7.1.1 Validation of the Simulation Model ............................................................................................ 62 7.1.2 Validation of the Excel Model ..................................................................................................... 62
7.2 VALIDATION BY COMPARING SIMUL8 RESULTS WITH EXCEL-BASED MODEL ......................................................... 63 7.2.1 Validation by Means of Producing Similar Conclusions .............................................................. 63 7.2.2 Validation by Numerical Comparison of Results ........................................................................ 66
8.0 CONCLUSION AND RECOMMENDATIONS ......................................................................................... 68
8.1 SUMMARY ............................................................................................................................................. 68 8.2 CONCLUSION .......................................................................................................................................... 68 8.3 RECOMMENDATIONS ............................................................................................................................... 70
8.3.1 Night Staffing ............................................................................................................................. 70 8.3.2 Day Staffing ................................................................................................................................ 70 8.3.3 Afternoon/Evening Staffing ........................................................................................................ 70 8.3.4 Break Periods .............................................................................................................................. 70 8.3.5 Shift Start Times ......................................................................................................................... 71
9.0 FUTURE WORK .................................................................................................................................. 72
9.1 CHANGING THE SHIFT SCHEDULE ................................................................................................................ 72 9.2 WORKFORCE SCHEDULING ........................................................................................................................ 72 9.3 NON-HOMOGENEOUS WORKFORCE ............................................................................................................ 73
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9.4 SIMUL8 OPTIMIZATION FUNCTION – OPTQUEST ........................................................................................... 73 9.5 INCREASING THE TIME GRANULARITY OF THE ANALYSIS/SEASONALITY ............................................................... 73 9.6 CREATING QUEUES FOR EACH CALL PRIORITY ................................................................................................ 74 9.7 WEEKEND STAFFING LEVELS ...................................................................................................................... 74
BIBLIOGRAPHY ....................................................................................................................................... 76
APPENDIX A: COMPLETE SIMUL8 RESULTS ............................................................................................. 77
APPENDIX B: USER MANUAL FOR SIMUL8 SIMULATION MODEL ............................................................ 92
APPENDIX C: USER MANUAL FOR EXCEL-BASED CALL TAKER MODEL ..................................................... 97
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List of Figures
Figure 1: Process Overview of the Thesis Methodology .................................................... 4
Figure 2: Example of Three Phone Lines at EMS Headquarters ...................................... 12
Figure 3: Example of Hourly Call Instances ..................................................................... 16
Figure 4: Example of Data Points Listings ....................................................................... 16
Figure 5: Example of Best Fit Software Fitting a Distribution ......................................... 17
Figure 6: Example Output for Erlang Parameters for Monday ......................................... 18
Figure 7: Example of Call Duration Determination .......................................................... 19
Figure 8: Average Call Duration for Various Call Types ................................................. 20
Figure 9: Duration of Emergency Calls Distribution ........................................................ 20
Figure 10: Duration of Emergency Calls Distribution in Ten Segments .......................... 21
Figure 11: Example of Call Duration Distribution used for Simul8 ................................. 22
Figure 12: Shift Patterns including Breaks ....................................................................... 28
Figure 13: Image of the Simul8 Model ............................................................................. 29
Figure 14: Image of the Excel Model – Numerical Representation .................................. 34
Figure 15: Image of the Excel Model – Graphical Representation ................................... 35
Figure 16: Image of Excel Model – Call Volume by Hour of the Week .......................... 36
Figure 17: Average Number of Calls, by Hour of Week, Last Three Years ..................... 37
Figure 18: Shift Patterns for Call Takers at EMS Call Centre .......................................... 39
Figure 19: Graph from Excel Model – Minimum Number of Call Takers ....................... 59
Figure 20: Actual (4-2-2-2) Staffing Levels vs. Required Staffing Levels ....................... 64
Figure 21: Actual (6-4-2-2) Staffing Levels vs. Required Staffing Levels ....................... 65
Figure 24: Example of Erlang distribution for calls on Monday from 8am-9am ............. 99
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List of Tables
Table 1: Clock Time Windows Examined ........................................................................ 40
Table 2: Number of Call Takers per Shift – Actual and Simulated .................................. 40
Table 3: Example Results Tableau as seen in Simul8 ....................................................... 43
Table 4: Results 0000- 0200 / 4-[2,3,4]-2-2 / 100% Call Volume .................................... 45
Table 5: Results 0200-0700 / 4-[2,3,4,5,6]-2-2 / 100% Call Volume ............................... 47
Table 6: Results 0700-1000 / [4,5,6]-2-2-2 / 100% Call Volume ..................................... 48
Table 7: Results 1000-1400 / [4,5,6]-2-[3,4,5]-2 / 100% Call Volume ............................ 48
Table 8: Results 1400-1900 / [4,5]-2-[2,3]-2 / 100% Call Volume .................................. 49
Table 9: Results 1900-2400 / 4-[2,3,4]-[2,3]-[2,3] / 100% Call Volume ......................... 49
Table 10: Results 0200-0230 / 4-[2,3,4,5,6,7]-2-2 / 100% Call Volume .......................... 50
Table 11: Results 0000-0200 / 4-[2,3,4]-2-2 / 115% Call Volume ................................... 51
Table 12: Results 0200-0700 / 4-[2,3,4,5,6,7]-2-2 / 115% Call Volume .......................... 51
Table 13: Results 0700-1000 / [4,5,6]-2-2-2 / 115% Call Volume ................................... 52
Table 14: Results 1000-1400 / [4,5,6]-2-[2,3,4]-2 / 115% Call Volume .......................... 53
Table 15: Results 1400-1900 / [4,5,6]-2-2-[2,3] / 115% Volume ..................................... 53
Table 16: Results 1900-2400 / 4-[2.3]-2-2 / 115% Call Volume ...................................... 54
Table 17: Results 0200-0230 / 4-[2,3,4,5,6,7]-2-2 / 115% Call Volume .......................... 54
Table 18: Minimum Staffing Level where at least 95% of Calls Answered Within 10
Seconds.............................................................................................................................. 55
Table 19: Shift Pattern versus Percentage of Calls Answered within Ten Seconds ......... 58
Table 20: Numerical Comparison of Excel and Simul8 Staffing Levels .......................... 66
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List of Thesis Project Responsibilities
Site Visits to EMS: Both
Simulation Model: Gillian Chin
Excel Model: Jason Coke
Analysis of Simul8 results: Both
Writing: Both, as described in thesis body
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1.0 Introduction
(written by Gillian Chin)
1.1 Purpose
The purpose of this document is to account for the work completed, the methodology
used and the results obtained for this fourth year Industrial Engineering thesis project. This thesis
project primarily focused on performing analyses of the call-taking functionality of the Toronto
EMS Call Centre, and was conducted through the construction and examination of simulation
models using Simul8 software. The goal is to optimize the staffing levels of call takers by striking
a balance between allowing for excess capacity, yet not wasting resources needlessly.
1.2 Background
The Toronto Emergency Medical Service (EMS) is currently the largest service of its
kind in Canada. It is one of the largest and most comprehensive pre-hospital emergency care
systems in the world and it is internationally recognized for its system’s design. It is the primary
source of both emergency and non-emergency medical transportation within the GTA, servicing a
population of approximately 3.5 million people, addressing over 425,000 9-1-1 calls and
transporting 165,000 medical patients each year [1]. It currently employs approximately 1,125
personnel, 76% of which are paramedics, while the remainder is composed of management,
dispatchers and support staff. In addition, there are currently 45 EMS stations posted throughout
the Toronto area, with ambulances reporting an average utilization rate of 45.29% in servicing the
public and covering over 650 square kilometres [1].
Toronto EMS is also responsible for providing 24 hr emergency and non-emergency pre-
hospital medical care, as well as offering transportation to individuals experiencing injury or
illness, fostering the motto of “People Helping People”. More specifically, the Mission Statement
of Toronto EMS is as follows:
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“Toronto Emergency Medical Services (EMS) exists to safeguard the quality of life in our city through the provision of outstanding ambulance-based health services, responding in particular to medical emergencies and to special needs of vulnerable communities through mobile health care.”[2]
1.3 Motivation
The Toronto Emergency Medical Service represents an integral part of the region’s health
care delivery system, and is viewed as an essential public safety service for the community and its
citizens. In order to maintain its level of service and responsibilities to the GTA, it is continually
attempting to improve and integrate its systems with other public services, so as to remain as
efficient and effective as possible. However, from the years 2000 to 2006, the number of medical
emergencies in Toronto per year rose dramatically from 188,000 to 215,000 [1]. Despite budget
increases during this period, the general consensus among EMS personnel was that the level of
effectiveness experienced by the increased investment into their division did not adequately
relieve the pressures and burdens felt by related resources and personnel [3]. It was also believed
that an exhaustive and in-depth analysis of the overall system was required, in order to suggest
possible redesign changes that would improve effectiveness and thoroughly address these issues
of service levels in conjunction with operator utilization.
While holistic and system wide improvements are in need of implementation in order to
regain optimal service levels and response times, the focus of this thesis will be limited
specifically to the EMS Call Centre. This is primarily due to the time versus complexity
constraints, and hence the focus will specifically be on the call-taking functionality. When a
medical emergency occurs, the Call Centre is the first point of contact for a victim or witness.
Being able to rapidly assess the caller’s situation and the medical severity of the victim, as well as
being able to dispatch an appropriate response unit based on location and readiness, in as little
time as possible, is a matter of life and death.
Since the focus of this project is on the call-taking functionality at the EMS Call Centre, a
thorough understanding of the process and system is required. For example, it is important to
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know that in addition to answering emergency 9-1-1 calls, call takers in the Call Centre must also
respond to administrative and non-emergency calls. An added complexity to the analysis is that
the call takers are unaware beforehand which kind of call they will be receiving, as it is entirely
possible that emergency calls are received from non-emergency lines, and vice versa.
The pattern of incoming calls is also an important aspect to study; the amount of calls being
received by EMS personnel on weekdays tends to follow a fairly stable daily pattern that rises and
falls quite predictably [3]. A similar pattern can be found for weekends. Despite the “average”
amount of calls being stable and predictable, on any given day there will be random variations,
and effects such as the weather or civic events can have an effect on the number of calls.
Therefore, given that EMS needs to ensure that call demand during peak hours (10am – 2pm on
weekdays) is met by a sufficient supply of call takers, much thought needs to put into the staffing
levels of call takers, and therefore this is one of the primary objectives of this thesis project.
1.4 Objectives
The primary objective of this thesis is to build a simulation model that accurately reflects
the EMS Call Centre, its incoming calls and the rates at which they are processed by call takers.
In order to achieve this, two other objectives must be completed. First, historical call data must be
analyzed to determine the frequency and duration of calls. These are used as input parameters for
the simulation model. The simulation is then run for a number of trials while varying parameters
like the number of call takers on duty and the volume of incoming calls. After the results of the
simulation have been obtained, they must be validated. This occurs in two ways; first, they are
validated by experts at EMS. Secondly, they are validated mathematically by an Excel-based
model of the Call Centre. A flow chart of the process can be seen in Figure 1 below.
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Figure 1: Process Overview of the Thesis Methodology
Once the model has been validated, the results will be analyzed and the most important
questions will be answered. These questions are as follows:
� Are current staffing levels sufficient to meet current call demand?
� Are there times when the Call Centre is overstaffed or understaffed?
� If so, what should the number of call takers be during any given hour of the week?
� Are current staffing levels sufficient to meet an increase in call volume in the future?
� If not, what staffing levels will be required to meet that increase in volume?
In addition to answering these questions, given the current data available and the current
simulation model, the intention is to provide EMS with a workable simulation model that can be
used in future analyses.
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2.0 Literature Review
(written by Gillian Chin)
The use of simulation and queuing theory in analyzing large scale complex systems has
been well-documented in a diverse group of industries and applications. This section of the thesis
report will thoroughly discuss and review the concepts behind the topics of simulation, queuing
theory, and their applications specifically to call centres, as well as justify their validity and worth
to the analysis in this thesis. It will also document theories and concepts taken from academic and
industrial sources, in an attempt to develop a more comprehensive description of the associated
topics, and further highlight their usefulness to the analysis performed.
2.1 The Use of Simulation for Modeling/Analysis
Simulation has been proven useful in numerous industries and under a wide variety of
applications, providing insight into complex, organizational behaviour and developing
improvements in real world operations without imposing any real changes to the system or
physical structure. When analyzing a system, in some instances many simulation models can be
solved using algorithmic or mathematical means; however, there are many cases where the
system is so inherently complex, it makes it virtually impossible to solve to optimality through
mathematical measures. In the latter case, computer simulation provides an invaluable tool in
analyzing complex systems for the behaviour of the system can be imitated over time. As a result,
data can be analyzed and collected as if the real system were being observed and this also allows
for alternate configurations of the existing system to be assessed, without any real changes being
made to the physical structure [4]. Historically, a model is defined as “a representation of a
system for the purpose of studying the system” [4]. Furthermore, a simulation model is defined as
“the imitation of the operation of a real-world process or system over time. Whether done by
hand or on a computer, simulation involves the generation of an artificial history of a system, and
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the observation of the artificial history to draw inferences concerning the operating characteristics
of the real system” [4]. Thus, through the method of constructing and analyzing system behaviour
through careful investigation, logical inferences can be made that may improve system
performance and/or design, without altering the present system, making simulation a very
powerful tool.
Though simulation has been proven to be a very effective and powerful tool in a diverse
group of industries, its use must be carefully regulated. Situations where simulation is deemed
appropriate for use are listed below [4]:
1. Simulation enables the study of and experimentation with the internal interactions of a
complex system or of a subsystem within a complex system
2. Informational, organizational and environmental changes can be simulated and the effect
of these alterations on the model’s behaviour can be observed
3. The knowledge gained in designing a simulation model may be of great value toward
suggesting improvement in the system under investigation
4. By changing simulation inputs and observing the resulting outputs, valuable insight may
be obtained into which variables are most important and how variables interact
5. Simulation can be used as a pedagogical device to reinforce analytical solution
methodologies
6. Simulation can be used to experiment with new designs or policies prior to
implementation, so as to prepare for what may happen
7. Simulation can be used to verify analytical solutions
8. By simulating different capabilities for machines, requirements can be determined
9. Simulation models designed for training allow learning without the cost and disruption of
on-the-job learning
10. The modern system is so complex that the interactions can be treated only through
simulation
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Although simulation has been termed a powerful and revolutionary tool in systems
management, there are many caveats associated with its use. The primary disadvantages of
simulation are as follows [4]:
1. Model building requires special training
2. Simulation results can be difficult to interpret
3. Simulation modeling and analysis can be time consuming and expensive
4. Simulation is used in some cases when an analytical solution is possible or even
preferable
2.2 Queuing Theory as a Viable Methodology of Data Representation
While it may be quite difficult to formulate and conceptualize complex systems in terms
of their overall structure and description, it is often quite possible to develop a representative
mathematical model of mostly any complex system, which allows the general characteristics and
behaviour to be assessed and analyzed, in an attempt to determine insightful observations and
useful information. This can typically be performed through the use of queuing theory. Queuing
Theory is often used to describe the “more specialized mathematical theory of waiting lines, or
queues,” [5] and has been proven useful in many simulation models. It is also typically associated
with business strategies or plans associated with allocating resources with the express objective of
providing a level of service. Coincidentally, “the subject of queuing theory has been developed
largely in the context of telephone traffic engineering” [5] which is particularly useful in the
analysis of this thesis where “such models can be defined in terms of three characteristics: the
input process, the service mechanism, and the queue discipline” [5]. The input process defines
how arrivals are structured and what mathematical model can be used to imitate its behaviour,
meaning it specifies the population of the individuals who represent potential clients of the
system, also known as the calling population. The service mechanism determines how each
activity or item is handled once they are selected from the queue, and the queue discipline
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determines the manner in which the activities or items are processed. For example, the service
mechanism may specify the service time or the amount of time it takes to service a customer,
while queue disciple will determine the way and order they are served, such as: FIFO (First In,
First Out) and LIFO (Last In, First Out) [5].
The use of queuing theory also allows for the calculation of key performance measures or
deliverables, which evaluates the efficiency and effectiveness of the underlying system by
calculating, for example, the average wait time in the system. Conversely however, queuing
theory does have its limitations. Many of the assumptions made in queuing theory may not reflect
the real world environment and may adversely affect calculations: for example, infinite capacity
in a queue or infinite calling populations. Therefore, care must be taken when utilizing queuing
theory as a means of data representation, to ensure that any simplifying assumptions made do not
sufficiently distort the analysis, creating false data and incorrect conclusions.
2.3 Simulation and Queuing Theory in relation to Call Centres
In terms of the use of queuing theory and call centres, most of the preliminary study and
research in queuing theory was associated with telephone systems. For example, one of the first
published articles pertaining to queuing theory was a paper published by Johannsen in 1907 titled
“Waiting Times and Number of Calls” [6]. Furthermore, in terms of the importance and long
range impact in queuing theory, A.K. Erlang published a series of articles starting from 1909 and
covering the next 20 years. “Erlang himself was a Danish telephone engineer who developed his
ideas while trying to solve the operational problems of the telephone system” [6]. Thus, much of
the initial research into queuing theory was developed and associated with real world problems or
applications that were experienced at the time of invention, many problems of which were
associated with the telephone or communication system.
By definition, a call centre “constitutes a set of resources which enable the delivery of
service over the telephone […] Typically, call centre goals are formulated as the provision of
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service at a given quality, subject to a specific budget” [7]. Specifically, queues in service
operations are a vital measure and diagnostic tool for determining quality levels. Customers
derive their experience from their time spent in the queue and/or system; as stated by Koole and
Mandelbaum, queues in service play the same role as inventory does in manufacturing. Queues
can be used as an indicator for control and improvement opportunities, and they “provide
unbiased quantifiable measures in terms of performance, which is relatively easy to monitor and
goals are naturally formed” [7].
However, over the next few years, call centres will continue to grow exponentially in
operational complexity. Call volume will undoubtedly escalate, with increasing complex
schedules, routing rules and different operator skills. While mathematical models have proven
useful in coordinating call centres, simulation has begun to play a more important role in
scheduling and call centre management. As specified by Mehrotra et al, there are three major
ways that simulation can be utilized within the call centre industry, to supplement the
mathematical analysis:
Traditional Simulation Analysis: A simulation model is built to analyze a specific operation.
Embedded Application: Routing: These include a routing simulation to provide insight about the
impact of different decisions when it comes to the routing design.
Embedded Application: Agent Scheduling: This is a complex scheduling problem, which
becomes even more complex when both calls and agents are non-homogenous. [8]
The analysis that was performed for this specific thesis project is a hybrid between a
Traditional Simulation Analysis, and the Embedded Application: Agent Scheduling. While the
simulation model that was built focuses on the specific operation of call-taking, we are concerned
with the scheduling of homogenous agents required to service different classes of calls.
Another example of simulation use in call centres would be the case at Bell Canada. Bell
was concerned with maintaining a positive relationship with their customers, and viewed this
relationship as an essential component, critical to their success. The analysis was prompted more
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as an improvement measure, and was initiated internally. The result from the analysis was a
greater understanding of the system, and improved operations through the discovery of
bottlenecks and redundant work. In conclusion, Bell managed to build an operational business
design and decision tool that analyzed and measured customer experience, through the use of
simulation at their call centres [9]. Thus, simulation is a vital tool in analyzing complex systems,
such as a call centre, and has certain advantages over mathematical methods, and renders itself a
vital component to achieving improvements in operations.
2.4 Simulation and Queuing Theory in relation to Emergency Services
There have been many documented cases of the use of simulation and queuing theory
applications in the emergency services sector. Many, however, are focused on the holistic view of
emergency services rather than addressing the issue of call centres specifically. In addition, the
majority of published academic articles on call centres to date seem to be restricted to
applications in commercial environments rather than of public service. However, given these
circumstances, the use of simulation and queuing theory in the emergency sector is an established
practice. For example, Wafik H. Iskander presented a paper at the 1989 Winter Simulation
Conference, on “Simulation Modeling for Emergency Medical Service Systems”. This paper
presented the development of a simulation model that was built with the express purpose of
aiding EMS planners and managers with a tool that would aid in planning their operations as well
as making decisions. This simulation model analyzed the entire process of delivering emergency
care, from receipt of call to return of ambulance to centre after transporting patients. The result of
the paper was that the developed simulation model was flexible enough to be adapted to any
geographical area, and could aid in pivotal decision making and operations planning [10]. E.S.
Savas also published a paper in the Management Science Journal in 1969, titled “Simulation and
Cost-Effectiveness Analysis of New York’s Ambulance Service”. The general ideas of the paper
were to highlight the advantages of using computer simulation to analyze possible improvements
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that could result from changing the number and locations of ambulances, and from which a cost
effectiveness analysis could be produced to analyze the changes. The result of the simulation
would be a lower operating cost for the emergency services, given optimal positioning of the
ambulance fleet, as well as a decision making tool for determining specific numbers and locations
of ambulances, that could be used on an iterative basis [11]. Finally, Syi Su and Chung-Liang
Shih published an article titled “Modeling an Emergency Medical Service System using
Computer Simulation”, which documented the use and advantages of utilizing computer
simulation in the Taipei Emergency Medical Service System, looking at the entire process of pre-
hospital care. In summary, the simulation managed to identify several areas in need of
improvement for delivering greater emergency care, in a method that was low cost, low risk and
easily operated [12]. Therefore, simulation has been well-documented in the emergency medical
service system, and implemented with great success in many cases, making simulation a powerful
tool for public service.
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3.0 Methodology
(written by Gillian Chin and Jason Coke)
This chapter describes the methodology used for the analysis of the EMS Call Centre,
and is separated into three major components. The first is the data analysis performed to construct
the simulation parameters. The second is the entry of those parameters into the simulation model
and the running of the model. The third is the use of an Excel scenario sheet which attempts to
validate the results found in the simulation model. As complete descriptions of the simulation
model and Excel model are discussed in Chapter 4 and Chapter 5, respectively, they will not be
discussed in depth in this chapter.
3.1 Description of Call Receiving System
The following sections describe the process of call reception at the EMS Call Centre.
3.1.1 Description of General System for Call Receiving:
The current system is set up with a total of 277 lines on which calls to the EMS Centre
can be received, 12 of which are designated 9-1-1 emergency lines. These 9-1-1 emergency lines
are divided into two separate trunks, each of which is designated to a specific area of Toronto;
one trunk for the East and one trunk for the West. Each line out of the total 277 is set up with two
separate priority codes, forming a two-dimensional priority scheme. To explain these two
schemes, an example is shown in Figure 2 below:
LinesFromAVTECDB
Line+umber Line+ame LineType EmergencyLine Priority ACDPriority
182 TOR FD 2 PHONE
05-28
P Y 7 7
196 397-9590 PHONE 03-
07
P Y 5 7
197 397-9591 PHONE 04-
07
P Y 8 7
Figure 2: Example of Three Phone Lines at EMS Headquarters
13
The ACD Priority number is the number designated for the Automatic Call Distribution
(ACD) priority, and this is the more influential priority number of the pair. The AVTEC
computer, which initially receives and prioritizes the calls, will first assess the ACD Priority
number, which in all three cases is “7”. Within the ACD Priority Code “7”, there is an additional
priority scheme, the Priority Number. The Priority Number determines the sequence within an
assigned priority code, with the assumption that the higher the number, the greater the priority of
the call. These priority codes are attributed to these lines upon installation, and have nothing to do
with the actual content of the call (whether emergency, administrative or non-emergency).
Therefore, for this example, the sequence would be as follows: line 197, line 182, line 196. Line
197 is at the front of the queue, following the assumption that first, the call with the higher
priority ACD number, and second, the call with the higher priority code within that specific ACD
priority number, will be moved to the front of the queue.
For a call that is coming from the 9-1-1 Police Headquarters, there are 12 emergency
lines, as mentioned before. If a call is sent to an available line from the 9-1-1 headquarters, it will
ring for 5 seconds, and then switch to another line within the same trunk; Lines 1-5 and 12 are in
the first trunk, while Lines 6-11 are in the second trunk. These calls are not “answered” by a
human operator at EMS, but rather by the computer system known as AVTEC. AVTEC will
receive the call, and based on the line it entered from, priority levels will be assessed and the call
is placed within the queue that waits for an available call taker. If none of the twelve 9-1-1
emergency lines are available, the call is rejected.
Once a call is placed within the queue to the call takers, it waits in line until answered by
the next available call taker; synonymous to the queue in a bank. (View Figure 13: Image of the
Simul8 Model for a complete diagram of the call receiving system) Once a call is answered, the
call taker assesses the medical status of the victim and assigns a priority level, ranging from alpha
(lowest) to echo (highest). The call information is then sent to the dispatch area. In dispatch, there
14
are four dispatchers, one for each quadrant of the city. The call will be sent to the appropriate
dispatcher based on the location of the call. At that point, the dispatcher will then determine the
closest available ambulance unit and route it to the scene. If a call has been received by the
AVTEC computer, yet has not been answered by an available call-taker within ten seconds, each
line at every station within the Call Centre will begin ringing, including that of non-ACD staff:
for example, dispatchers. Therefore, for this analysis, the service goal that the model will attempt
to attain will be represented by this ten second interval after entry.
Throughout the field of systems modeling, simulation is known to be a valid
mathematical modeling and analysis tool that has been proven valuable to many industry
situations, including that of modeling EMS systems.
3.1.2 Description of ACD Specific Call Receiving System
The focus of this thesis project is to analyze the staffing requirements for the call taking
functionality and propose optimal, or near optimal results, with the primary objective of
maximizing the number of calls processed within a specific service level given a minimal amount
of workers. For this specific analysis, the service level that the model hopes to attain would be
that each call is answered by a call taker within ten seconds of receipt into the system. Therefore,
the focus of this thesis project is restricted only to the calls that call-takers will be responsible for,
and these are represented under the heading ACD or Automatic Call Distribution lines. These
lines are composed of the 12 emergency lines, discussed in the previous section, as well as 20
additional lines, that are primarily used for paramedics who are on scene and request aid, or for
scheduled patient transfer. As the scope of the analysis is limited to the responsibilities of the call
takers, which are confined to ACD specific lines, the simulation will be restricted to these lines
alone.
15
3.2 Data Analysis
This section describes the methodology used for determining the distribution of calls for
each hour of the week and hence their inter-arrival rates, as well as the call duration and call
distribution for each of the call types.
3.2.1 Incoming Call Distributions/Inter-arrival Rates EMS provided an Access database with details on all calls to EMS between July 2005
and September 2007. The initial format given was not very usable, so modification was
necessary. Primarily, it was required to change the date formats so that analysis could be
performed succinctly based on the dates. It was, however, found that entire blocks of dates were
missing from the database. Of the 802 total days between the start and end dates in the data, 83
days were missing, bringing the total number of days with data to a reduced total of 719.
The data was broken into three tables based on the three call types: ACD_2N
(Administrative), ACD_2Y_7_8 (Non-Emergency) and ACD_9 (Emergency). Using SQL
queries, these tables were further broken down based on day of week and hour of day. Then, the
total number of calls in each hour was determined. The final result was a table exported into
Excel that listed the number of calls in an hour, for every instance of that hour in the two year
period. An example of this can be seen in Figure 3 below.
16
Figure 3: Example of Hourly Call Instances
Once sorting had been performed to group all hours of each day together, the result was a
list of approximately 100 values that represented the spread of values for the number of calls in
each hour of the week. Due to the fact that some of the dates within the time range were missing,
not every hour of the week had as much as 100 values for it. The spread was between 79 and 105,
with the vast majority of the cases having more than 95 values. In any case, having this many data
points for each hour means there is a sufficient amount of data from which to create a valid
distribution.
An example of the listing of the number of these data points can be seen in Figure 4
below. The variability of these values increased greatly for ACD_2N and ACD_2Y_7_8 calls as
compared to ACD_9 calls, which were quite stable.
Figure 4: Example of Data Points Listings
17
The Best Fit 4.5 (Student version) software package was then used to determine the
distribution parameters for incoming calls. That is to say, for each call type, day and hour, the
data points were fitted to an Erlang distribution and the parameters alpha and beta were
calculated. An example of this can be seen in Figure 5 below.
Figure 5: Example of Best Fit Software Fitting a Distribution
A primary assumption of this model is that the call arrivals follow an Erlang distribution,
but as [4] has shown, incoming calls to a call centre do tend towards and Erlang distribution.
In addition to the three separate call types (administrative, non-emergency and
emergency), distributions were also fit to an overall call arrival rate that grouped all calls
together, rather than breaking them up. This was performed to allow for the possibility of using
only one call type that would have the properties of all three types combined into one. Thus, the
final output of this analysis was a chart that included, for each hour of the week, parameters alpha
and beta. Below, Figure 6 shows the final output for the amalgamated call type, as well as the
three specific call types and their distribution parameters for Monday only.
18
TOTAL CALLS Erlang Distribution ACD_9 Erlang Distribution ACD_2N Erlang Distribution ACD_2Y_7_8 Erlang Distribution
Day of Week Hour alpha beta Day of Week Hour alpha beta Day of Week Hour alpha beta Day of Week Hour alpha beta
Mon 0 8 3.7929 Mon 0 8 2.6029 Mon 0 2 2.5053 Mon 0 2 2.4505
Mon 1 9 3.1166 Mon 1 8 2.3664 Mon 1 3 1.8035 Mon 1 2 2.1224
Mon 2 6 4.2712 Mon 2 6 3.0768 Mon 2 2 2.1845 Mon 2 2 1.8791
Mon 3 8 2.7120 Mon 3 8 1.8419 Mon 3 2 2.1989 Mon 3 2 1.6722
Mon 4 6 3.2092 Mon 4 6 2.1356 Mon 4 2 1.9551 Mon 4 2 1.6978
Mon 5 6 3.4167 Mon 5 7 1.9958 Mon 5 2 2.1607 Mon 5 2 1.6467
Mon 6 11 2.7540 Mon 6 8 1.9596 Mon 6 6 1.7199 Mon 6 2 2.6064
Mon 7 13 3.5505 Mon 7 11 2.0455 Mon 7 5 3.4000 Mon 7 4 1.9100
Mon 8 10 5.8725 Mon 8 9 3.4346 Mon 8 5 4.3216 Mon 8 3 2.4455
Mon 9 12 5.8513 Mon 9 12 2.9845 Mon 9 8 3.4459 Mon 9 3 2.7288
Mon 10 15 5.0033 Mon 10 23 1.6147 Mon 10 6 4.9688 Mon 10 4 2.4175
Mon 11 12 6.1988 Mon 11 13 2.9513 Mon 11 6 4.5122 Mon 11 4 2.5975
Mon 12 12 6.3366 Mon 12 25 2.9830 Mon 12 7 3.5104 Mon 12 3 3.6403
Mon 13 16 4.6293 Mon 13 17 2.3145 Mon 13 8 3.2174 Mon 13 4 2.5900
Mon 14 17 4.3674 Mon 14 16 2.4130 Mon 14 6 4.5653 Mon 14 4 2.4208
Mon 15 15 4.7641 Mon 15 15 2.5320 Mon 15 6 3.9553 Mon 15 4 2.7279
Mon 16 17 4.0969 Mon 16 15 2.4876 Mon 16 7 3.2474 Mon 16 5 2.1644
Mon 17 19 3.3473 Mon 17 14 2.9492 Mon 17 7 2.4698 Mon 17 4 2.5172
Mon 18 15 4.1373 Mon 18 15 2.4196 Mon 18 6 2.8986 Mon 18 3 3.1056
Mon 19 17 3.3535 Mon 19 17 2.0346 Mon 19 5 2.5794 Mon 19 3 3.3856
Mon 20 15 3.6085 Mon 20 15 2.2373 Mon 20 4 3.2320 Mon 20 3 2.7582
Mon 21 17 2.9487 Mon 21 15 2.0647 Mon 21 4 2.9768 Mon 21 3 2.6633
Mon 22 14 3.4041 Mon 22 14 2.1043 Mon 22 4 2.6418 Mon 22 3 2.7157
Mon 23 15 2.5484 Mon 23 13 1.9563 Mon 23 2 3.4531 Mon 23 3 2.1837
Figure 6: Example Output for Erlang Parameters for Monday
19
These values were then used as the input parameters for the simulation model to describe
the rate of incoming calls of each call type.
3.2.2 Call Durations The other necessary variable obtained from the data was the average duration of the
various call types. Because Microsoft Access does not offer an “average” function for time
lengths (only integers and floats) it was necessary to copy the database table with call durations
into Excel, and then break it into minutes and seconds, sum them appropriately and then calculate
the average duration. It was specified by EMS that all calls longer than 9:59 were to be ignored,
so this was taken into account when taking the average. Figure 7 below shows the calculation of
the average duration times for emergency calls.
Figure 7: Example of Call Duration Determination
The final results of this analysis are shown in Figure 8 below. Because there are many
more ACD_9 (emergency) calls than other types, the greater duration for these calls has a large
impact on the average duration for the total calls.
20
ACD_Type Minutes Seconds Total_Seconds Total_Instances
ACD_2N 1 39.683 99.683 224957
ACD_2Y_7_8 1 6.994 66.994 130609
ACD_9 2 31.703 151.703 506081
Total_Calls 2 5.185 125.185 861647 Figure 8: Average Call Duration for Various Call Types
3.2.3 Call Duration Distribution For the sake of determining which service times would be used in the simulation model,
it was initially assumed that the average could be used. However, upon later reflection and input
from EMS, it was decided that the duration of each call type is distributed in real life, and that the
model should reflect this. When using an Excel add-in tool called XLSTAT 2008, it became
readily apparent that even within each call type, there were bimodal distributions for call
duration, as shown in Figure 9.
Figure 9: Duration of Emergency Calls Distribution
Various probability distribution types were used for attempting to fit the data; however,
each type had a p-value of less than 0.0001. This bimodalism of EMS calls is likely because even
within each call type, there will be two or more “types” of calls. That is to say, one type is a quick
call to briefly inform EMS about something, while another is a longer call that requires more
interaction between the two parties. Alternatively, this bimodalism can be linked back to the
21
concept of line installation. Upon installation of each line, specific ACD priority numbers are
assigned to each line, and the AVTEC computer uses these pre-specified values to assess the
priority level of each call being received. It is entirely possible that the content of the call may not
reflect the line it arrives on. For example, a non-emergency call could arrive on a pre-specified
emergency line, and this could account for the bimodal function of the call duration.
None of the probability distributions fit the reality of these call distributions, but a
method of representing the call duration was still required for the simulation model. Thus, it was
decided to break the call length into ten equal segments, and using XLSTAT, determine the
probability of being within each segment. Figure 10 shows the distribution of call duration once
broken down into ten segments.
Figure 10: Duration of Emergency Calls Distribution in Ten Segments
For the sake of representing these values in the simulation model, a custom distribution
was used based on the probabilities taken from Figure 10, while the midpoint of each of the ten
segments was taken as the duration.
22
3.3 Entering Data into the Simulation Model
This section describes how the data analysis performed resulted in the input parameters
for the simulation model.
3.3.1 Incoming Call Distributions/Inter-arrival Rates
The results of the data analysis for the call distribution were the Erlang parameters: alpha
and beta, as shown in Figure 6. The complete data includes three sets of 168 alpha and 168 beta
parameters. This is exported from an Excel file into a spreadsheet within the “Information Store”
in the Simul8 file, where the values are then read and applied appropriately for any given hour.
3.3.2 Call Duration Distribution
The resulting outcome of section 3.2.3, where the call duration was broken into ten
segments, is a table like what is shown in Figure 11 below.
probability call length (sec)
22 30
22 90
25 150
15 210
6.5 270
3.5 330
2 390
2 450
1 510
1 570
Figure 11: Example of Call Duration Distribution used for Simul8
Simul8 allows for the use of custom distributions when specifying the duration of work
items at work stations. Thus, a table as shown above in Figure 11 was copied into the custom
distribution list for each of the three call types.
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4.0 The Simulation Model
(written by Gillian Chin)
This chapter describes the how the call receiving system was first understood, and
then constructed in a simulation model.
4.1 Data Development: Learning the System
A great deal of the initial effort for this thesis was spent at the Toronto EMS Call Centre,
learning the system, and ensuring that the final simulation would indeed reflect reality. Most of
these efforts have been documented in Chapter 3. Adrian, a data analyst at Toronto EMS,
compiled several Microsoft Access tables that provided the majority of the data used in the
analysis, and many consultations were held to ensure that the data was in a fashion that was
relevant, tractable, and easily understood. Several visits were also conducted at the Toronto EMS
Call Centre with Dave Lyons, the manager of the Toronto EMS System Control Centre Design
Project, to ensure that the scope of the project was appropriate, as well as discussing the general
system structure. The following topics were discussed:
• ACD (Automatic Call Distribution) Priority Categories
• Pre-emptive Call Priorities
• Physical Structure: e.g. number of physical stations available
• Current Shift and Break Patterns
• Current Staffing Levels
Determining this information was essential to constructing the simulation model and performing
the analysis, and had significant impact on the development and construction of the final model.
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14.2 Physical Structure of the Simulation
The following section describes the parts of the simulation model, an image of which is
shown in Figure 13.
4.2.1 Call Arrivals
The current system structure for the EMS Call Centre was constructed in the simulation
model. There are three priorities of incoming calls that a call taker will receive, each of which
will have different inter-arrival times based on the hour of the week, thus creating three different
entry points for the simulation model. Label “A” in Figure 13 highlights the three entry points.
Calls of priorities one, two and three correspond to, respectively, administrative, non-emergency
and emergency calls.
Entry points signify a pool from which arrivals may enter the system, and each entry
point has a different arrival distribution. These arrival distributions change every hour, and the
method of determining these distributions was discussed in detail in Chapter 3.
4.2.2 Queue for Incoming Calls
Another aspect that was incorporated in the simulation model was the concept of a single
queue after the point of entry. The queue is indicated by label “B” in Figure 13. Every arrival into
the system enters a single queue, where each call is sorted and sequenced based firstly on the
priority level, then on the arrival time. If both a work centre (label “C” in Figure 13) and a call
taker resource (label “D” in Figure 13) are available, the call at the front of the queue will leave
the line and enter the work station. After being processed at the call centre, the call will proceed
to an exit node (label “E” in Figure 13), and the call is considered complete. While there is
additional processing that usually takes place after the call has been handled by a call taker, these
25
actions are considered to be outside of the scope of analysis. Therefore, after each call is
processed by the call taker, the call is considered to be complete.
4.2.3 Call Stations
There are currently nine available call stations in place; however, as of June 2008, a tenth
station will be installed. As this model was built with the intention of being used for future
investigations, the tenth station was incorporated in this simulation model and analysis. Call
stations are noted in Figure 13 by the label “C”. Call stations can process calls only when a
resource (that is, a call taker, label “D” in Figure 13) is present at that station.
4.3 Visual Logic Commands
Once the surface structure had been constructed in the simulation model, visual logic was
used to coordinate and enforce specific regulations held by Toronto EMS.
4.3.1 Inter-Arrival Rate Parameter Reset
The simulation analysis was performed at the time scale granularity of examining each
hour of the week. As the inter-arrival rate parameters were subject to change for this level of time
granularity, it was necessary to incorporate visual logic that would reset the inter-arrival rate
parameters for each of the three priority calls, at the start of every hour of the week. The updates
performed for the distribution parameter values for the inter-arrival rates were based on the values
obtained from data analysis performed on the historical data. Chapter 3 discusses explicitly the
methods of data analysis used.
The methodology of updating the parameters is as follows. An “Information Store”, in
simulation vernacular, or a spreadsheet, is located within the simulation model that records the
parameters of the Erlang distribution for each call priority based on the hour of the week. Upon
the start of each hour, the visual logic code reads the spreadsheet for the appropriate hour and
updates the inter-arrival parameters, depending on the call priority and the hour of the week. The
26
work centre labeled “Bouncer” (see label “F” in Figure 13) is the means for achieving time-based
parameter changes.
4.3.2 Call Durations
Since each of the three call types is not subject to changing duration distributions, it is
assumed that each priority level call has one distribution that specifies its total duration.
Therefore, the call duration of each priority level call does not need to be reset based on the hour
of the week, which is necessary in the case of inter-arrival rates. To incorporate the historical data
into the simulation model, a customized probability distribution profile was created for each
priority level call type, specifying the duration of each priority level call. Upon arrival into the
work centre, visual logic code assesses the priority level of the incoming call, and extracts the
corresponding duration distribution for processing the call. A detailed explanation of the method
used to obtain these distributions is given in Chapter 3.
4.3.3 Pre-emptive Call Priorities
Due to the inherent nature of the EMS Call Centre, a call taker has the option of putting a
lower priority call on hold to answer a call with a higher priority level. Therefore, the
methodology used to map this into the simulation model was to develop visual logic code to
enforce the call pre-emption specifications. Specifically, when a call of priority level two or three
enters the queue, the visual logic code creates a counter that will parse through each work centre
to determine if all work centres are busy. If there is an available call station (or work centre), then
the code “breaks” or does not perform any further actions, because the queue is already organized
according to priority levels; therefore the call with a higher priority level (level two or three) is
moved to the head of the queue, and taken into the available work centre. If all work centres are
in use, however, a counter would then parse through each work centre to determine the priority
level of the call being processed. The call stations are searched in ascending order, and upon
discovery of a work centre processing a call of priority level one, the call will be removed from
27
the work centre and moved back to the queue, while the higher priority call would be moved into
the newly available work centre for call processing. This methodology was enforced through the
use of several loops and counters within the visual logic code.
4.3.4 Incorporating Shift Patterns Due to the existing structure of shift patterns currently in place at Toronto EMS Call
Centre, incorporating the shift patterns into the simulation model in an efficient approach became
very difficult as there were no mathematical patterns that could be exploited for coding purposes.
It also became quite difficult to sequence lunch breaks, as the duration of the entire lunch break
across all staff was dependent on the total number at the start of the shift, in conjunction with the
number allowed to go on break together.
Therefore, incorporating existing shift patterns into the simulation model, in a method
that would be economical, became quite difficult. The objective was to build a simulation with
the current shift patterns in place, but one that facilitated future changes so that the simulation
will still be a valuable tool upon such an event. Thus, the methodology used was to break the
entire 24 hour day into 15 minute intervals, and specify how many call takers are available within
each 15 minute interval.
To specify the number of call takers available during each 15 minute interval, a
supplementary Excel sheet was used. In the spreadsheet, the number of call takers staffed on all
shifts is inputted, and taking into account the break pattern, the number of total call takers is
calculated for each 15 minute interval. This sheet can be seen below in Figure 12.
28
Figure 12: Shift Patterns including Breaks
Based on the staff levels specified in the supplementary Excel sheet, the numbers
representing the sum are be imported into an “Information Store”, or spreadsheet, within the
simulation model titled “Shift Patterns”. The visual logic accesses the spreadsheet at the start of
the simulation, and populates the shift patterns for the call taker resource. The shift pattern for the
call taker resource is also be broken down into 15 minute intervals, to ensure that the correct
correspondence of granularity in terms of worker availability.
29
Figure 13: Image of the Simul8 Model
A
D
B
C
F
E
30
5.0 The Excel Model
(written by Jason Coke)
5.1 Rationale for the need of an Excel Model
At the outset of this thesis project, it was determined that a means of validating the
simulation model, previously discussed in Chapter 4, would be to construct an Excel-based
model. This model, while not capable of having work entry points, queues, or work stations,
would rather calculate mathematically the number of call takers required to meet a certain
call volume for each hour of the week.
5.2 Methodology for Constructing the Excel Model
The method of obtaining the Erlang parameters alpha and beta for each hour of the
week was thoroughly discussed in Chapter 3. These values are imported into Excel and
matched appropriately to each hour of the week. Using the gamma inverse function in Excel,
GAMMAINV (probability, alpha, beta), it was possible to calculate the arrival rate of each
call type for each hour of the week. A definition of the term “probability” in this context is
provided below in section 5.3.1.2. Excel has no specific Erlang function, but since Erlang
distributions are a special kind of Gamma distribution, it is possible to use the gamma inverse
function as a direct substitute.
Then, based on the average duration of each call type, the fictitious value “fractional
amount of call takers” required to meet call volume in each hour is calculated. The sum of
these fractional amounts from each call type was then calculated to represent the total amount
of fractional call takers required for each hour. Finally, this fractional amount is rounded up
31
to the nearest whole number, and this value is taken as the minimum number of call takers
required to be available and answering calls, during any given hour of the week.
5.2.1 The Numerical Representation
The Excel model has two representations for the staffing levels; numerical and
graphical. The numerical representation can be seen in Figure 14, and the columns and cells
listed below are best understood by referring to that figure. The day of week and hour of day
are shown in columns F and G, respectively. Columns AC and AD, respectively, show the
alpha and beta parameters for that hour. Column AE shows the calculated arrival rate of calls
per hour based on the average duration, shown in cell AE5, for the non-emergency call type,
as labeled in cell AE4. The other two call types, administrative and emergency, are shown in
previous columns, but due to space viewing limitations, they could not all be shown in one
image. Column AF shows the fractional amount of call takers required to handle the volume
of calls of the non-emergency call type. Column AH then shows the fractional sum of the
three call types, and column AI shows the integer value once it has been rounded up to the
nearest whole integer. The values in this column are the primary output of the Excel model.
5.2.2 The Graphical Representation
The graphical representation of the model output is shown in Figure 15. It is a bar
chart that shows the number of call takers required for each hour of the week. While the
numerical representation is more useful for performing analysis, the graphical representation
is more helpful for the user to observe changes in staffing levels as the model parameters are
varied.
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5.3 Functionality
The Excel-based model is not static; various functionalities are included to allow the
user some flexibility in their modeling efforts.
5.3.1 Parameter Changes
The three parameters of desired busy rate, probability, and total call volume may be
varied within this mode. In Figure 14, the cells with parameter values are in the top left
corner in bright green.
5.3.1.1 Desired Busy Rate
The desired busy rate is the fraction of time that call takers are talking on the phone.
The default is set to 0.65, meaning they are on the phone 65% of the time. The remaining
35% is excess capacity.
One shortcoming of the model is that this value cannot change depending on the hour
of the week. In reality, this busy rate would change depending on time of day and staffing
levels. However, if the assumption that EMS always wants the same amount of excess
capacity holds true, then this value is valid.
5.3.1.2 Probability
The probability value represents the percentile in the Erlang distribution for call
volume for a given hour, from which the number of calls arriving is selected. For example, a
value of 0.5 will calculate the arrival rate from the 50th percentile of historical calls for each
hour.
33
5.3.1.3 Total Call Volume
The total call volume determines the overall number calls arriving to the system.
When set to 100%, the exact average of incoming calls based on historical data is used. This
functionality was included so that a future increase in call volume could be simulated.
5.3.2 Two Methods of Adjusting Call Volume
To allow for more flexibility in this parameter, two methods of adjusting call volume
are possible.
5.3.2.1 Adjusting by Total Call Volume
The call volume for all hours of the week can be adjusted simultaneously by
changing the value in cell G5 (Figure 14) from the default of 100% to any other value. For
example, simulating an increase in call volume of 10% is achieved by entering “110%” into
the cell.
5.3.2.2 Adjusting Call Volume by Hour of the Week
In order to simulate a crisis or some other event that would cause a large increase in
call volume over a period of one or more hours, functionality was included to allow for these
events. For example, in Figure 16, the call volume for Saturday at 6pm was increased to
150% of normal volume to simulate a large accident. Immediately, the graph on the left will
reflect this change by showing that two extra call takers would be required at 6pm on
Saturday.
34
Figure 14: Image of the Excel Model – +umerical Representation
35
Figure 15: Image of the Excel Model – Graphical Representation
36
Figure 16: Image of Excel Model – Call Volume by Hour of the Week
37
6.0 Analysis of Results
(written by Gillian Chin and Jason Coke)
This chapter will present and analyze the results obtained from the Simul8 trials.
6.1 – Analysis Overview
As seen in Figure 17 below, the average number of calls arriving in any given hour of
the week varies by time of day and day of week. Thus, it was necessary to run the simulation
model numerous times while changing certain variables for each trial.
Figure 17: Average +umber of Calls, by Hour of Week, Last Three Years
All final results were obtained using the “Trial” function in Simul8. The Trial
function allows each simulation to be run 20-30 times, and then the averages, along with the
99% confidence intervals, were taken for each key performance indicator once the trial was
complete. On average, each trial lasted about one minute in real time, but each of the 20-30
simulations in a trial ran for the duration of a full month (30.417 days).
Although Figure 17 above shows a distinct difference in call volume between
weekdays and weekends, EMS has the same shift patterns seven days a week. Since any staff
level that could accommodate weekday volume would most certainly be able to
38
accommodate weekend volume, the model did not focus specifically on weekends.
Additionally, it was found that trying to model only the weekends in Simul8 would require
extensive visual logic coding; unfortunately, there is no easy way to run a model for Saturday
and Sunday only. However, since it is considered valuable to consider weekends, section
6.5.1 does document analysis performed specifically on weekends; additionally, a section in
Future Work (Chapter 9) is devoted to discussion of this topic.
The variables changed are as follows:
� The time of day
� The number of call takers on each shift
� The volume of calls
Specifics on how these variables were changed are discussed in the subsequent section.
6.2 – Variables
This section describes how and why the three variables specified above were chosen
and manipulated for the simulation trials.
6.2.1 – Time of Day
Call taker shifts at EMS always run for 12 hours. There are four shifts per day; 7am-
7pm, 7pm-7am, 11am-11pm and 2pm-2am. Figure 18, below, shows the active time of day in
green for each shift.
39
Figure 18: Shift Patterns for Call Takers at EMS Call Centre
For most hours of the day, there are two or more shifts on duty at the same time.
However, the red bar to the right of the chart indicates that from 2am-10am, there is only one
shift on duty within this block of time. Because the start or end of a shift will have a
significant impact on the total number of call takers in a given hour, simulations were run for
segments of each day depending both on shift start and end times, as well as call volume.
This was a logical decision because having time windows that overlap both shift changes and
rapid changes in call volume would produce a meaningless “average” result. 10am-2pm is the
period of time each day when the highest volume of calls are received, so it was examined,
even though a new shift starts at 11am.
In addition, many trials were run with each simulation lasting one full month (30.417
days) for 24 hours each day, including weekends. While the results within a specified time
range, for example, 7am-10am, are more meaningful since they focus in on “bottleneck”
times of the day, the 24 hour trials were used to add robustness and validity to the results by
40
comparing the trends found in those results with the trends found in the restricted time
windows.
Table 1 below shows the clock times of day that were simulated:
Clock Time Windows
12am-2am
2am-7am
7am-10am
10am-2pm
2pm-7pm
7pm-12am
2am-2:30am *
Table 1: Clock Time Windows Examined
* 2am-2:30am was looked at closely because it appeared to be a time that caused a serious bottleneck
for incoming calls.
By segmenting the clock time and taking advantage of the shift start and end times,
the number of combinations of variables are reduced. This is because, when a shift is not
within the time window being examined, it remains a static value, as it has no bearing on the
results of that time period.
6.2.2 – Call Takers per Shift
The number of call takers on each shift was varied appropriately, depending on the
time window that was being simulated. The current range for the number of call takers on
each shift is shown in Table 2 below. Also shown are the numbers of call takers used in at
least one of the simulation trials.
+umber of Call Takers Per Shift
Shift 7am-7pm 7pm-7am 11am-
11pm
2pm-2am
Number of call takers (actual) 4-6 2-3 2 2
Simulated 4-7 2-6 2-4 2-4
Table 2: +umber of Call Takers per Shift – Actual and Simulated
41
The total possible number of combinations of call-takers was 4*5*3*3 = 180.
However, by intelligently using time windows in the clock time, it was possible to drastically
reduce the number of combinations. Also, by observing the intermediate results and trends in
the key performance indicators, it was possible to limit the combinations along a particular
axis, or shift, when, for example, 99% or more of calls were being answered in less than ten
seconds, which is the critical time limit used in the EMS Call Centre.
6.2.3 – Call Volume
Analysis showed that over the past three years, EMS has received an average of
about 36,000 calls per month, with a standard deviation of 2,367. The simulation trials were
run in two batches. First, they were run at 100% of the average volume, or 36,000 calls per
month. Second, they were run at 115%, or 41,400 calls per month. This was performed to
simulate a future increase in the average volume of calls. The value of 115% was an arbitrary
selection; however, assuming a normal distribution for the number of calls in a month, five
percent of the time, values should be more than 40,734, which represent two standard
deviations above the mean. Indeed, the highest single monthly value in the database was for
August of 2006, with 40,256 calls. These calculations were made without including the
months that did not have complete data.
6.3 Key Performance Indicators
The following measures are the key performance indicators that were used in
analyzing the results of the trials. In Simul8, the averages, as well as the 99% confidence
interval for each measure were presented in the results.
42
� Maximum Queue Size. The largest number of simulation objects (calls) that were
waiting in queue to be answered by a call taker at one time.
� Maximum Queuing Time (in minutes). The longest time that any call had to wait in
the queue.
� Average Queuing Time (in minutes). The average queue time of all calls.
� Average (non-zero) Queuing Time (in minutes). The average time spent in the queue,
counting only calls that had to wait for a call taker to become available.
� % Queued less than time limit. The percentage of calls that were answered in less
than 10 seconds.
� Utilization %. The percentage of time that a call taker is on the phone, averaged over
all call takers and all hours of the simulation duration.
All of the above performance measures can be used to gain an understanding of the
system for a given set of variables. However, two Key Performance Indicators (KPIs) are the
most critical to this analysis and must be examined: the percentage of calls that queued for
less than ten seconds, and the utilization rate of the call takers. Of these, the former is
considered to be the most important, and therefore will be given preference over the latter
when proposing recommendations.
It should also be noted that while the maximum queue time can be a valuable
indicator of system performance, some of the results indicate an extraordinarily high wait
times that are much longer than the actual span of the simulation. First, it is uncertain how the
software calculates these values, and second, the values may be influenced by the visual logic
code that enforces pre-emptive priority for emergency and non emergency calls over
43
administrative calls. In the cases where there are obviously too few call takers to handle
incoming call volume, as the queue grows, incoming high priority calls will continuously be
pushed to the front of the queue ahead of the lower priority calls. This results in the lower
priority calls remaining in the queue for a considerable time. Thus, this indicator should be
viewed in terms of its magnitude as opposed to its absolute value, and should be viewed in
conjunction with other performance indicators, in order to reach a comprehensive conclusion
about the system.
6.4 Discussion of Results
The following section will present and discuss the results of the simulation trials
performed.
6.4.1 Example of Results Obtained
An example of a results tableau from a simulation trial is shown in Table 3.
Performance Measure -99% Average 99%
Maximum queue size 33.34 36.47 39.59
Maximum Queuing Time (min) 132.36 149.07 165.78
Items Entered 35812.71 35856.10 35899.49
Average Queuing Time (min) 0.93 0.97 1.01
Average (non-zero) Queuing
Time (min) 4.83 4.99 5.15
St Dev of Queuing Time 5.43 5.74 6.05
% Queued less than 10 sec. 82.75 83.05 83.34
Utilization % 46.50 46.65 46.79
Table 3: Example Results Tableau as seen in Simul8
For the purpose of analysis in this thesis, it is assumed that the acceptable level of
service is having 95% of calls answered within ten seconds. In this example trial, the average
values for the two critical KPIs are in bold. 83% of calls were answered in less than ten
seconds, and the call takers were busy answering calls almost 47% of the time. While those
KPIs indicate that on average most calls are answered quickly (83%) and call takers are not
44
over-worked, there are other indicators that should raise a red flag of warning. The maximum
queuing time is 149 minutes, and the average non-zero queuing time is five minutes. Since
the average queuing time is less than one minute, this shows that there must be some periods
of time where the volume of incoming calls greatly exceed the service capacity of the on-duty
call takers.
Thus, the data indicates that there exists a certain degree of disparity between call
demand and call taker supply. These results were returned for a simulation running over 24
hours, seven days a week, and they demonstrate the necessity for further time window
analysis that will further explore the details of the system and determine specifically when the
bottlenecks occur.
6.4.1.1 Example of Use of Results
The determination of periods of time where severe inconsistencies between incoming
call volume and call taker availability are observed will lead to recommendations being made
regarding the number of call takers to staff at certain hours of the day. For example, if it is
found that the average utilization rate of call takers is 20% between 2pm and 3pm, the
recommendation would be to remove one of the call takers from a shift that covers that time
of day. By contrast, if 75% of calls between 1am and 2am are not answered within ten
seconds (below the acceptable standard of 95%), and the call takers have a 98% busy rate, the
recommendation would be to add at least one more call taker.
In the simulation trials, the effects of adding or removing call takers are readily
available and are measured in further trials where fewer or more call takers are used.
45
Depending on what EMS deems as acceptable threshold values for the two main KPIs, the
optimal staffing level can be chosen through thorough examination of this data.
Therefore, this is the method used for analyzing data, resolving the objectives of this
thesis, and suggesting appropriate recommendations.
6.4.2 Results by Time Window at 100% Call Volume
Below are the results assuming 100% volume, delineated by time window and
specific shift patterns. Shift patterns are in the format of x-x-x-x, for example, 5-4-3-2 means
five staff on the 7am-7pm shift, four on the 7pm-7am shift, three on the 11am-11pm shift and
two on the 2pm-2am shift. The minimum staffing level is generally assumed to be 4-2-2-2,
and represents the current standard shift pattern at the EMS Call Centre.
12am-2am 4-2-2-2 4-3-2-2 4-4-2-2
Performance Measure Average Average Average
Maximum queue size 27.07 14.30 5.95
Maximum Queuing Time (min) 59.56 33.37 10.03
Items Entered 35856.10 35869.45 35869.45
Average Queuing Time (min) 0.82 0.12 0.01
Average (non-zero) Queuing
Time (min) 3.32 1.24 0.65
St Dev of Queuing Time 3.25 0.84 0.17
% Queued less than 10 sec. 78.72 92.19 98.48
Utilization % 48.47 41.18 33.14
Table 4: Results 0000- 0200 / 4-[2,3,4]-2-2 / 100% Call Volume
Table 4 shows that the minimum staffing level of 4-2-2-2 is insufficient to meet call
demand between 12am-2am because the averages for maximum queue size and queuing time
are unacceptably high. Only 78.7% of calls are answered within ten seconds. Adding a third
call taker on the 7pm-7am shift increases this performance measure to 92%, while a fourth
increases it further to 98.5%.
46
Despite the minimum staffing level having a low performance measure of 78.7%, the
utilization rate is relatively low. This suggests that there is some variation within this two-
hour period in terms of the equivalence between call volume and call taker availability, likely
due to call takers going on breaks. For example, between 12am and 12:30am, both the 7pm-
7am and 2pm-2am have a break. Therefore, with two people on each shift, that results in only
two out of four call takers able to answer the phones. Thus during this half hour, the two call
takers are unable to keep pace with incoming calls; the queue continues to grow, and hence
the high maximum queue size and maximum queuing time is relatively large. When the two
call takers return from their breaks, the queue quickly diminishes and this results in excess
capacity among the call takers, hence the low utilization rate. The utilization rate takes into
account the average busy rate only for the time that call takers are not on break, so it is
weighted disproportionately towards the low end because the highest service rates occur
when no one is on break. For example, with four call takers on duty, when two go on break,
the other two are very busy. When all breaks are finished, the four are not very busy. Hence,
the utilization rate is calculated as: two times the busiest rate plus four times the idle rate.
This observation should be kept in mind for all of the seemingly low utilization rates
presented in this report. It also represents another reason as to why the percentage of calls
answered within ten seconds is considered to be of greater importance than call taker
utilization.
47
2am to 7am 4-2-2-2 4-3-2-2 4-4-2-2 4-5-2-2 4-6-2-2
Performance Measure Average Average Average Average Average
Maximum queue size 2641.83 129.10 37.10 18.75 7.70
Maximum Queuing Time (min) 20556.27 507.68 106.59 49.90 15.79
Items Entered 35856.10 35869.45 35869.45 35869.45 35869.45
Average Queuing Time (min) 1085.84 10.59 1.19 0.20 0.03
Average (non-zero) Queuing
Time (min) 1089.93 16.46 3.83 1.56 0.76
St Dev of Queuing Time 3530.00 37.40 4.87 1.31 0.29
% Queued less than 10 sec. 3.45 42.01 73.10 89.35 97.02
Utilization % 99.81 70.78 53.08 42.47 35.38
Table 5: Results 0200-0700 / 4-[2,3,4,5,6]-2-2 / 100% Call Volume
From 2am-7am, only the night shift (7pm-7am) is present at this time, so the only
staffing variable to change is the number of call takers on that shift. Trials were run with two,
three, four, five and six call takers on this shift. With only two call takers, there is an
extremely high utilization rate, maximum queue size, average queue time, and only 3.45% of
calls were answered within ten seconds. The likely cause of these results is that when the
2pm-2am shift leaves at 2am, only two 7pm-7am call takers remain. However, because of the
break pattern, from 2am-3am and 4:30am-5:30am, only one of the two call takers is on duty.
During these times, the single call taker cannot keep up with the volume of calls and therefore
the queue continually grows.
With each addition of an extra call taker on the 7pm-7am shift, the performance
measures exhibit drastic improvements. The first instance of relatively acceptable
performance measures occurs when five call takers are on this shift, with 89% of calls
answered in less than ten seconds. However, it is questionable as to whether EMS would
48
want one call out of ten to wait above the time limit, thus the simulation was run again with
six call takers, and the performance measure jumped to a highly acceptable value of 97%.
7am to 10am 4-2-2-2 5-2-2-2 6-2-2-2
Performance Measure Average Average Average
Average Queuing Time (min) 0.91 0.16 0.02
Average (non-zero) Queuing
Time (min) 3.40 1.49 0.74
% Queued less than 10 sec. 77.26 91.17 97.58
Utilization % 50.88 40.75 33.96
Table 6: Results 0700-1000 / [4,5,6]-2-2-2 / 100% Call Volume
The period from 7am-10am also has only one shift present, and thus only one
variable to consider. With four call takers, the concern is that only 77% of calls are answered
within ten seconds. This measure is 91% and 98% for five and six call takers, respectively,
and while 91% is deemed to be moderately acceptable, having six call takers clearly has a
substantially positive impact.
10am to 2pm 4-2-2-2 4-2-3-2 5-2-2-2 6-2-2-2
Performance Measure Average Average Average Average
Maximum queue size 8.85 7.65 5.70 3.90
Average Queuing Time (min) 0.03 0.02 0.01 0.00
% Queued less than 10 sec. 96.56 98.36 98.89 99.74
Utilization % 37.76 33.15 31.97 27.73
Table 7: Results 1000-1400 / [4,5,6]-2-[3,4,5]-2 / 100% Call Volume
Table 7 shows that even at the minimum staffing level of 4-2-2-2, performance
measures are acceptable, with 96.5% of calls answered within ten seconds. Adding a third
call taker to the 11am-11pm shift then makes that value 98.4%. Having five or six call takers
on the 7am-7pm shift, regardless of other shift levels, guarantees a performance level of
about 99% or higher. Although all call taker combinations of four, five or six on the 7am-
7pm shift and three, four or five on the 11am-11pm shift were run in trials, not all the results
49
of the remaining combinations are shown because they are fairly redundant in that they all
have extremely high performance measures in the range greater than 99.0%. 6-2-4-2, for
example, answers 99.96% of calls in less than ten seconds.
2pm to 7pm 4-2-2-2 4-2-2-3 5-2-2-2
Performance Measure Average Average Average
Maximum queue size 3.05 1.60 1.65
Maximum Queuing Time (min) 2.85 1.07 1.15
Average Queuing Time (min) 0.00 0.00 0.00
Average (non-zero) Queuing
Time (min) 0.44 0.33 0.34
% Queued less than 10 sec. 99.86 99.99 99.98
Utilization % 26.96 23.59 23.92
Table 8: Results 1400-1900 / [4,5]-2-[2,3]-2 / 100% Call Volume
Table 8 shows that from 2pm-7pm, even with the minimum staffing level of 4-2-2-2,
99.86% of all calls are answered. Additions to any of the day or evening shifts result in even
higher values. It should be noted however, that the addition of a 2pm-2am shift member is
marginally more valuable than adding a 7am-7pm call taker.
In general, the number of incoming calls is falling steadily during this time of the
day, yet there are always three shifts on duty simultaneously, so it is very easy to meet
demand.
7pm-12am 4-2-2-2 4-3-2-2 4-4-2-2
Performance Measure Average Average Average
Average Queuing Time (min) 0.37 0.05 0.03
Average (non-zero) Queuing
Time (min) 3.12 1.16 1.01
% Queued less than 10 sec. 89.79 96.74 98.05
Utilization % 36.89 30.89 27.16
Table 9: Results 1900-2400 / 4-[2,3,4]-[2,3]-[2,3] / 100% Call Volume
50
Table 9 shows that from 7pm-12am, with the minimum staffing level on duty, less
than 90% of calls are answered within ten seconds. Adding a call taker to either the 7pm-7am
shift or 2pm-2am shift proves slightly more beneficial than to the 11am-11pm shift, however,
this could be because the arbitrary time window runs until midnight, one hour after the 11pm
shift ends.
2am-2:30am 4-2-2-2 4-3-2-2 4-4-2-2 4-5-2-2 4-6-2-2 4-7-2-2
Performance Measure Average Average Average Average Average Average
Maximum queue size 18551.0 284.20 284.20 32.00 9.90 9.90
Maximum Queuing Time (min) 8200.78 1033.64 1033.64 120.97 23.62 23.62
Average Queuing Time (min) 4126.47 62.92 62.92 0.65 0.05 0.05
Average (non-zero) Queuing
Time (min) 4136.04 74.15 74.15 2.23 0.80 0.80
St Dev of Queuing Time 2376.93 150.68 150.68 3.58 0.42 0.42
% Queued less than 10 sec. 0.28 21.36 21.36 75.83 95.02 95.02
Utilization % 99.85 85.03 85.03 56.59 42.47 42.47
Table 10: Results 0200-0230 / 4-[2,3,4,5,6,7]-2-2 / 100% Call Volume
The period from 2am-2:30am was examined in great detail because it appeared to be
somewhat of a bottleneck in terms of meeting call demand. This appears to be the case
because at 2am, the 2pm-2am shift is finished, leaving only the 7pm-7am shift. Compounding
the problem, the 7pm-7am shift has a scheduled break starting at 2am. The results for three
and four, as well as six and seven call takers are the same because if three are on duty, one
will go on break at 2am, whereas if four are on duty then two will go on break together
(leaving the same number of available call takers). A similar situation exists for six and seven
call takers.
Anything less than five call takers leads to extraordinarily high queue sizes and wait
times. Having six call takers gives the first moderately acceptable performance measures.
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6.4.3 Results by Time Window at 115% Call Volume
In this section, a 15% increase in call volume has been introduced to the simulations.
This is to simulate both the possibility of an increased call volume over time (a shift of the
mean), or the possibility of a high-volume month by the natural variance of call volume (a
month where the call volume is more than two standard deviations above the mean).
12am-2am 4-2-2-2 4-3-2-2 4-4-2-2
Performance Measure Average Average Average
Maximum queue size 35.40 20.55 9.35
Maximum Queuing Time (min) 80.52 46.71 15.75
Items Entered 41230.25 41232.00 41232.00
Average Queuing Time (min) 1.51 0.28 0.03
Average (non-zero) Queuing
Time (min) 4.36 1.66 0.75
St Dev of Queuing Time 5.05 1.52 0.30
% Queued less than 10 sec. 69.95 86.63 96.90
Utilization % 55.74 47.32 38.07
Table 11: Results 0000-0200 / 4-[2,3,4]-2-2 / 115% Call Volume
Table 11 shows that with a 15% increase in call volume, having two or three call takers
on the 7pm-7am shift results in too few (70% and 86.6%, respectively) calls being answered
in ten seconds or less from 12am-2am. Having four call takers on that shift is the minimum
acceptable staffing level. It should also be noted that while Table 4, which represents the
same time window but at 100% call volume, has just under 35,900 items entered, the 15%
increase here has raised the number of monthly calls to over 41,200.
2am-7am 4-2-2-2 4-3-2-2 4-4-2-2 4-5-2-2 4-6-2-2 4-7-2-2
Performance Measure Average Average Average Average Average Average
Maximum queue size 9865.40 246.40 55.10 29.00 11.50 9.45
Maximum Queuing Time (min) 16550.48 894.02 162.52 68.99 24.90 16.22
Average Queuing Time (min) 2047.06 43.59 2.73 0.47 0.07 0.03
Average (non-zero) Queuing
Time (min) 2054.46 53.73 6.12 2.23 0.89 0.75
St Dev of Queuing Time 4309.39 114.80 9.45 2.52 0.50 0.28
% Queued less than 10 sec. 2.02 25.41 61.20 82.65 94.23 97.43
Utilization % 99.93 81.38 60.97 48.77 40.64 34.84
Table 12: Results 0200-0700 / 4-[2,3,4,5,6,7]-2-2 / 115% Call Volume
52
Table 12 indicates that with a 15% increase in call volume, having only two or three
call takers on the 7pm-7am shift would be disastrous, with exceedingly high queue sizes and
wait times. Even having four call takers produces poor results, with only 61% of calls being
answered within ten seconds. This is a time period in the day when only one shift is on duty,
and if call volume were to increase by 15%, EMS would need to drastically increase the
number of call takers available during this time.
It should also be noted that of the five hour period from 2am-7am, the total amount of
break time will vary between two hours and three hours, depending on the total number of
call takers. Therefore, to state that four call takers are on duty is somewhat deceptive; all four
call takers will be available for only two of the five hours, and during the other three hours
there will be either two or three people actively taking calls.
7am-10am 4-2-2-2 5-2-2-2 6-2-2-2 7-2-2-2
Performance Measure Average Average Average Average
Maximum Queuing Time (min) 130.79 66.78 19.80 14.2565
Average Queuing Time (min) 2.12 0.38 0.06 0.02124
% Queued less than 10 sec. 66.36 85.48 95.24 97.8976
Utilization % 58.48 46.82 39.01 33.4362
Table 13: Results 0700-1000 / [4,5,6]-2-2-2 / 115% Call Volume
From 7am-10am at 115% call volume, four or five call takers are insufficient to meet
the call demand. Depending on the threshold that EMS deems acceptable, the 95%
performance measure that six call takers produce may or may not be enough. This is the
second time window where only one shift is on duty; therefore, any breaks taken will have a
large impact on the actual number of call takers available.
53
10am-2pm 4-2-2-2 5-2-2-2 6-2-2-2 4-2-3-2 4-2-4-2 5-2-3-2
Performance Measure Average Average Average Average Average Average
Maximum queue size 12.20 8.85 4.90 10.20 9.45 8.85
Maximum Queuing Time (min) 24.20 15.63 5.57 19.03 15.85 15.63
Average Queuing Time (min) 0.08 0.02 0.00 0.04 0.03 0.02
Average (non-zero) Queuing
Time (min) 0.90 0.71 0.48 0.78 0.82 0.71
St Dev of Queuing Time 0.56 0.26 0.08 0.34 0.30 0.26
% Queued less than 10 sec. 93.17 97.59 99.38 96.74 97.37 97.59
Utilization % 43.38 36.74 31.85 38.08 33.93 36.74
Table 14: Results 1000-1400 / [4,5,6]-2-[2,3,4]-2 / 115% Call Volume
Table 14 shows that only the minimum staffing level is below acceptable
performance levels. The addition of just one call taker to either the 7am-7pm shift or 11am-
11pm shift immediately brings service levels up a sufficient degree.
Essentially, this indicates that if, in the future there is a 15% increase in call volume
to EMS, then the “new” minimum staffing level should become 5-2-2-2.
2pm-7pm 4-2-2-2 4-2-2-3 5-2-2-2
Performance Measure Average Average Average
Average Queuing Time (min) 0.00 0.00 0.00
Average (non-zero) Queuing
Time (min) 0.45 0.40 0.41
% Queued less than 10 sec. 99.65 99.95 99.94
Utilization % 30.98 27.11 27.48
Table 15: Results 1400-1900 / [4,5,6]-2-2-[2,3] / 115% Volume
Similar to the results found at 100% call volume, Table 15 indicates that even the
minimum staffing level can easily meet call demand in the period from 2pm-7pm. This is
likely because the three shifts on duty at this time have eight call takers in total, minus those
that are on break, and call demand is steadily falling from the mid-day peak. Thus, even at the
minimum staffing level, the call centre has excess capacity during this time.
54
7pm-12am 4-2-2-2 4-3-2-2 4-4-2-2
Performance Measure Average Average Average
Maximum queue size 37.20 18.65 13.55
Average Queuing Time 0.68 0.10 0.06
% Queued less than 10 sec. 85.54 94.43 96.48
Utilization % 42.39 35.48 31.22
Table 16: Results 1900-2400 / 4-[2.3]-2-2 / 115% Call Volume
Table 16 shows that even a minimum staffing level is sufficient to meet call demand
in this time. Increasing the 7pm-7am shift by one call taker gives a marginal improvement
(99.25% versus 98.47%) in the primary performance measure, but the extra call taker is not
necessary.
2am-2:30am 4-2-2-2 4-3-2-2 4-4-2-2 4-5-2-2 4-6-2-2 4-7-2-2
Performance Measure Average Average Average Average Average Average
Maximum queue size 23984.65 555.35 555.35 60.30 13.10 13.10
Maximum Queuing Time (min) 12888.42 2773.05 2773.05 229.30 29.94 29.94
Average Queuing Time (min) 6400.11 225.33 225.33 2.29 0.12 0.12
Average (non-zero) Queuing
Time (min) 6408.38 230.74 230.74 4.99 0.94 0.94
% Queued less than 10 sec. 0.17 7.86 7.86 60.98 90.52 90.52
Utilization % 99.92 97.65 97.65 65.02 48.77 48.77
Table 17: Results 0200-0230 / 4-[2,3,4,5,6,7]-2-2 / 115% Call Volume
At 115% call volume, the performance measures for 2am-2:30am are very poor for
less than six call takers. At 2am, the 2pm-2am shift leaves, and the break time for the 7pm-
7am shift starts. Even with five call takers on duty, only three remain to answer calls, and this
is insufficient to meet the call volume. If call volume does increase by 15% in the future, then
EMS would need to begin staffing at least six call takers on the night shift.
6.4.4 Summary of Results
Throughout sections 5.3.2 and 5.3.3, a variety of results are presented that reflect the
performance of the EMS Call Centre at various times of day, staffing levels and incoming
call volumes. The primary performance measure used was the percentage of calls that were
55
answered within ten seconds. The second most important measure, utilization rate of the call
takers, was found to be skewed to the low end for values that were not already very high.
This is likely because it is calculated as an average rate that could include both the very busy
times and very idle times which occur as a result of call takers going on or returning from
their breaks, except idle times occur when more call takers are present, so the “low” busy rate
is multiplied by a greater number of call takers. Thus, it was not viewed as an equally
valuable measure, except when it indicated extremely high utilization rates.
Call taker breaks had a very high impact on the service levels of the call centre. In the
periods from 2am-7am and 7am-10am, only one shift is on duty at a time; therefore, the break
times often left too few call takers available to handle the incoming call volume.
Minimum Staffing Level for which at least 95% of Calls are Answered Within 10 Seconds
12am-2am 2am-7am 7am-10am 10am-2pm 2pm-7pm 7pm-12am 2am-2:30am
100% call
volume 4-4-2-2 4-6-2-2 6-2-2-2 4-2-2-2 4-2-2-2 4-3-2-2 4-6-2-2
115% call
volume 4-4-2-2 4-6-2-2* 6-2-2-2
5-2-2-2 or
4-2-3-2 4-2-2-2 4-4-2-2 > 4-7-2-2
Existing
Staff Level 4-[2,3]-2-2 4-[2.3]-2-2 [4,5,6]-2-2-2 [4,5,6]-2-2-2 [4,5,6]-2-2-2 4-[2,3]-2-2 4-[2,3]-2-2
Table 18: Minimum Staffing Level where at least 95% of Calls Answered Within 10 Seconds
* 4-6-2-2 gives a performance measure of 94%
Table 18 shows that with the current average call volume, existing staffing levels are
sufficient from 7am to midnight if six (not four or five) call takers are on the 7am to 7pm
shift, and if three call takers (not two) are on the 7pm to 7am shift. The 11am to 11pm and
2pm to 2am shifts are sufficiently staffed with two call takers each, and although these
simulations did not test for less than two per shift, it may well be the case that not both call
takers are needed on both these shifts.
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From 12am-7am, however, Table 18 shows that current staffing levels are
insufficient. The simulations indicate that at least six call takers are needed for the 7pm-7am
shift to meet demand, particularly for the period from 2am-7am.
If call volume were to increase 15%, the period from 10am-2pm would need one
additional call taker for either the 7am-7pm shift or the 11am-11pm shift. This need,
however, is dominated by the period from 7am-10am, when six call takers are needed. Since
the only shift available at this time is 7am-7pm, six call takers are required for that shift, and
will be remain on duty throughout the day. This phenomenon of dominance will be discussed
in the conclusion of this thesis. Additionally, the 7pm-7am shift would require six call takers.
In general, there appears to be sufficient capacity from 10am to 2pm, and excess
capacity from 2pm to 7pm, when three shifts are on duty. However, there appears to be
insufficient staffing for the 7pm to 7am shift. An unexpected result from the simulation trials
is that the period from 2am-7am requires just as many call takers (six) as 7am-10am, even
though call volume is considerably higher in the latter period. One explanation of this could
be that a break occurs immediately at 2am, which could cause an unrecoverable backlog,
since each break period last 1.5 hours with four or more call takers on duty, and there are two
break periods in the five hour period from 2am-7am. Meanwhile, the 7am-7pm shift does not
start break until 8am and has only one 1.5 hour break period before 10am.
6.5 Comparison of Time Window Results to 24/7 Results
While running trials for specific time windows is a valuable method for looking
closely at the effects of parameter changes over smaller periods of time, it is also important to
examine the “larger picture”. In addition to the simulation trials mentioned previously in this
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chapter, additional trials were conducted for 24 hours a day, seven days a week. Trends found
in the results of these “macro” trials will now be compared to the results of the time window
trials. For the purpose of comparison, only the simulations running at 100% of call volume
are included.
The primary performance measure, the percentage of calls answered within
ten seconds, is the only indicator used for this analysis.
Table 19 below shows the trends for the primary performance measure as the shift
pattern is varied. The far left column shows which shift is being varied, while the inside cells
show the actual shift pattern and the respective performance value, in percent. On the right
are columns for first improvement and second improvement. The first improvement is the
difference of the performance measure, in percent, between the lowest staffing level listed
and the addition of one more call taker. For example, in the first row, 93.09 – 90.50 = 2.59.
The second improvement is the difference between the first addition and the second addition.
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Shift Pattern vs. Percentage of Calls
Answered within 10 Seconds
First
Improvement
Second
Improvement
x-2-2-2 4-2-2-2 5-2-2-2 6-2-2-2 7-2-2-2 2.59 0.93
90.50 93.09 94.02 94.27
4-x-2-2 4-2-2-2 4-3-2-2 4-4-2-2 4.20 0.79
90.50 94.70 95.49
5-x-2-2 5-2-2-2 5-3-2-2 5-4-2-2 4.16 0.87
93.09 97.25 98.12
6-x-2-2 6-2-2-2 6-3-2-2 6-4-2-2 4.22 0.78
94.02 98.24 99.02
4-2-x-2 4-2-2-2 4-2-3-2 4-2-4-2 0.92 0.16
90.50 91.42 91.58
4-2-2-x 4-2-2-2 4-2-2-3 4-2-2-4 1.23 0.13
90.50 91.73 91.86
5-2-2-x 5-2-2-2 5-2-2-3 5-2-2-4 1.28 0.07
93.09 94.37 94.44
Table 19: Shift Pattern versus Percentage of Calls Answered within Ten Seconds
Table 19 indicates similar trends to those found in the time window simulation. The
addition of call takers to the 7pm-7am shift produces the largest increase in performance (the
cells in yellow). The next best improvement, 2.59%, is obtained by adding a call taker to the
7am-7pm shift. Meanwhile, adding call takers to the 11am-11pm or 2pm-2am had little
impact, and, as is shown by the very low values for second improvement (0.16 and 0.13),
virtually no improvement could be made by further additions to these two shifts.
Thus, the 24 hour simulation results are in complete agreement with the time window
results. They both suggest that performance will increase by adding at least one more call
taker to the 7am-7pm shift, and at least one more to the 7pm-7am shift, while the 11am-11pm
and 2pm-2am shifts are already sufficiently staffed.
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6.5.1 Weekends
Although it was not possible to conduct simulations for weekends alone, the Excel-
based model readily accounts for all hours of the week. With the default values of 0.65 for
desired busy rate, 0.9 for probability, and 100% for call volume, Figure 19 below
demonstrates the resulting bar chart for the required number of call takers for each hour of the
week.
Figure 19: Graph from Excel Model – Minimum +umber of Call Takers
Weekends clearly follow a distinctively different trend than weekdays. The
highest number of call takers required for weekends is five, while for all weekdays,
the required value is six. Additionally, the weekends required a minimum of three call
takers during the night, while weekdays require only two as a minimum. Thus,
weekends have lower requirements in the day but higher requirements at night. Given
that the previous analyses suggest a shortage of staffing at night during the week, it is
likely that this shortage becomes even more severe on Friday and Saturday nights.
Thus, it does not seem reasonable to have the same staffing patterns for
weekends as weekdays. Future work will be necessary to establish the proper staffing
requirements for weekends.
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6.6 Questions Answered
In Chapter 1, five questions were posed with regards to staffing levels and the
capabilities of the EMS Call Centre to meet call demand both currently and in the future. For
convenience, they are listed again below.
1) Are current staffing levels sufficient to meet current call demand?
2) Are there times when the Call Centre is overstaffed or understaffed?
3) If so, what should the number of call takers be during any given hour of the week?
4) Are current staffing levels sufficient to meet an increase in call volume in the
future?
5) If not, what staffing levels will be required to meet that increase in volume?
Based on the results found in this chapter, these questions are answered in the sections below.
6.6.1 Current Sufficiency of Staffing Levels
In response to question 1, current staffing levels are sufficient to meet demand during
the mid-morning, afternoon and evening times, however, they are insufficient during the late
night and early morning hours, particularly from 2am-7am.
6.6.2 Overstaffing and Understaffing
In response to question 2, overstaffing occurs from 2pm-7pm, when there are three
shifts concurrently on duty. Even at the minimum staffing level of 4-2-2-2, there is excess
capacity during this time. Understaffing occurs for the 7pm-7am shift and is particularly
noticeable from 2am-7am, once the 2pm-2am shift has left.
6.6.3 Sufficiency of Current Staffing levels in the Future
In response to question 4, if a 15% increase in call volume were to occur in the
future, the current staffing levels would not be sufficient. In particular, there would be too
few call takers during the 7am to 7pm and 7pm to 7am shifts.
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6.6.4 Required Staffing Levels
In response to questions 3 and 5, the required levels of staffing for both current
volume and a future increase of 15% are listed in Table 18. These values are determined
under the assumption that a reasonable target for the primary performance measure is 95% of
calls being answered within ten seconds. If this target value was lowered, then similarly, there
would be a decrease in the staffing numbers determined by the simulation model.
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7.0 Validation
(written by Jason Coke)
Validation of simulations models is of great importance [4]. Since pivotal decisions
can be made by management on the basis of simulation results, the validity of the model and
accuracy of these results must be subject to intense investigation [4].
Therefore, this chapter discusses validation attempts for the simulation model by
several means. Validation is achieved through two methods; first, by checking with an expert
from Toronto EMS to ensure that the simulation is a valid representation of the real-world
system, and secondly, by comparing the results in the simulation model to those of the Excel-
based model. The results of the Excel-based model were also validated by experts at Toronto
EMS.
7.1 Validation by an Expert
7.1.1 Validation of the Simulation Model
Once the simulation model was fully constructed, a meeting was arranged with Dave
Lyons, Manager of the Toronto EMS System Control Centre Design Project. The model, its
visual logic code and all work paths were fully explored and explained. Mr. Lyons confirmed
that the model is, in fact, a valid representation of the real world system, insofar as the
simulation software allows.
7.1.2 Validation of the Excel Model
The Excel model was examined both by Mr. Lyons and by the call centre supervisory
staff. With the default values of 100% call volume, 65% busy rate for call takers, and a
probability value of 0.9, all EMS staff consulted agreed that the numbers produced were quite
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reasonable and realistic. Thus, while the Excel model is imperfect and limited in its
functionality, it has been validated by showing that the values produced are realistic.
7.2 Validation by comparing Simul8 results with Excel-based Model
One fundamental difference between the Excel-based model and the Simul8 model is
that while it is possible to account for breaks in the Simul8 model, it is not feasible to do so in
the Excel model. The Excel model does not represent the shift staffing levels, but rather the
actual number of call takers who should be at their stations and available to take calls. Since a
direct numerical comparison may not be possible, validation can be achieved if the results
from each model are found to support the same conclusion.
7.2.1 Validation by Means of Producing Similar Conclusions
In Figure 20 below, the blue line shows the actual number of call takers available to
answer calls, taking into account break patterns, and based on staffing levels of 4-2-2-2. The
red line represents the required staffing level based on the default parameters mentioned
above, and was calculated by taking the average of the minimum staffing levels of each hour
of each day from Monday to Thursday. In this figure, values are presented for every 15-
minute section of the day.
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Figure 20: Actual (4-2-2-2) Staffing Levels vs. Required Staffing Levels
Within Figure 20, any area where the red line (required staff) exceeds the blue line
(actual staff, given a 4-2-2-2 pattern) represents a shortage of call takers. Ideally, the blue line
should always be at or above the red line. Similar to the results from Simul8, Figure 20 shows
that the 4-2-2-2 staffing pattern is insufficient to meet call demand from 2am-7am. The gap is
particularly large for 2am-3am, which would certainly produce similar results to the findings
for 2am-2:30am in Table 10: Results 0200-0230 / 4-[2,3,4,5,6,7]-2-2 / 100% Call
Volume. In the afternoon and evening, there is excess capacity, which was also observed
within the Simul8 model. The only discrepancy between the two models is for the period
from 10am to 1pm. In Figure 20, there are clearly too few call takers to meet demand until
1pm, while the Simul8 results suggest that 4-2-2-2 is sufficient for this time period. This
discrepancy likely exists because the parameter for probability in the Excel model was
established as 0.9, meaning the call volume was sampling from the 90th percentile of call
volume. Meanwhile, the Simul8 model takes the mean value from probability 0.5 but samples
anywhere between 0 and 1. Also, the Excel model will tend to estimate the required staff
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level on the higher side for the busiest time of the day, 10am to 2pm, when a relatively low
busy rate, 65% in this case, is chosen. Despite these limitations of the Excel model, the two
models do appear to present similar results.
Figure 21: Actual (6-4-2-2) Staffing Levels vs. Required Staffing Levels
Figure 21 shows the change in the actual levels (the blue line, with staffing level 6-4-
2-2) relative to the required levels (the red line) once four call takers are added to each 24-
hour period; two more starting at 7am and two more starting at 7pm . Like the Simul8 results,
this now indicates that the 6-4-2-2 staffing level is sufficient to meet demand from 2am-7am.
Similar to Figure 20, there is a slight disparity from 8am-1pm, with the supply of call takers
just at or below the required level. The large excess of capacity in the afternoon and evening
hours is readily visible, and it can be seen from this graph that with a few minor 15-30 minute
periods, the 2pm-2am shift is virtually unneeded.
The Excel model thus validates the Simul8 model by producing similar conclusions.
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7.2.2 Validation by Numerical Comparison of Results
It is difficult to make a direct numerical comparison between the Excel and Simul8
models for two reasons. First, the Excel model cannot account for breaks, and in a 24-hour
cycle there are a substantial number of breaks that occur. Second, the Simul8 model provides
the average number of call takers over several hours (a time window), rather than for each
hour. Despite these problems, an attempt to compare the resulting values for the number of
call takers required in each hour is made below in Table 20.
Average Hourly Call Takers Simul8
Adjusted Hour From Excel From Simul8
0 3 5 or 6 3 or 4
1 3 5 or 6 3 or 4
2 2.75 5 or 6 3 or 4
3 2 5 or 6 3 or 4
4 2 5 or 6 3 or 4
5 2 5 or 6 3 or 4
6 3 5 or 6 3 or 4
7 4 6 4
8 5 6 4
9 6 6 4
10 6 8 6
11 6 8 6
12 6 8 6
13 5.75 8 6
14 6 8 6
15 6 8 6
16 6 8 6
17 5.25 8 6
18 5 8 6
19 5 7 5
20 5 7 5
21 4.5 7 5
22 4 7 5
23 4 7 5
Table 20: +umerical Comparison of Excel and Simul8 Staffing Levels
The values in the Simul8 column represent the total staffing level, while the Excel
column represents the number of staff ready and answering calls. As a large generalization, it
can be said that two call takers (from any on-duty shift) are on break in a given hour.
Therefore, subtracting two from the Simul8 column should give the approximate value that
can be used for comparison with the Excel value. When this subtraction is done in the
“Simul8 Adjusted” column, it is not a stretch to conclude that the values are very similar.
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Therefore, the Excel model validates the Simul8 model by producing comparable
numerical values in terms of actively available call takers.
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8.0 Conclusion and Recommendations
(written by Jason Coke)
8.1 Summary
In this thesis project, a simulation model of the Toronto EMS Call Centre was
developed and created. The goal of the simulation model was to determine optimal staffing
levels based on historical call volumes, but also to allow for flexibility in terms of call
volume and call taking staff in case there are future changes to these values.
The method of determining if staff volume is sufficient to meet call demand was to
determine if the primary performance measure, the percentage of calls answered within ten
seconds, was within a certain threshold value. For the purpose of this thesis, the threshold
value was assumed to be 95%. If EMS deems that a different value would be more
appropriate, then further simulation analysis may not be necessary; rather, the current results
shown in Appendix A should provide the appropriate staffing level for a given threshold
limit.
Additionally, an Excel model was constructed to determine mathematically what the
minimum number of call takers are to meet the demand of a given hour of the week. The
values found in this model were similar to those found from the simulation trials, thus
validating the Simul8 model.
8.2 Conclusion
In Chapter 1, five questions were posed that represent the essence of this thesis. For
convenience, they are listed once again below.
1) Are current staffing levels sufficient to meet current call demand?
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2) Are there times when the Call Centre is overstaffed or understaffed?
3) If so, what should the number of call takers be during any given hour of the week?
4) Are current staffing levels sufficient to meet an increase in call volume in the
future?
5) If not, what staffing levels will be required to meet that increase in volume?
The results from the simulation show that current staffing levels may not be sufficient
to meet current call volume, and they would almost certainly not be sufficient if call volume
were to increase by 15%. The most severe shortage of call takers was consistently found to be
during the night shift, from 7pm-7am. Currently there are either two or three call takers
staffed on this shift, but the analysis showed that, due to the break patterns, even four call
takers was too few for the period of time from 2am-7am. During this period, only the night
shift is on duty, therefore during the break periods which last for three hours of this five hour
time window, the loss of one or two call takers has a significant impact on service levels.
Analysis showed that having five or six call takers on this shift would improve service to
acceptable levels.
During the day shift from 7am-7pm, four to six call takers are currently staffed.
Although only four call takers are needed for this shift once the 11am-2pm shifts start,
analysis shows that the period from 7am-10am does indeed require six call takers. Thus, this
period of time can be considered a bottleneck and effectively dictates how many call takers
are required for this shift.
The 11am-11pm and 2pm-2am shifts are currently staffed with two call takers each.
The analysis showed that this amount is more than sufficient, even leading to excess capacity.
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8.3 Recommendations
8.3.1 Night Staffing
The first and most important recommendation is to have additional staffing on the
night shift. By having at least four call takers on the 7pm-7am shift, service levels should rise
dramatically, particularly in the period from 2am-7am.
8.3.2 Day Staffing
The next recommendation is to have six call takers on the day shift from 7am-7pm.
This is specifically to meet the call demand prior to the 11am shift arriving.
8.3.3 Afternoon/Evening Staffing
Current staffing levels for the 11am-11pm and 2pm-2am shifts are more than
adequate and allow sufficient excess capacity to deal with a sudden surge in call volume. No
reductions of staffing levels are recommended for these shifts. If it is possible to have only
once call taker on the 2pm shift, then moving the second call taker from the 2pm shift to the
7pm shift would provide a better match between call takers and call volume.
8.3.4 Break Periods
During periods of time when only one shift is on duty, such as from 2am until 10am,
break times have a significant on the ability of the Call Centre to meet call volume. This
simulation model assumes 30 minute break periods and 45 minute lunches. Any reduction in
the break times, say, from 30 minutes to 20 minutes, would have a strong effect on call centre
performance. For example, in the period of time from 2am-7am, a ten minute reduction in
each break period would increase the availability of the full call taking workforce from two
hours to three hours, which in turn would positively impact the key performance measures.
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Furthermore, the number and sequence of call takers going on break at one time
should also be examined. If four call takers are present, two will go on break for the first half
hour, then the third in the second half hour, and then the fourth in the third half hour. For the
breaks that start at 2am for the night shift, it would be more beneficial to have the two call
takers going on break together occupy the third break period, rather than the first. Since call
volume is still falling at this hour, this provides a better match between service and demand.
By contrast, call volume is continually rising during the 8am-9:30am break period of
the day shift, so it is better to have the two call takers take the first break period together, and
the singles take the next two (that is, a 2-1-1 break pattern), assuming there are four in total.
These patterns should be implemented for all shifts that don’t have three, six or nine call
takers. In these cases, the breaks patterns are by default 1-1-1, 2-2-2 or 3-3-3.
8.3.5 Shift Start Times
Although it may not be currently possible to change the starting times of the four call
taker shifts at EMS, some consideration should be given to the possibility. One of the key
discoveries made in the analysis is that caller utilization is often highest during the break
times when only one shift is on duty. Thus, if the shifts were somehow split so that two shifts
were always on duty, this problem could be avoided. Additionally, the 2pm-2am shift was
found to be virtually unneeded, so the staff of this shift would be better starting at a different
time. Further details on changing the shift times are discussed in Future Work in Chapter 9.
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9.0 Future Work
(written by Gillian Chin and Jason Coke)
Although the thesis effort has been successfully completed and results have identified
areas of significant improvement, there are still further extensions of the analysis that could
be implemented, if time were permitting. Performing these extensions may provide further
insight and additional depth to the analysis. Areas which could be further explored are as
follows:
9.1 Changing the Shift Schedule
Toronto EMS currently has four shifts for every 24 hours, where each shift is 12
hours in length. The start times are 7am, 11am, 2pm and 7pm. While these start times were
likely chosen to have the best effects on the social and physical well-being of call takers, it
does cause a significant disparity between the incoming call volume and call taker
availability, particularly in the early morning hours. Examinations could be made into:
� different start times
� having two shifts on duty at all times (thus, one shift starting every six hours)
� having five shifts for every 24 hours
� having a split between 8-hour and 12-hour shifts. For example, 8-hour shifts on
weekdays and 12-hour shifts on weekends would minimize the number of
weekends worked
9.2 Workforce Scheduling
The analysis performed to date specifies how many call takers are required to be
available to fulfill a specific service requirement. However, being able to schedule the
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available workers to meet the call volume requirements could bring additional value to
Toronto EMS. Unfortunately, due to time constraints, it was not possible to incorporate
scheduling software as a part of this analysis, but could perhaps be performed as future work.
9.3 Non-homogeneous Workforce
The assumption made in the simulation model was that every worker is viewed as
identical, having the same needs and requirements. However, this is not the case in the real
world; many individuals may have different hours they can work, or different needs on the
job. Constraint-Based Programming is an Operations Research technique that is readily
applied to workforce scheduling problems. Therefore, it can be considered as a tool to help
incorporate the differences between workers in future analysis.
9.4 Simul8 Optimization Function – OptQuest
Simul8 has a built-in optimization function that allows for certain systems or models
to solve to optimality based on specified variables and cost/profit functions. Although such
functionality is very useful, further expertise in the use of Simul8 would be required prior to
beginning this analysis. Costs would need to be associated with call takers, and some form of
penalty cost would be required for calls that were not answered within ten seconds. If
OptQuest were better understood, it would save more time in performing analysis, and
potentially arrive at a better solution.
9.5 Increasing the Time Granularity of the Analysis/Seasonality
The analysis was performed according to a time scale of each hour of the week. This
decision was a basic choice made on behalf of all parties, as a weekly cycle was deemed as
acceptable for the analysis. If a larger time granularity was used, for example, per hour of
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month, perhaps the simulation would more adequately reflect reality and the results of the
analysis may have been improved. This would also allow for the incorporation of seasonality
of call volume, if any exists.
9.6 Creating Queues for each Call Priority
Further queuing analysis could be performed by looking at the results of queuing
times for each call type. Currently, the results are only given for the queue as a whole,
irrespective of the type of calls that may be temporarily stored in the queue. This manner of
analysis would give further insight into what happens in the real system, and segregate the
results for more insightful conclusions for each priority level.
9.7 Weekend Staffing Levels
According to Figure 17: Average Number of Calls, by Hour of Week, Last
Three Years, the volume of calls on the weekends is significantly lower than during
weekdays. Despite this volume difference however, call taker staffing levels remain the same
for weekends as weekdays. Indeed, the Excel model (Figure 19: Graph from Excel Model –
Minimum Number of Call Takers) suggests that weekends need fewer call takers in the day
but more at night in comparison to weekdays. Therefore, analyzing the weekends
independently and in-depth would be a worthwhile effort.
Since Simul8 does not provide an easy way to run simulations for only weekends, it
would be possible to create another simulation model that only has the input parameters for
the weekends. Since Simul8 does include functionality for limiting the number of days in a
week, it could be easily set to run for two days only. While Simul8 would appear to be
running for Monday and Tuesday, it would in fact be running Saturday and Sunday, because
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the input parameters would be specified for these specific days only. In this manner, it is
possible to model the weekend independently from weekdays.
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Bibliography
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overview/overview.htm: Accessed: September 21, 2007.
[2] Toronto EMS, Overview of Organization: Statistics, Website: http://www.toronto.
ca/ems/overview/statistics.htm: Accessed: September 21, 2007.
[3] David Lyons, Re-Engineering the Process: The Application of Queuing Theory in EMS,
Toronto EMS Communication Centre Design Project, November 2005.
[4] Jerry Banks, John S Carson II, Barry L Nelson, David M Nicol, Discrete Event
Simulation, Fourth ed. , Prentice Hall, 2004.
[5] Robert B Cooper, Introduction to Queuing Theory, Third ed. , North Holland, 1981.
[6] Walter C Giffin, Queuing: Basic Theory and Applications, First ed. , Grid, 1978.
[7] Ger Koole, Avishai Mandelbaum, " Queuing Models of Call Centres: An Introduction,"
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[8] Vijay Mehrotra, Jason Fama, " Call Centre Simulation Modeling: Methods, Challenges
and Opportunities," Proceedings of the 2003 Winter Simulation Conference, pp. 135-143,
2003.
[9] Oryal Tanir, Richard J Booth, " Call Centre Simulation in Bell Canada," Proceedings of
the 1999 Winter Simulation Conference, pp. 1640-1647, 1999.
[10] Wafik H. Iskander, " Simulation Modeling for Emergency Medical Service Systems,"
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[11] E.S. Savas, " Simulation and Cost-Effectiveness Analysis of New York's Emergency
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77
Appendix A: Complete Simul8 Results
This appendix gives the complete results from the Simul8 trials that were run for this
thesis. Section 1 (Time Windows) shows the results that are specific to each defined time
period, and is separated into one part for 100% call volume and another for 115% call
volume. Section 2 shows the results from the simulations that were run for 24 hours a
day, seven days a week. It is also separated into parts based on call volume. Section 2 is
valuable in that it shows the trends that result from varying the number of call takers on
one shift at a time. For example, “x-2-2-2” means that the number of call takers on the
7am-7pm shift were varied while all other shifts remained constant at two call takers.
The structure of the diagrams is as follows:
1. Time Windows
1.1 100% Call Volume
1.1.1 12am-2am
1.1.2 2am-7am
1.1.3 7am-10am
1.1.4 10am-2pm
1.1.5 2pm-7pm
1.1.6 7pm-12am
1.1.7 2am-2:30am
1.2 115% Call Volume
1.2.1 12am-2am
1.2.2 2am-7am
1.2.3 7am-10am
1.2.4 10am-2pm
1.2.5 2pm-7pm
1.2.6 7pm-12am
1.2.7 2am-2:30am
2. 24-Hour Results
2.1 100% Call Volume
2.1.1 Varying x-2-2-2
2.1.2 Varying 4-x-2-2
2.1.3 Varying 5-x-2-2
2.1.4 Varying 6-x-2-2
2.1.5 Varying 4-2-x-2
2.1.6 Varying 4-2-2-x
2.1.7 Varying 5-2-2-x
2.2 115% Call Volume
2.2.1 Varying x-2-2-2
2.2.2 Varying 4-x-2-2
78
2.2.3 Varying 5-x-2-2
2.2.4 Varying 6-x-2-2
2.2.5 Varying 4-2-x-2
2.2.6 Varying 4-2-x-2
2.2.7 Varying 4-2-2-x
2.2.8 Varying 5-2-2-x
Note: the indicator x-x-x-x represents the number of call takers on each of four shifts. For
example, 5-4-3-2 means five call takers for 7am-7pm, four for 7pm-7am, three for 11am-
11pm and two for 2pm-2am.
79
12am-2am 100% volume 4-2-2-2 4-3-2-2 4-4-2-2
Performance Measure -99% Average 99% -99% Average 99% -99% Average 99%
Maximum queue size 5.38 6.60 7.82 12.55 14.30 16.05 4.90 5.95 7.00
Maximum Queuing Time 7.91 12.96 18.00 28.10 33.37 38.64 6.57 10.03 13.49
Items Entered 35811.45 35869.45 35927.45 35811.45 35869.45 35927.45 35811.45 35869.45 35927.45
Average Queuing Time 0.01 0.01 0.02 0.11 0.12 0.13 0.01 0.01 0.02
Average (non-zero)
Queuing Time 0.63 0.70 0.77 1.17 1.24 1.32 0.59 0.65 0.71
St Dev of Queuing Time 0.15 0.20 0.24 0.76 0.84 0.92 0.14 0.17 0.20
% Queued less than time
limit 98.39 98.47 98.54 91.94 92.19 92.44 98.39 98.48 98.58
Utilization % 33.01 33.13 33.26 41.03 41.18 41.33 33.02 33.14 33.27
2am-7am 100% volume 4-2-2-2 4-3-2-2 4-4-2-2
Performance Measure -99% Average 99% -99% Average 99% -99% Average 99%
Maximum queue size 2536.53 2641.83 2747.13 108.15 129.10 150.05 32.34 37.10 41.86
Maximum Queuing Time 19662.91 20556.27 21449.63 453.70 507.68 561.66 92.78 106.59 120.39
Items Entered 35812.71 35856.10 35899.49 35811.45 35869.45 35927.45 35811.45 35869.45 35927.45
Average Queuing Time 1028.57 1085.84 1143.12 9.59 10.59 11.59 1.12 1.19 1.26
Average (non-zero)
Queuing Time 1032.49 1089.93 1147.38 14.97 16.46 17.95 3.63 3.83 4.03
St Dev of Queuing Time 3330.07 3530.00 3729.93 33.85 37.40 40.94 4.50 4.87 5.24
% Queued less than time
limit 3.38 3.45 3.52 41.46 42.01 42.56 72.75 73.10 73.46
Utilization % 99.77 99.81 99.86 70.50 70.78 71.05 52.88 53.08 53.28
2am-7am 100% volume 4-5-2-2 4-6-2-2
Performance Measure -99% Average 99% -99% Average 99%
Maximum queue size 14.36 18.75 23.14 6.10 7.7 9.29
Maximum Queuing Time 38.58 49.90 61.21 10.49 15.78639 21.08
Items Entered 35811.45 35869.45 35927.45 35811.45 35869.45 35927.45
Average Queuing Time 0.18 0.20 0.23 0.02 0.031 0.035
Average (non-zero) Queuing
Time 1.39 1.56 1.72 0.68 0.76 0.84
St Dev of Queuing Time 1.05 1.31 1.56 0.23 0.28 0.34
% Queued less than time limit 89.09 89.35 89.62 96.87 97.02 97.17
Utilization % 42.30 42.47 42.63 35.23 35.38 35.53
Section 1: Results from Time Window Analysis
80
7am-10am 100% volume 4-2-2-2 5-2-2-2 6-2-2-2
Performance Measure -99% Average 99% -99% Average 99% -99% Average 99%
Maximum queue size 30.11 33.07 36.03 14.58 16.80 19.02 6.63 7.75 8.87
Maximum Queuing Time 82.28 91.53 100.79 37.98 45.87 53.76 10.13 13.31 16.50
Items Entered 35812.71 35856.10 35899.49 35811.45 35869.45 35927.45 35811.45 35869.45 35927.45
Average Queuing Time 0.86 0.91 0.95 0.15 0.16 0.17 0.02 0.02 0.03
Average (non-zero) Queuing
Time 3.26 3.40 3.54 1.40 1.49 1.59 0.70 0.74 0.79
St Dev of Queuing Time 3.81 4.03 4.26 1.01 1.13 1.24 0.22 0.24 0.27
% Queued less than time limit 76.98 77.26 77.55 90.99 91.17 91.36 97.49 97.58 97.66
Utilization % 50.72 50.88 51.04 40.59 40.75 40.90 33.84 33.96 34.08
10am-2pm 100% volume 4-2-2-2 4-2-3-2 4-2-4-2 5-2-2-2
Performance Measure -99% Average 99% -99% Average 99% -99% Average 99% -99% Average 99%
Maximum queue size 7.07 8.85 10.63 5.71 7.65 9.59 4.88 6.95 9.02 4.62 5.70 6.78
Maximum Queuing Time 13.82 18.86 23.90 7.84 13.38 18.93 7.80 11.75 15.70 6.59 10.21 13.84
Items Entered 35811.45 35869.45 35927.45 35811.45 35869.45 35927.45 35811.45 35869.45 35927.45 35811.45 35869.45 35927.45
Average Queuing Time 0.03 0.03 0.04 0.01 0.02 0.02 0.01 0.01 0.02 0.01 0.01 0.01
Average (non-zero) Queuing
Time 0.70 0.75 0.80 0.61 0.70 0.79 0.64 0.73 0.82 0.57 0.63 0.69
St Dev of Queuing Time 0.26 0.32 0.37 0.14 0.21 0.27 0.14 0.18 0.23 0.11 0.14 0.17
% Queued less than time limit 96.44 96.56 96.68 98.25 98.36 98.48 98.58 98.67 98.77 98.80 98.89 98.97
Utilization % 37.60 37.76 37.91 33.03 33.15 33.28 29.43 29.55 29.67 31.84 31.97 32.09
10am-2pm 100% volume 5-2-3-2 5-2-4-2 6-2-2-2 6-2-3-2
Performance Measure -99% Average 99% -99% Average 99% -99% Average 99% -99% Average 99%
Maximum queue size 3.20 4.00 4.80 3.52 4.10 4.68 3.40 3.90 4.40 1.84 2.25 2.66
Maximum Queuing Time 2.67 5.02 7.37 2.45 4.74 7.04 3.48 4.42 5.37 1.24 1.68 2.13
Items Entered 35811.45 35869.45 35927.45 35811.45 35869.45 35927.45 35811.45 35869.45 35927.45 35811.45 35869.45 35927.45
Average Queuing Time 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Average (non-zero) Queuing
Time 0.42 0.50 0.59 0.44 0.52 0.61 0.44 0.49 0.54 0.31 0.38 0.44
St Dev of Queuing Time 0.04 0.06 0.08 0.04 0.06 0.08 0.04 0.05 0.06 0.01 0.02 0.02
% Queued less than time limit 99.64 99.66 99.69 99.67 99.70 99.74 99.71 99.74 99.76 99.93 99.94 99.95
81
Utilization % 28.52 28.62 28.73 25.79 25.88 25.98 27.61 27.73 27.84 25.07 25.17 25.27
2pm-7pm 100% volume 4-2-2-2 4-2-2-3
Performance Measure -99% Average 99% -99% Average 99%
Maximum queue size 2.56 3.05 3.54 1.07 1.60 2.13
Maximum Queuing Time 1.96 2.85 3.74 0.61 1.07 1.53
Items Entered 35811.45 35869.45 35927.45 35811.45 35869.45 35927.45
Average Queuing Time 0.00 0.00 0.00 0.00 0.00 0.00
Average (non-zero) Queuing
Time 0.37 0.44 0.51 0.23 0.33 0.43
St Dev of Queuing Time 0.02 0.03 0.04 0.00 0.01 0.01
% Queued less than time limit 99.83 99.86 99.89 99.98 99.99 99.99
Utilization % 26.85 26.96 27.07 23.50 23.59 23.67
7pm-12am 100% volume 4-2-2-2 4-3-2-2 4-4-2-2 4-2-2-3
Performance Measure -99% Average 99% -99% Average 99% -99% Average 99% -99% Average 99%
Maximum queue size 26.27 28.80 31.33 9.96 11.85 13.74 7.11 9.10 11.09 11.19 13.00 14.81
Maximum Queuing Time 52.09 56.86 61.63 19.62 24.13 28.64 13.18 18.95 24.71 21.65 24.92 28.20
Items Entered 35812.71 35856.10 35899.49 35811.45 35869.45 35927.45 35811.45 35869.45 35927.45 35811.45 35869.45 35927.45
Average Queuing Time 0.36 0.37 0.39 0.04 0.05 0.05 0.02 0.03 0.03 0.04 0.04 0.05
Average (non-zero) Queuing
Time 3.01 3.12 3.23 1.10 1.16 1.22 0.92 1.01 1.10 1.15 1.21 1.27
St Dev of Queuing Time 2.14 2.24 2.34 0.43 0.48 0.52 0.26 0.32 0.38 0.44 0.48 0.53
% Queued less than time limit 89.62 89.79 89.96 96.64 96.74 96.83 97.94 98.05 98.16 96.95 97.07 97.19
Utilization % 36.77 36.89 37.00 30.77 30.89 31.00 27.05 27.16 27.27 31.62 31.75 31.87
2am-2:30am 100% volume 4-2-2-2 4-3-2-2 4-4-2-2
Performance Measure -99% Average 99% -99% Average 99% -99% Average 99%
Maximum queue size 18316.50 18551.50 18786.50 261.45 284.20 306.95 261.45 284.20 306.95
Maximum Queuing Time 7811.43 8200.78 8590.13 996.29 1033.64 1071.00 996.29 1033.64 1071.00
Items Entered 35742.69 35842.70 35942.71 35811.45 35869.45 35927.45 35811.45 35869.45 35927.45
Average Queuing Time 3873.52 4126.47 4379.43 60.40 62.92 65.44 60.40 62.92 65.44
Average (non-zero) Queuing Time 3880.33 4136.04 4391.75 71.33 74.15 76.96 71.33 74.15 76.96
St Dev of Queuing Time 2244.03 2376.93 2509.82 146.82 150.68 154.55 146.82 150.68 154.55
% Queued less than time limit 0.06 0.28 0.50 20.92 21.36 21.80 20.92 21.36 21.80
Utilization % 99.72 99.85 99.98 84.70 85.03 85.36 84.70 85.03 85.36
82
2am-2:30am 100% volume 4-5-2-2 4-6-2-2 4-7-2-2
Performance Measure -99% Average 99% -99% Average 99% -99% Average 99%
Maximum queue size 26.46164 32 37.53836 8.01019 9.9 11.78981 8.01019 9.9 11.78981
Maximum Queuing Time 92.76416 120.97268 149.18119 16.79839 23.61716 30.43592 16.79839 23.61716 30.43592
Items Entered 35812.451 35870 35927.549 35811.449 35869.45 35927.451 35811.449 35869.45 35927.451
Average Queuing Time 0.57686 0.65005 0.72324 0.04851 0.05352 0.05853 0.04851 0.05352 0.05853
Average (non-zero) Queuing
Time 1.99839 2.23266 2.46693 0.7433 0.80059 0.85788 0.7433 0.80059 0.85788
St Dev of Queuing Time 2.89452 3.5776 4.26068 0.34543 0.42421 0.50299 0.34543 0.42421 0.50299
% Queued less than time limit 75.38613 75.82751 76.26889 94.85387 95.02248 95.1911 94.85387 95.02248 95.1911
Utilization % 56.37336 56.59478 56.81619 42.30602 42.4679 42.62977 42.30575 42.46772 42.62969
12am-2am 115% volume 4-2-2-2 4-3-2-2 4-4-2-2
Performance Measure -99% Average 99% -99% Average 99% -99% Average 99%
Maximum queue size 32.54 35.40 38.26401 18.50 20.55 22.60 8.33 9.35 10.37
Maximum Queuing Time 68.19 80.52 92.85375 40.05 46.71 53.36 13.12 15.75 18.38
Items Entered 41167.65 41230.25 41292.852 41171.02 41232.00 41292.98 41171.02 41232.00 41292.98
Average Queuing Time 1.47 1.51 1.55413 0.25 0.28 0.30 0.03 0.03 0.04
Average (non-zero) Queuing Time 4.26 4.36 4.46508 1.55 1.66 1.77 0.71 0.75 0.80
St Dev of Queuing Time 4.87 5.05 5.23926 1.38 1.52 1.67 0.27 0.30 0.33
% Queued less than time limit 69.65 69.95 70.24886 86.30 86.63 86.95 96.75 96.90 97.06
Utilization % 55.52 55.74 55.95714 47.13 47.32 47.51 37.91 38.07 38.23
2am-7am 115% volume 4-2-2-2 4-3-2-2 4-4-2-2
Performance Measure -99% Average 99% -99% Average 99% -99% Average 99%
Maximum queue size 9704.05 9865.40 10026.75 226.10 246.40 266.70 49.07 55.10 61.13
Maximum Queuing Time 15945.21 16550.48 17155.75 848.28 894.02 939.76 131.94 162.52 193.09
Items Entered 41182.13 41226.23 41270.34 41171.02 41232.00 41292.98 41171.02 41232.00 41292.98
Average Queuing Time 1934.20 2047.06 2159.92 41.27 43.59 45.91 2.56 2.73 2.90
Average (non-zero) Queuing Time 1941.18 2054.46 2167.74 50.96 53.73 56.50 5.78 6.12 6.46
St Dev of Queuing Time 4084.23 4309.39 4534.54 110.22 114.80 119.37 8.63 9.45 10.28
83
% Queued less than time limit 1.96 2.02 2.09 24.97 25.41 25.84 60.77 61.20 61.62
Utilization % 99.89 99.93 99.98 81.05 81.38 81.71 60.72 60.97 61.21
2am-7am 115% volume 4-5-2-2 4-6-2-2 4-7-2-2
Performance Measure -99% Average 99% -99% Average 99% -99% Average 99%
Maximum queue size 24.74 29.00 33.26 9.54 11.50 13.46 7.57 9.45 11.33
Maximum Queuing Time 61.81 68.99 76.17 19.49 24.90 30.31 12.84 16.22 19.59
Items Entered 41171.02 41232.00 41292.98 41167.65 41230.25 41292.85 41171.02 41232.00 41292.98
Average Queuing Time 0.44 0.47 0.51 0.06 0.07 0.08 0.02 0.03 0.03
Average (non-zero) Queuing Time 2.08 2.23 2.38 0.82 0.89 0.96 0.69 0.75 0.82
St Dev of Queuing Time 2.26 2.52 2.77 0.43 0.50 0.57 0.24 0.28 0.32
% Queued less than time limit 82.32 82.65 82.98 93.96 94.23 94.50 97.29 97.43 97.57
Utilization % 48.57 48.77 48.97 40.48 40.64 40.79 34.70 34.84 34.99
7am-10am 115% volume 4-4-2-2 4-4-2-2 4-4-2-2 4-4-2-2
Performance Measure -99% Average 99% -99% Average 99% -99% Average 99% -99% Average 99%
Maximum queue size 11.37 13.55 15.73 8.33 9.35 10.37 49.07 55.10 61.13 500.64 555.35 610.06
Maximum Queuing Time 22.81 27.45 32.09 13.12 15.75 18.38 131.94 162.52 193.09 2429.35 2773.05 3116.75
Items Entered 41171.02 41232.00 41292.98 41171.02 41232.00 41292.98 41171.02 41232.00 41292.98 41171.02 41232.00 41292.98
Average Queuing Time 0.05 0.06 0.06 0.03 0.03 0.04 2.56 2.73 2.90 200.77 225.33 249.88
Average (non-zero) Queuing
Time 1.19 1.27 1.35 0.71 0.75 0.80 5.78 6.12 6.46 206.47 230.74 255.02
St Dev of Queuing Time 0.50 0.56 0.61 0.27 0.30 0.33 8.63 9.45 10.28 380.35 439.85 499.35
% Queued less than time limit 96.35 96.48 96.62 96.75 96.90 97.06 60.77 61.20 61.62 7.42 7.86 8.29
Utilization % 31.10 31.22 31.34 37.91 38.07 38.23 60.72 60.97 61.21 97.29 97.65 98.00
84
10am-2pm 115% volume 4-2-2-2 4-2-3-2 4-2-4-2 5-2-2-2
Performance Measure -99% Average 99% -99% Average 99% -99% Average 99% -99% Average 99%
Maximum queue size 46.55 50.85 55.15 8.20 10.20 12.20 7.62 9.45 11.28 46.55 50.85 55.15
Maximum Queuing Time 117.95 130.79 143.62 14.06 19.03 24.01 12.27 15.85 19.42 117.95 130.79 143.62
Items Entered 41171.02 41232.00 41292.98 41171.02 41232.00 41292.98 41171.02 41232.00 41292.98 41171.02 41232.00 41292.98
Average Queuing Time 2.00 2.12 2.24 0.03 0.04 0.04 0.03 0.03 0.03 2.00 2.12 2.24
Average (non-zero) Queuing
Time 5.17 5.43 5.69 0.71 0.78 0.85 0.75 0.82 0.89 5.17 5.43 5.69
St Dev of Queuing Time 7.39 7.87 8.35 0.28 0.34 0.39 0.26 0.30 0.35 7.39 7.87 8.35
% Queued less than time limit 65.90 66.36 66.83 96.61 96.74 96.87 97.25 97.37 97.50 65.90 66.36 66.83
Utilization % 58.26 58.48 58.71 37.92 38.08 38.23 33.79 33.93 34.08 58.26 58.48 58.71
10am-2pm 115% volume 5-2-3-2 5-2-4-2 6-2-2-2 6-2-3-2
Performance Measure -99% Average 99% -99% Average 99% -99% Average 99% -99% Average 99%
Maximum queue size 7.52 8.85 10.18 4.28 5.20 6.12 4.28 4.90 5.52 2.71 3.30 3.89
Maximum Queuing Time 11.74 15.63 19.52 5.19 6.58 7.97 4.35 5.57 6.79 1.81 2.50 3.19
Items Entered 41171.02 41232.00 41292.98 41171.02 41232.00 41292.98 41171.02 41232.00 41292.98 41171.02 41232.00 41292.98
Average Queuing Time 0.02 0.02 0.03 0.00 0.01 0.01 0.00 0.00 0.01 0.00 0.00 0.00
Average (non-zero) Queuing
Time 0.66 0.71 0.76 0.48 0.53 0.58 0.45 0.48 0.52 0.34 0.38 0.43
St Dev of Queuing Time 0.22 0.26 0.30 0.08 0.09 0.11 0.07 0.08 0.09 0.02 0.03 0.04
% Queued less than time limit 97.45 97.59 97.72 99.21 99.29 99.37 99.31 99.38 99.45 99.80 99.83 99.86
Utilization % 36.58 36.74 36.90 29.62 29.74 29.86 31.72 31.85 31.98 28.78 28.90 29.03
2pm-7pm 115% volume 4-2-2-2 4-2-2-3 4-2-2-4
Performance Measure -99% Average 99% -99% Average 99% -99% Average 99%
Maximum queue size 3.41 3.80 4.19 2.29 2.85 3.41 2.13 2.65 3.17
Maximum Queuing Time 3.34 4.02 4.70 1.45 2.01 2.56 1.08 1.73 2.38
Items Entered 41171.02 41232.00 41292.98 41171.02 41232.00 41292.98 41171.02 41232.00 41292.98
Average Queuing Time 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Average (non-zero) Queuing Time 0.41 0.45 0.48 0.33 0.40 0.47 0.30 0.38 0.46
85
St Dev of Queuing Time 0.05 0.05 0.06 0.01 0.02 0.02 0.01 0.01 0.02
% Queued less than time limit 99.63 99.65 99.68 99.93 99.95 99.96 99.95 99.96 99.97
Utilization % 30.86 30.98 31.11 27.00 27.11 27.21 24.44 24.54 24.63
2pm-7pm 115% volume 4-2-3-2 4-2-3-3 4-2-3-4
Performance Measure -99% Average 99% -99% Average 99% -99% Average 99%
Maximum queue size 2.13 2.75 3.37 1.16 1.80 2.44 0.96 1.45 1.94
Maximum Queuing Time 1.15 2.05 2.95 0.39 0.82 1.26 0.15 0.47 0.78
Items Entered 41171.02 41232.00 41292.98 41171.02 41232.00 41292.98 41171.02 41232.00 41292.98
Average Queuing Time 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Average (non-zero) Queuing Time 0.29 0.36 0.44 0.18 0.29 0.40 0.16 0.25 0.35
St Dev of Queuing Time 0.01 0.02 0.03 0.00 0.01 0.01 0.00 0.00 0.01
% Queued less than time limit 99.91 99.93 99.95 99.98 99.99 100.00 99.99 100.00 100.00
Utilization % 27.17 27.28 27.39 24.14 24.23 24.33 22.08 22.17 22.26
7pm-12am 115% volume 4-2-2-2 4-3-2-2 4-4-2-2
Performance Measure -95% Average 95% -95% Average 95% -95% Average 95%
Maximum queue size 34.67 37.20 39.73 16.85 18.65 20.45 11.95 13.55 15.15
Maximum Queuing Time 64.39 67.91 71.44 29.51 32.46 35.41 24.05 27.45 30.85
Items Entered 41184.45 41230.25 41276.05 41187.39 41232.00 41276.61 41187.39 41232.00 41276.61
Average Queuing Time 0.65 0.68 0.71 0.10 0.10 0.11 0.05 0.06 0.06
Average (non-zero) Queuing
Time 3.88 4.01 4.14 1.41 1.47 1.53 1.22 1.27 1.33
St Dev of Queuing Time 3.33 3.45 3.58 0.79 0.84 0.89 0.52 0.56 0.60
% Queued less than time limit 85.36 85.54 85.72 94.33 94.43 94.54 96.38 96.48 96.58
Utilization % 42.27 42.39 42.51 35.38 35.48 35.58 31.13 31.22 31.31
2am-2:30am 115% volume 4-2-2-2 4-3-2-2 4-4-2-2
Performance Measure -99% Average 99% -99% Average 99% -99% Average 99%
Maximum queue size 23857.08 23984.65 24112.22 500.64 555.35 610.06 500.64 555.35 610.06
Maximum Queuing Time 12691.41 12888.42 13085.44 2429.35 2773.05 3116.75 2429.35 2773.05 3116.75
Items Entered 41171.02 41232.00 41292.98 41171.02 41232.00 41292.98 41171.02 41232.00 41292.98
Average Queuing Time 6257.99 6400.11 6542.24 200.77 225.33 249.88 200.77 225.33 249.88
Average (non-zero) Queuing Time 6265.54 6408.38 6551.21 206.47 230.74 255.02 206.47 230.74 255.02
86
St Dev of Queuing Time 3693.38 3762.02 3830.67 380.35 439.85 499.35 380.35 439.85 499.35
% Queued less than time limit 0.07 0.17 0.27 7.42 7.86 8.29 7.42 7.86 8.29
Utilization % 99.87 99.92 99.98 97.29 97.65 98.00 97.29 97.65 98.00
2am-2:30am 115% volume 4-5-2-2 4-6-2-2 4-7-2-2
Performance Measure -99% Average 99% -99% Average 99% -99% Average 99%
Maximum queue size 50.78 60.30 69.82 10.49 13.10 15.71 10.49 13.10 15.71
Maximum Queuing Time 184.28 229.30 274.33 22.91 29.94 36.97 22.91 29.94 36.97
Items Entered 41171.02 41232.00 41292.98 41171.02 41232.00 41292.98 41171.02 41232.00 41292.98
Average Queuing Time 1.97 2.29 2.61 0.11 0.12 0.13 0.11 0.12 0.13
Average (non-zero) Queuing
Time 4.33 4.99 5.65 0.88 0.94 1.00 0.88 0.94 1.00
St Dev of Queuing Time 9.30 11.34 13.37 0.61 0.71 0.81 0.61 0.71 0.81
% Queued less than time limit 60.32 60.98 61.64 90.21 90.52 90.83 90.21 90.52 90.83
Utilization % 64.75 65.02 65.29 48.57 48.77 48.96 48.57 48.77 48.96
87
100% volume 4-2-2-2 5-2-2-2 6-2-2-2 7-2-2-2
Performance Measure -99% Average 99% -99% Average 99% -99% Average 99% -99% Average 99%
Maximum queue size 27.89 30.10 32.31 27.75 29.47 31.18 27.29 29.90 32.51 27.50 29.40 31.30
Maximum Queuing Time 124.21 142.10 160.00 122.44 141.10 159.76 121.18 139.41 157.64 121.59 138.28 154.97
Items Entered 35812.71 35856.10 35899.49 35812.71 35856.10 35899.49 35812.71 35856.10 35899.49 35812.71 35856.10 35899.49
Average Queuing Time 0.52 0.56 0.60 0.45 0.49 0.53 0.44 0.48 0.53 0.45 0.48 0.51
Average (non-zero) Queuing
Time 4.74 5.11 5.48 5.78 6.26 6.74 6.64 7.27 7.90 7.10 7.60 8.10
St Dev of Queuing Time 4.20 4.63 5.06 4.09 4.50 4.90 4.06 4.54 5.02 4.13 4.51 4.89
% Queued less than time limit 90.33 90.50 90.67 92.98 93.09 93.20 93.92 94.02 94.13 94.18 94.27 94.37
Utilization % 41.85 41.98 42.11 38.05 38.17 38.29 34.88 34.99 35.10 32.20 32.29 32.39
100% volume 4-2-2-2 4-3-2-2 4-4-2-2
Performance Measure -99% Average 99% -99% Average 99% -99% Average 99%
Maximum queue size 27.89 30.10 32.31 12.35 13.30 14.25 11.98 13.27 14.55
Maximum Queuing Time 124.21 142.10 160.00 39.82 47.07 54.32 31.95 35.78 39.62
Items Entered 35812.71 35856.10 35899.49 35812.71 35856.10 35899.49 35812.71 35856.10 35899.49
Average Queuing Time 0.52 0.56 0.60 0.10 0.11 0.12 0.08 0.09 0.09
Average (non-zero) Queuing
Time 4.74 5.11 5.48 1.56 1.66 1.75 1.49 1.55 1.60
St Dev of Queuing Time 4.20 4.63 5.06 0.88 0.98 1.09 0.75 0.80 0.85
% Queued less than time limit 90.33 90.50 90.67 94.55 94.70 94.84 95.34 95.49 95.63
Utilization % 41.85 41.98 42.11 38.02 38.14 38.25 34.81 34.92 35.03
100% volume 5-2-2-2 5-3-2-2 5-4-2-2
Performance Measure -99% Average 99% -99% Average 99% -99% Average 99%
Maximum queue size 27.75 29.47 31.18 7.59 8.70 9.81 6.64 7.43 8.22
Maximum Queuing Time 122.44 141.10 159.76 28.70 37.45 46.20 16.66 19.94 23.23
Items Entered 35812.71 35856.10 35899.49 35812.71 35856.10 35899.49 35812.71 35856.10 35899.49
Average Queuing Time 0.45 0.49 0.53 0.04 0.05 0.05 0.02 0.03 0.03
Average (non-zero) Queuing
Time 5.78 6.26 6.74 1.18 1.36 1.54 0.97 1.04 1.11
St Dev of Queuing Time 4.09 4.50 4.90 0.46 0.59 0.72 0.28 0.32 0.36
% Queued less than time limit 92.98 93.09 93.20 97.26 97.35 97.44 98.04 98.12 98.20
Section 2: Results from 24 Hour Analysis
88
Utilization % 38.05 38.17 38.29 34.84 34.96 35.07 32.15 32.24 32.34
100% volume 6-2-2-2 6-3-2-2 6-4-2-2
Performance Measure -99% Average 99% -99% Average 99% -99% Average 99%
Maximum queue size 27.29 29.90 32.51 7.37 9.10 10.83 6.44 7.23 8.02
Maximum Queuing Time 121.18 139.41 157.64 27.33 36.13 44.93 17.13 20.81 24.50
Items Entered 35812.71 35856.10 35899.49 35812.71 35856.10 35899.49 35812.71 35856.10 35899.49
Average Queuing Time 0.44 0.48 0.53 0.03 0.03 0.04 0.01 0.01 0.02
Average (non-zero) Queuing Time 6.64 7.27 7.90 1.31 1.50 1.69 1.03 1.15 1.26
St Dev of Queuing Time 4.06 4.54 5.02 0.40 0.52 0.64 0.22 0.27 0.31
% Queued less than time limit 93.92 94.02 94.13 98.17 98.24 98.31 98.96 99.02 99.07
Utilization % 34.88 34.99 35.10 32.18 32.28 32.38 29.84 29.94 30.04
100% volume 4-2-2-2 4-2-3-2 4-2-4-2
Performance Measure -99% Average 99% -99% Average 99% -99% Average 99%
Maximum queue size 27.89 30.10 32.31 27.55 29.47 31.38 28.01 30.17 32.33
Maximum Queuing Time 124.21 142.10 160.00 122.16 136.50 150.85 130.16 146.77 163.38
Items Entered 35812.71 35856.10 35899.49 35812.71 35856.10 35899.49 35812.71 35856.10 35899.49
Average Queuing Time 0.52 0.56 0.60 0.51 0.55 0.58 0.51 0.55 0.59
Average (non-zero) Queuing
Time 4.74 5.11 5.48 5.19 5.58 5.96 5.35 5.73 6.12
St Dev of Queuing Time 4.20 4.63 5.06 4.18 4.55 4.91 4.21 4.63 5.04
% Queued less than time limit 90.33 90.50 90.67 91.26 91.42 91.57 91.42 91.58 91.74
Utilization % 41.85 41.98 42.11 38.07 38.19 38.31 34.93 35.03 35.13
100% volume 4-2-2-2 4-2-2-3 4-2-2-4
Performance Measure -99% Average 99% -99% Average 99% -99% Average 99%
Maximum queue size 27.89 30.10 32.31 28.05 30.33 32.61 27.23 29.17 31.10
Maximum Queuing Time 124.21 142.10 160.00 121.31 139.32 157.33 123.79 141.07 158.34
Items Entered 35812.71 35856.10 35899.49 35812.71 35856.10 35899.49 35812.71 35856.10 35899.49
Average Queuing Time 0.52 0.56 0.60 0.48 0.52 0.56 0.48 0.52 0.57
Average (non-zero) Queuing Time 4.74 5.11 5.48 5.04 5.45 5.87 5.17 5.58 5.99
St Dev of Queuing Time 4.20 4.63 5.06 4.09 4.56 5.02 4.12 4.57 5.01
% Queued less than time limit 90.33 90.50 90.67 91.58 91.73 91.89 91.72 91.86 92.00
89
Utilization % 41.85 41.98 42.11 38.08 38.19 38.31 34.88 34.99 35.10
100% volume 5-2-2-2 5-2-2-3 5-2-2-4
Performance Measure -99% Average 99% -99% Average 99% -99% Average 99%
Maximum queue size 27.75 29.47 31.18 27.19 29.03 30.88 27.36 29.27 31.18
Maximum Queuing Time 122.44 141.10 159.76 122.72 140.29 157.86 128.55 144.83 161.11
Items Entered 35812.71 35856.10 35899.49 35812.71 35856.10 35899.49 35812.71 35856.10 35899.49
Average Queuing Time 0.45 0.49 0.53 0.42 0.46 0.50 0.43 0.46 0.50
Average (non-zero) Queuing Time 5.78 6.26 6.74 6.65 7.19 7.73 6.88 7.38 7.89
St Dev of Queuing Time 4.09 4.50 4.90 4.09 4.51 4.94 4.18 4.54 4.91
% Queued less than time limit 92.98 93.09 93.20 94.27 94.37 94.48 94.35 94.44 94.53
Utilization % 38.05 38.17 38.29 34.88 34.99 35.11 32.21 32.31 32.41
115% volume 4-2-2-2 5-2-2-2 6-2-2-2 7-2-2-2
Performance Measure -99% Average 99% -99% Average 99% -99% Average 99% -99% Average 99%
Maximum queue size 36.76 39.50 42.24 36.11 39.13 42.16 36.11 40.00 43.89 37.79 40.93 44.08
Maximum Queuing Time 197.02 212.92 228.83 191.31 207.00 222.69 195.46 212.14 228.81 200.75 216.74 232.72
Items Entered 41182.13 41226.23 41270.34 41182.13 41226.23 41270.34 41182.13 41226.23 41270.34 41182.13 41226.23 41270.34
Average Queuing Time 0.97 1.04 1.11 0.81 0.87 0.93 0.80 0.86 0.93 0.78 0.84 0.91
Average (non-zero) Queuing Time 6.05 6.42 6.79 7.28 7.79 8.30 8.78 9.44 10.11 9.45 10.09 10.74
St Dev of Queuing Time 7.03 7.57 8.11 6.64 7.19 7.73 6.78 7.38 7.99 6.82 7.37 7.92
% Queued less than time limit 85.83 86.04 86.26 90.10 90.26 90.41 91.69 91.85 92.01 92.30 92.44 92.58
Utilization % 48.10 48.25 48.40 43.73 43.87 44.00 40.09 40.21 40.33 37.00 37.12 37.24
115% volume 4-2-2-2 4-3-2-2 4-4-2-2
Performance Measure -99% Average 99% -99% Average 99% -99% Average 99%
Maximum queue size 36.76 39.50 42.24 20.35 23.97 27.58 19.77 23.00 26.23
Maximum Queuing Time 197.02 212.92 228.83 68.24 80.80 93.35 55.72 71.18 86.64
Items Entered 41182.13 41226.23 41270.34 41182.13 41226.23 41270.34 41182.13 41226.23 41270.34
Average Queuing Time 0.97 1.04 1.11 0.22 0.25 0.27 0.18 0.20 0.22
Average (non-zero) Queuing Time 6.05 6.42 6.79 2.12 2.32 2.51 1.97 2.17 2.36
St Dev of Queuing Time 7.03 7.57 8.11 1.71 1.97 2.24 1.44 1.69 1.94
% Queued less than time limit 85.83 86.04 86.26 91.05 91.25 91.46 92.28 92.46 92.64
90
Utilization % 48.10 48.25 48.40 43.69 43.83 43.96 40.00 40.12 40.25
115% volume 5-2-2-2 5-3-2-2 5-4-2-2
Performance Measure -99% Average 99% -99% Average 99% -99% Average 99%
Maximum queue size 36.11 39.13 42.16 13.85 16.13 18.41 9.81 10.90 11.99
Maximum Queuing Time 191.31 207.00 222.69 58.37 66.72 75.08 27.98 31.82 35.65
Items Entered 41182.13 41226.23 41270.34 41182.13 41226.23 41270.34 41182.13 41226.23 41270.34
Average Queuing Time 0.81 0.87 0.93 0.09 0.10 0.11 0.05 0.05 0.06
Average (non-zero) Queuing
Time 7.28 7.79 8.30 1.64 1.80 1.97 1.15 1.23 1.31
St Dev of Queuing Time 6.64 7.19 7.73 1.05 1.22 1.40 0.50 0.56 0.62
% Queued less than time limit 90.10 90.26 90.41 95.31 95.44 95.56 96.57 96.68 96.78
Utilization % 43.73 43.87 44.00 40.05 40.17 40.29 36.93 37.04 37.16
115% volume 6-2-2-2 6-3-2-2 6-4-2-2
Performance Measure -99% Average 99% -99% Average 99% -99% Average 99%
Maximum queue size 36.11 40.00 43.89 12.28 14.73 17.19 8.19 9.63 11.07
Maximum Queuing Time 195.46 212.14 228.81 53.31 63.08 72.84 23.27 27.86 32.45
Items Entered 41182.13 41226.23 41270.34 41182.13 41226.23 41270.34 41182.13 41226.23 41270.34
Average Queuing Time 0.80 0.86 0.93 0.06 0.07 0.08 0.02 0.03 0.03
Average (non-zero) Queuing
Time 8.78 9.44 10.11 1.77 2.02 2.27 1.09 1.20 1.31
St Dev of Queuing Time 6.78 7.38 7.99 0.91 1.09 1.27 0.35 0.41 0.47
% Queued less than time limit 91.69 91.85 92.01 96.97 97.08 97.19 98.16 98.24 98.32
Utilization % 40.09 40.21 40.33 36.96 37.08 37.20 34.31 34.41 34.51
115% volume 4-2-2-2 4-2-3-2 4-2-4-2
Performance Measure -99% Average 99% -99% Average 99% -99% Average 99%
Maximum queue size 36.76 39.50 42.24 35.38 38.87 42.35 36.59 40.33 44.08
Maximum Queuing Time 197.02 212.92 228.83 197.59 213.04 228.49 195.78 213.95 232.11
Items Entered 41182.13 41226.23 41270.34 41182.13 41226.23 41270.34 41182.13 41226.23 41270.34
Average Queuing Time 0.97 1.04 1.11 0.91 0.98 1.06 0.93 0.99 1.06
Average (non-zero) Queuing Time 6.05 6.42 6.79 6.60 7.09 7.59 6.95 7.42 7.88
St Dev of Queuing Time 7.03 7.57 8.11 6.75 7.34 7.94 6.87 7.48 8.08
% Queued less than time limit 85.83 86.04 86.26 87.65 87.86 88.06 88.01 88.19 88.36
91
Utilization % 48.10 48.25 48.40 43.76 43.89 44.03 40.14 40.27 40.40
115% volume 4-2-2-2 4-2-2-3 4-2-2-4
Performance Measure -99% Average 99% -99% Average 99% -99% Average 99%
Maximum queue size 36.76 39.50 42.24 36.51 39.97 43.42 36.71 39.63 42.55
Maximum Queuing Time 197.02 212.92 228.83 197.14 212.54 227.93 187.20 205.42 223.65
Items Entered 41182.13 41226.23 41270.34 41182.13 41226.23 41270.34 41182.13 41226.23 41270.34
Average Queuing Time 0.97 1.04 1.11 0.90 0.96 1.03 0.86 0.94 1.01
Average (non-zero) Queuing Time 6.05 6.42 6.79 6.47 6.89 7.31 6.35 6.88 7.40
St Dev of Queuing Time 7.03 7.57 8.11 6.87 7.41 7.96 6.58 7.23 7.87
% Queued less than time limit 85.83 86.04 86.26 87.80 88.00 88.20 88.07 88.27 88.46
Utilization % 48.10 48.25 48.40 43.74 43.88 44.02 40.11 40.23 40.35
115% volume 5-2-2-2 5-2-2-3 5-2-2-4
Performance Measure -99% Average 99% -99% Average 99% -99% Average 99%
Maximum queue size 36.11 39.13 42.16 36.05 38.77 41.48 36.84 39.93 43.03
Maximum Queuing Time 191.31 207.00 222.69 188.74 205.43 222.12 190.67 208.41 226.14
Items Entered 41182.13 41226.23 41270.34 41182.13 41226.23 41270.34 41182.13 41226.23 41270.34
Average Queuing Time 0.81 0.87 0.93 0.72 0.78 0.84 0.74 0.81 0.88
Average (non-zero) Queuing Time 7.28 7.79 8.30 8.02 8.60 9.18 8.51 9.21 9.91
St Dev of Queuing Time 6.64 7.19 7.73 6.42 6.99 7.56 6.58 7.21 7.83
% Queued less than time limit 90.10 90.26 90.41 91.97 92.10 92.23 92.15 92.30 92.45
Utilization % 43.73 43.87 44.00 40.07 40.20 40.33 37.01 37.12 37.23
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Appendix B: User Manual for SIMUL8 Simulation Model
The SIMUL8 simulation model was constructed to imitate the occurrences of
the system over time, in an attempt to infer possible improvements in call taking
functionality. This appendix gives a brief description of the model, and several
instructions on how to operate and modify the model.
Purpose
The purpose of the simulation model was to determine a minimal workforce
level for the call taking functionality, subject to a pre-determined service goal. This
was achieved by constructing a virtual imitation of the physical system, endowing the
simulation with real world parameters and data, and performing numerous trials with
variable workforce levels, to determine the percentage of calls processed within a
given service level. While several trials were run over a 24 hour period, the user is
also able to manipulate the analysis to focus on specific time windows in order to
address certain problem periods, if necessary.
93
Step 1: Using the Supplementary Excel File
The supplementary Excel file is a program that takes a given shift
combination, which will state the number of workers assigned per shift, and breaks
down the worker availability into 15 minute intervals. This is required as the
simulation model specifies the workforce level availability every 15 minutes.
Upon opening the supplementary Excel file, go to the sheet titled “Call Takers
per Shift”. Enter the required shift combination into the yellowed cells: Cell C14:F14.
Then, proceed to sheet “Shift Export” and copy the numbers within the bolded box,
which are represented by Cells B4:B99.
Step 2: Update the Simulation Model with Altered Shift Pattern
Upon opening the Simul8 file, access the “Information Store” function,
located under the tab “Objects”; this can also be accessed by pressing the following
keys: Ctrl-I. Under the “Spreadsheet” objects, open the spreadsheet “Shift Patterns”
by selecting the file and choosing the options “Properties” in the vertical menu option
in “Information Store”. Upon opening the spreadsheet “Shift Patterns”, select the
option “View” in the vertical menu option; this will result in the Excel sheet being
opened. Select the “Edit Formats” option in the vertical menu option, indicated
below, and open the Formula One Workbook; opening the Formula One Workbook
allows for pasting large values or subsets of data into the spreadsheet. Paste the
copied shift pattern into the Excel workbook. Close the file, and select “Ok” for all
preceding applications still open.
94
Step 3: Run Simulation Model
Ensure the clock is reset; run the simulation model by selecting the “Run”
button on the main menu.
Edit Formats
“Run” button
Figure 23: Image of Simul8 Toolbar
Figure 22: Image of Simul8 Information Store – Spreadsheet for
Staffing Levels
95
Additional Applications
1. Changing Simulation Duration
Select the option “Clock” in the main menu bar. Select the option “Go to
Simulation Time” and enter the appropriate duration.
2. Changing Clock Properties
Select the option “Clock” in the main menu bar. Select the option “Clock
Properties”. Within this option, the time unit, the associated days, as well as
hour of the days analyzed (time windows), can be specified. The appearance
of the clock can also be altered within this option.
3. Accessing the Results Summary
Select the option “Results” in the main menu bar. Select the option “Results
Summary”.
4. Adding Article Variables to the Results Summary
Open the desired article (for example: work centre, resource, queue etc.).
Open the “Results” option and right click the desired variable.
5. Conduct Trials
To conduct trials instead of a single run, select the option “Trials” in the main
menu bar. Enter the number of trials required, the necessary Base Random
Number Set, and the Name of the trial. Visual display of results can also be
modified by options available within this functionality. To start the trial, select
the option “Run trial”.
96
6. Adding Another Work Centre
Physically Add Another Work Centre
To physically add another work centre, select and copy any current work
centre; this can typically be performed by pressing the following keys:
Ctrl-C. Paste the new work centre and connect to the main diagram with
flow arrows. Flow arrows should be connected from the queue “Queue for
Calls” to the new work centre, and then from the work centre to the
“Completed Calls” Finished Node. It is necessary to copy and paste a new
work centre to ensure that all visual logic code is also perpetuated to the
new work centre created.
Update the Visual Logic/Information Store for the queue “Queue for Calls”
The visual logic that references the number of work centres within the
simulation model was built with a variable that is located in the
“Information Store”. The total number of work centres must be updated
for the visual logic code to be viable. Therefore, the only required step to
update the total number of work centres is an update of this variable. To
access the variable, select the option “Objects” and select the option
“Information Store”. Under the heading of “Numbers”, select the object
“num_wc” and update the “Contents” to the variable amount.
97
Appendix C: User Manual for Excel-based Call Taker Model
An Excel-based model was constructed in order to validate the results found
in Simul8. This appendix describes the model and how to use it in Excel.
Purpose
The purpose of the Excel-based model is to allow a user to manipulate a
number of variables that affect call volume, and based on those variables, the model
calculates the minimum required number of call takers to meet that volume.
Presentation of Results
The output of the model, which is the minimum number of call takers, comes
in two forms, numerical and graphical. The numerical form is found in the sheet “Min
Call Takers” in columns M and AI. The graphical form is found in the sheet “Weekly
Graph” and shows, for each hour of the week, a bar graph with the minimum number
of call takers.
Two ways of modeling the information are available. One method assumes an
average call duration that combines all call types into one. It is represented in “Min
Call Takers” in columns I through M and in “Weekly Graph” in Figure 1. The second
way assumes three distinct call types, emergency, non-emergency, and
administrative. Each has its own distinct characteristics. This method is represented in
columns S to AI in “Min Call Takers” and in Figure 2 in “Weekly Graph”. Although
both methods produce fairly similar results, the second method is believed to be more
accurate since it creates a better representation of reality.
98
Description of the Model
The top left corner of the sheet “Min Call Takers” can be considered as the home
screen for this model. The cells coloured in bright green are variables that may be
changed. Many cells have a small red triangle in the upper right corner; these indicate
that comments are available for this cell. By placing the mouse on top of the cell,
comments will become visible in a nearby yellow box. Most of these boxes either
give instructions on how to manipulate that cell, or in the case where the cell is not
manipulable, it says what the value means.
Below are some definitions of the cells in yellow whose titles correspond to
manipulable values for the cells in green.
Desired Busy Rate: the fraction of time that, on average, call takers will be on phone
answering calls. For example, a 100% busy rate implies that the call taker never
hangs up their phone.
Availability Rate: the inverse of the busy rate, this value is the fraction of time that
call takers will be idle and thus available to answer any incoming calls. This value is
a function of the desired busy rate and will change automatically when the busy rate
is changed.
Probability: from a given Erlang distribution, this number represents the percentile
from which the number of calls arriving in one hour will be used. For example,
Figure 24 below shows the call distribution for Monday from 8am-9am. The Erlang
distribution which best fits the data has parameters alpha = 9 and beta = 3.4346. The
90th percentile, which is represented by the red bar at the bottom, happens to be 44.63
99
calls per hour. If the probability value was changed to 0.5, the 50th percentile would
be used, which (not shown in the figure below) is 29.77 calls per hour.
Figure 24: Example of Erlang distribution for calls on Monday from 8am-9am
Total Call Volume and Hourly Call Changes: These cells represent, in effect, a
“switch” between two possible modes that the model has. Only one mode can be
turned on at a time. A mode is turned on by typing “1” in the green cell next to it, and
“0” in other mode’s green cell. If both cells are “1”, a red error message will appear.
The Total Call Volume mode allows the user to change the average call
volume for every hour of the week at once. The default is set to 100%, which is
approximately the average of 36,000 calls per month. By changing the value to, for
example, 115%, it means that a 15% increase in call volume will occur everywhere
(that is, for every hour of the week).
100
The Hourly Call Changes is the second mode, and it allows the user to
manually manipulate call volume for any hour(s) of the week. When this mode is
turned on, the user can go to the sheet “Weekly Graph” and scroll the right, where
there is a group of cells for every hour of the week. Any of the values can be changed,
and the effect of that change can immediately be seen in the graphs to the left
(description of the graphs are below). For example, to simulate a large accident on a
Saturday afternoon that increased call volume by 50%, the value of “150%” could be
typed into the chart for Saturday for the hours of 3pm, 4pm and 5pm. The resulting
effect – an increase in the required number of call takers – will be immediately seen
in the graphs to the left.
It should be noted that when using this mode to simulate such a situation, the
busy rate should be increased, say, to 95%, otherwise the model will calculate the
number of call takers required for an increased number of calls, while still assuming a
65% busy rate.