Project Report New

Project Supervisor’s Comments

1. The Queue should be on BRT Buses

2. Data should include Inter-Arrival Time of Buses, Service Time of Buses. The Server is One

Bus at a time unless some stations entertain more than one bus at a time.

3. Fix a distribution to the Inter-Arrival Time and Service Time during the peak hours.

4. You will compare Arrival Rate and Service Rate in different terminals.

5. Determine the Appropriate Queue Model in each Terminal.

6. Based on your findings you can now make recommendations as to how to improve the

nature of deployment of buses to different terminals within the peak houre.

1

CHAPTER ONE

1.0 INTRODUCTION

Virtually everybody in Lagos state was used to rushing in and out of his/her home

before the inception of this present administration that came in 2007. The previous

Governor of Lagos state Bola Tinubu came up with the plans to ease the problem

of transportation by introducing Bus Rapid Transit (BRT) in conjunction with

National Union of Road Transportation Workers (NURTW). The first phase of

BRT was opened on March 24, 2008 by the present Governor Babatunde Raji

Fashola. With all of the efforts put together to ease transportation problems there

are still queue at each BRT terminal.

Waiting in lines is part of our everyday life. Waiting in lines may be due to

overcrowding, overfilling or due to congestion. Any time there is more customer

demand for a service than can be provided, a waiting line forms. We wait in lines

at the movie theater, at the bank for a teller, at a grocery store. Waiting depends on

the number of people waiting before a customer join the same queue, the number

of servers serving line, and the amount of service time for each individual

customer. Customers can be either humans or an object such as customer orders

waiting to be process, a machine waiting for repair. Mathematical analytical

method of analyzing the relationship between congestion and the delay caused by

it can be modeled using Queuing analysis. Queuing theory provides tools needed

for analysis of systems of congestion. Mathematically, systems of congestion

appear in many diverse and complicated ways and can vary in extent and

complexity.

2

http://en.wikipedia.org/wiki/Bola_Tinubu

A waiting line system or queuing system is defined by two important elements: the

population source of its customers and the process or service system. The customer

population can be considered as finite or infinite. The customer population is finite

when the number of customers affects potential new customers for the service

system already in the system. When the number of customers waiting in line does

not significantly affect the rate at which the population generates new customers,

the customer population is considered infinite. Customer behavior can change and

depends on waiting line characteristics. In addition to waiting, a customer can

choose other alternative. When customer enters the waiting line but leaves before

being serviced, process is called Reneging. When customer changes one line to

another to reduce waiting, process is called Jockeying. Balking occurs when

customer do not enter waiting line but decides to come back latter. Another

element of queuing system is service mechanism. The number of waiting lines, the

number of servers, the arrangements of the servers, the arrival and service patterns,

and the service priority rules characterize the service system. Queue system can

have channels or multiple waiting lines. Examples of single waiting line are bank

counter, airline counters, restaurants, amusement parks. In these examples multiple

servers might serve customers. In the single line multiple servers has better

performance in terms of waiting times and eliminates jockeying behavior than the

system with a single line for each server. System serving capacity is a function of

the number of service facilities and server proficiency.

In queuing system, the terms server and channel are used interchangeably. Queuing

systems are either single server or multiple servers. Single server examples include

gas station food mart with single checkout counter, a theater with a single person

selling tickets and controlling admission into the show. Multiple server examples

include gas stations with multiple gas pumps, grocery stores with multiple cashiers,

and multiple tellers in a bank. Services require a single activity or services of

activities called phases. In a single-phase system, the service is completed all at

3

once, such as a bank transaction or grocery store checkout counter. In a multiphase

system, the service is completed in a series of phases, such as at fast-food

restaurant with ordering, pay, and pick-up windows.

Queuing system is characterized by rate at which customers arrive and served by

service system. Arrival rate specifies the average number of customers per time

period. The service rate specifies the average number customers that can be

serviced during a time period. The service rate governs capacity of the service

system. It is the fluctuation in arrival and service patterns that causes wait in

queuing system. Waiting line models that assume that customers arrive according

to a Poisson probability distribution, and service times are described by an

exponential distribution. The Poisson distribution specifies the probability that a

certain number of customers will arrive in a given time period. The exponential

distribution describes the service times as the probability that a particular service

time will be less than or equal to a given amount of time. A waiting line priority

rule determines which customer is served next. A frequently used priority rule is

first-come, first-served. Other rules include best customers first, high-test profit

customer first, emergencies first, and so on. Although each priority rule has merit,

it is important to use the priority rule that best supports the overall organization

strategy. The priority rule used affects the performance of the waiting line system.

Waiting line models are important to a business because they directly affect

customer service perception and the costs of providing service. If system average

utilization is low, that suggests the waiting line design is inefficient. Poor system

design can result in over staffing. Long waits suggest a lack of concern by the

organization or can be view as a perception of poor service quality. Queuing

analysis has changed the way businesses use to run and has increased efficiency

and profitability of businesses.

4

1.1 AIMS AND OBJECTIVES

The objectives of this study are as follows:

1. To develop queuing model for analyzing behavior of the commuters at each

terminal of Lagos BRT Mile-12 to TBS route.

2. To determine the average number of commuters in each BRT terminal queue

during peak hours

3. To determine the average time commuter spends in each BRT terminal at the

peak period

4. Be able to determine the probability of arriving commuter waiting at each

terminal at the peak period of 7am to 9am and 4pm to 6pm.

1.2 SIGNIFICANCE OF STUDY

The significance of this study is to be able to develop a queue model that will be

used to know the character of queues and its effects on commuters at BRT major

terminals. The result of this study will aid decision making in order to make

service delivery efficient.

1.3 SCOPE AND LIMITATION

The scope of this study is Bus Rapid Transit (BRT) Lagos State Transportation

System under the administration of Lagos State Management of Transportation

Agency (LAMATA). Mile-12 to TBS (Tafawa Balewa Square) route out of other

several routes was used for this study work. This route was chosen because it is

one of the busiest that links the Mainland and the Island axis in Lagos state. The

bus terminals considered are Mile-12, Ketu, Ojota, Fadeyi, Leventis and TBS since

they are the busiest with regards to the peak periods on each day. The data

collected was on three consecutive days which are Monday, Tuesday and

5

Wednesday and the time for data collection are 7am to 9am and 4pm to 6am

consecutively at each bus terminal. The limitations are cost and time.

1.4 LITERATURE REVIEW

The word queue comes via French, from the Latincauda, meaning tail. The spelling

"queueing" over "queuing" is typically encountered in the academic research in the

field. In fact, one of the flagship journals of the profession is named "Queueing

Systems". "Queueing" - the correct spelling - is the only word in the English

language with five consecutive vowels.

Queueing theory is generally considered a branch of operations research because

the results are often used when making business decisions about the resources

needed to provide service. It is applicable in a wide variety of situations that may

be encountered in business, commerce, industry, healthcare, public service and

engineering. Applications are frequently encountered in customer service situations

as well as transport and telecommunication. Queueing theory is directly applicable

to intelligent transportation systems, call centers, PABXs, networks,

telecommunications, server queueing, mainframe computer queueing of

telecommunications terminals, advanced telecommunications systems, and traffic

flow.

Notation for describing the characteristics of a queueing model was first suggested

by David G. Kendall in 1953. Kendall's notation introduced an A/B/C queueing

notation that can be found in all standard modern works on queueing theory, Tijms,

H.C (2003)

The A/B/C notation designates a queueing system having A as inter-arrival time

distribution, B as service time distribution, and C as number of servers. For

example, "G/D/1" would indicate a General (may be anything) arrival process, a

6

http://en.wikipedia.org/wiki/Kendall's_notation

http://en.wikipedia.org/wiki/David_George_Kendall

http://en.wikipedia.org/wiki/Queueing_model

http://en.wikipedia.org/wiki/Traffic_flow

http://en.wikipedia.org/wiki/Traffic_flow

http://en.wikipedia.org/wiki/Computer

http://en.wikipedia.org/wiki/Mainframe_computer

http://en.wikipedia.org/wiki/Server_(computing)

http://en.wikipedia.org/wiki/Telecommunication

http://en.wikipedia.org/wiki/Telecommunications_network

http://en.wikipedia.org/wiki/PABX

http://en.wikipedia.org/wiki/Call_center

http://en.wikipedia.org/wiki/Intelligent_transportation_system

http://en.wikipedia.org/wiki/Telecommunication

http://en.wikipedia.org/wiki/Transport

http://en.wikipedia.org/wiki/Customer_service

http://en.wikipedia.org/wiki/Operations_research

http://en.wikipedia.org/wiki/Latin_language

http://en.wikipedia.org/wiki/French_language

Deterministic (constant time) service process and a single server. More details on

this notation are given in the article about queueing models.

Application to Telephony

The public switched telephone network (PSTN) is designed to accommodate the

offered traffic intensity with only a small loss. The performance of loss systems is

quantified by their grade of service, driven by the assumption that if sufficient

capacity is not available, the call is refused and lost, Flood, J.E (1998)

Alternatively, overflow systems make use of alternative routes to divert calls via

different paths — even these systems have a finite traffic carrying capacity.

However, the use of queueing in PSTNs allows the systems to queue their

customers' requests until free resources become available. This means that if traffic

intensity levels exceed available capacity, customer's calls are not lost; customers

instead wait until they can be served, Bose S.J (2002). This method is used in

queueing customers for the next available operator.

A queueing discipline determines the manner in which the exchange handles calls

from customers. It defines the way they will be served, the order in which they are

served, and the way in which resources are divided among the customers.

Queuing is handled by control processes within exchanges, which can be modeled

using state equations. Queuing systems use a particular form of state equations

known as a Markov chain that models the system in each state. Incoming traffic to

these systems is modeled via a Poisson distribution and is subject to Erlang’s

queuing theory assumptions viz.

Pure-chance traffic – Call arrivals and departures are random and

independent events.

7

http://en.wikipedia.org/wiki/Poisson_distribution

http://en.wikipedia.org/wiki/Markov_chain

http://en.wikipedia.org/wiki/State_equation

http://en.wikipedia.org/wiki/Routing_in_the_PSTN

http://en.wikipedia.org/wiki/Grade_of_service

http://en.wikipedia.org/wiki/Network_performance

http://en.wikipedia.org/wiki/PSTN

http://en.wikipedia.org/wiki/Public_switched_telephone_network


Statistical equilibrium – Probabilities within the system do not change.

Full availability – All incoming traffic can be routed to any other customer

within the network.

Congestion is cleared as soon as servers are free.

Classic queuing theory involves complex calculations to determine waiting time,

service time, server utilization and other metrics that are used to measure queueing

performance.

Queuing Networks

Networks of queues are systems which contain an arbitrary, but finite, number m

of queues. Customers, sometimes of different classes, travel through the network

and are served at the nodes. The state of a network can be described by a vector

, where ki is the number of customers at queue i. In open networks,

customers can join and leave the system, whereas in closed networks the total

number of customers within the system remains fixed.

The first significant result in the area was Jackson networks, for which an efficient

product form equilibrium distribution exists.

Role of Poisson process, exponential distributions

A useful queueing model represents a real-life system with sufficient accuracy and

is analytically tractable. A queueing model based on the Poisson process and its

companion exponential probability distribution often meets these two

requirements. A Poisson process models random events (such as a customer

arrival, a request for action from a web server, or the completion of the actions

requested of a web server) as emanating from a memoryless process. That is, the

length of the time interval from the current time to the occurrence of the next event

does not depend upon the time of occurrence of the last event. In the Poisson

8


http://en.wikipedia.org/wiki/Poisson_process


http://en.wikipedia.org/wiki/Product_form_solution

http://en.wikipedia.org/wiki/Jackson_network

probability distribution, the observer records the number of events that occur in a

time interval of fixed length. In the (negative) exponential probability distribution,

the observer records the length of the time interval between consecutive events. In

both, the underlying physical process is memoryless.

Models based on the Poisson process often respond to inputs from the environment

in a manner that mimics the response of the system being modeled to those same

inputs. The analytically tractable models that result yield both information about

the system being modeled and the form of their solution. Even a queueing model

based on the Poisson process that does a relatively poor job of mimicking detailed

system performance can be useful. The fact that such models often give "worst-

case" scenario evaluations appeals to system designers who prefer to include a

safety factor in their designs. Also, the form of the solution of models based on the

Poisson process often provides insight into the form of the solution to a queueing

problem whose detailed behavior is poorly mimicked. As a result, queueing models

are frequently modeled as Poisson processes through the use of the exponential

distribution.

Limitations of mathematical approach

Classic queuing theory is often too mathematically restrictive to be able to model

real-world situations exactly. This restriction arises because the underlying

assumptions of the theory do not always hold in the real world. The complexity of

production lines with product-specific characteristics cannot be handled with

mathematical models. Therefore special tools like Plant Simulation have been

developed to simulate, analyze, visualize and optimize time dynamic queueing line

behavior.

For example; the mathematical models often assume infinite numbers of

customers, infinite queue capacity, or no bounds on inter-arrival or service times,

9

http://en.wikipedia.org/wiki/Plant_Simulation

http://en.wikipedia.org/wiki/Exponential_distribution








when it is quite apparent that these bounds must exist in reality. Often, although

the bounds do exist, they can be safely ignored because the differences between the

real-world and theory is not statistically significant, as the probability that such

boundary situations might occur is remote compared to the expected normal

situation. In other cases the theoretical solution may either prove intractable or

insufficiently informative to be useful.

Alternative means of analysis have thus been devised in order to provide some

insight into problems that do not fall under the scope of queueing theory, although

they are often scenario-specific because they generally consist of computer

simulations or analysis of experimental data. See network traffic simulation.

Queueing In Transportation Industry

Customers’ queueing at a service facility is a common problem in transportation

industry. For dealing with long queue length, the conventional way is to adjust

supply by scheduling staffs and equipments. Models for this scheduling problem

have a long history in operations research literature, Ingolfsson et al (2010). But

this is not always possible, for example in marine container terminals, which serve

ships on the seaside and trucks on the landside simultaneously. Ships normally

receive higher service priority than trucks due to their high time value. Very often

a container terminal operator schedules the resources and equipments aiming to

load/unload ships efficiently. So the demand of trucks is not always met with a

proper level of supply. In such a case, it is necessary to manage truck arrivals in

order to keep demand and supply balanced over time.

At a marine container terminal, long truck queue at the gate is often the result of

fluctuating truck arrivals Huynh and Walton (2011). Queueing trucks generate

serious air pollution and limit the capacities of both trucks and terminal. So some

10

http://en.wikipedia.org/wiki/Network_traffic_simulation

http://en.wikipedia.org/wiki/Simulation

terminals in North America implement Terminal Appointment System (TAS) to

manage truck arrivals. It was firstly implemented in the port of Vancouver in 1999

and then in the ports of Los Angeles and Long Beach in 2003. In a TAS system, a

terminal operator announces opening hours and entry quota within each hour

through a proprietary web-based information system where truckers can choose an

entry hour as they prefer (in this paper, this scheme is called static TAS (STAS),

and the dynamic scheme (DTAS) will be discussed in a latter section). In practice

TAS has varied performances, for example Morais and Lord (2006) reported

successful application of TAS at the Port of Vancouver, while Giuliano and

O’Brien (2007) found that at the Ports of Los Angeles and Long Beach ‘there is no

evidence to suggest that TAS reduced queueing at terminal gates and hence heavy

diesel truck emissions’. The reason is recognized as the lack of specific guidelines

for implementing TAS Huynh and Walton (2011).

11

CHAPTER TWO

2.0 HISTORY OF BUS RAPID TRANSIT (BRT)

The first phase of the Lagos BRT was opened on March 24, 2008; although it was

initially slated for opening in November 2007 (the initiative to build the system

was initiated by the government of the previous governor, Bola Tinubu. It goes

from Mile 12 through Ikorodu Road and Funsho Williams Avenue up to CMS. At

current, the Lagos BRT Corridor is 22 km in length.

Two operators are offering their services to the Lagos BRT: NURTW Cooperative

and LAGBUS. LAGBUS is an Asset Management Company owned by the Lagos

State government.

26 bus shelters are offered along the Mile 12-CMS road; three bus terminals are

also placed along the corridor (at Mile 12, Moshalashi and CMS), with the bus

terminal at CMS designed to integrate with transport modes of rail and ferry that

are planned for future construction by LAMATA.

12

http://en.wikipedia.org/w/index.php?title=LAGBUS&action=edit&redlink=1

http://en.wikipedia.org/w/index.php?title=NURTW_Cooperative&action=edit&redlink=1

http://en.wikipedia.org/wiki/Bola_Tinubu

2.1 COLLECTION OF DATA

The data collected was a primary data, collected based on the outcome of our study

on when the peak hours for passengers are for each BRT bus terminal. The data

was collected at six BRT Bus major terminals on Mile-12 to TBS route out of other

LAMATA BRT routes, where we have empty buses start from before getting to

other terminals with lesser dense commuters population. At each terminal, three

consecutive days was designated for data collection of buses, which amounts to six

days altogether. The data collected are on Inter-arrival time, Service time,

departure time of randomly selected buses during the peak hours (7am to 9am and

4pm to 6pm), and number of arriving buses per minute within the peak hours of the

commuters and server rate at each terminal for three consecutive days. Data was

collected by the use of tags. And the waiting time is calculated by taking the

difference between arrival and departure time. Also, the bus officer (person who

collects tickets before commuters are allowed on the bus) is the server. The server

rate is the number of customers the selected server services in a minute during the

peak hours of the passengers.

2.2 PROBLEMS OF DATA COLLECTION

The following are the problems encountered during data collection:

i. Getting the number of persons that will support in collecting the data for this

research work was a difficult task.

ii. Choosing the right data for the work was challenging; data like Arrival time,

Inter-arrival time, departure time and server service time.

13

iii. Sometimes when seen collecting data at the bus stations we are either

harassed or not allowed to continue unless assisted based on tip off, as a

result tags where not used

iv. It was quite challenging to get the persons collecting the data to follow the

given instructions for accuracy purpose

v. Cost of transportation and getting to the bus terminal at the specified peak

periods for each bus terminus was a big problem due to traffic situation in

Lagos.

2.3 DEFINITION OF TERMS

First in first out

This principle states that customers are served one at a time and that the

customer that has been waiting the longest is served first.

Last in first out

This principle also serves customers one at a time; however the customer

with the shortest waiting time will be served first also known as a stack.

Processor sharing

Customers are served equally. Network capacity is shared between

customers and they all effectively experience the same delay.

Priority

Customers with high priority are served first.

14

http://en.wikipedia.org/wiki/Stack_(data_structure)

http://en.wikipedia.org/wiki/LIFO_(computing)

http://en.wikipedia.org/wiki/FIFO_(computing)

CHAPTER THREE

3.1 Presentation of Data

The data was collected at six major terminals where empty buses pick full load of

commuters. The following are the bus terminals where data was collected Mile-12,

Ketu, Ojota, Fadeyi, Leventis and TBS terminal, which are on Mile-12 to TBS

route. Peak period for commuters is when we have so many commuters in the

queue with lesser available buses which results to more delay/waiting time of

commuters. The peak period of Mile 12, Ketu, Ojota is 7:00 to 9:00am while peak

period for Fadeyi, Leventis and TBS is 6:00 to 8:00 pm. The data collected was

collected for three consecutive days which was then combined as revealed in the

data analysis (section 3.5). The three days combined gives 30 samples for each

variable.

15

3.2 Queue Model

Statistical distribution of both the inter-arrival times and the service times follow

the exponential distribution. Because of the mathematical nature of the exponential

distribution, a number of quite simple relationships are able to be derived for

several performance measures based on knowing the arrival rate and service rate.

The server for is one, that is to say on each BRT bus, there is always one bus

officer who takes care of ticket collection as the commuters are entering the bus.

Also, the queue discipline is First Come First Serve (FCFS).

Therefore, the queue model is M/M/1/∞/∞ represents a single server that has

unlimited queue capacity and infinite calling population, both arrivals and service

are Poisson (or random) processes.

The queue model for commuters is

M/M/1/∞/∞

First M represents the Poisson distribution for the arrival process

Second M represents the Poisson distribution for the Service process

1 is the number of server

∞ represents the maximum number of commuters allowed in the queueing

system (either being served or waiting for service)

The maximum number of commuter in total is infinite

3.3 Methodology

The data was collected on Commuters arrival rate and server service time at each

BRT buses terminal at their peak period/hours. The queue arrival rate, waiting

time, arrival of customers per minute and service rate were the data used for queue

16

analysis in order to get the queue behavior at each bus terminal. The commuters’

arrival rate will be used for the queue analysis, while the average waiting time in

the data collected will be used to compare the average waiting time of customers

from analytical approach. To use the queue model for commuter to solve the queue

problem, the analytical or queue theory (formula based) will be used.

3.4 Mean Performance Parameters of the Queue

The queue notations

is the average arrival rate of customers/passenger

Where is average expected service time, is average service demand and

is server’s capacity

is completion rate

is the utilization factor

i. Mean Number in system, N

ii. Mean number waiting in the queue, Nq

iii. Average time spent waiting in the system

iv. Mean Time spent in the system, W

17

This would require the following additional assumptions

FCFS system though the mean results will hold for any queue where

the server does not idle while there are customers in the system

The equilibrium state probability pk will also be the same as the

probability distribution for the number in the system as seen by an

arrival passenger/commuter.

The mean residual service time for the customer currently in service

when an arrival occurs will be Memory-less property satisfied

only by the exponential distribution

Using these assumptions, we can write

v. Mean Time Spent Waiting in Queue Wq

3.5 Data Analysis

The data analysis table shows three variables waiting time, server service rate and

arrival rate of commuter/customers in minute.

I. Mile 12 Bus Terminal

Peak Period (7:00am to 9:00am)

The data table for server service time is in appendix B for Mile 12 table:

Average service time for a full load (46 passengers) for three consecutive

day is (3.15 + 3.25 + 3.04)min/3 = 3.27min

Average service time per passenger = (3.27 x 60)/46 = 4.261sec

18

Mile 12 Bus Terminalstart time Number of passengers

Day 1 Day 2 Day37:00 - 7:04 107 75 677:05 - 7:09 77 99 787:10 - 7:14 107 102 887:15 - 7:19 79 108 687:20 - 7:24 82 110 967:25 - 7:29 113 88 707:30 - 7:34 89 101 867:35 - 7:39 109 69 807:40 - 7:44 70 106 1057:45 - 7:49 176 119 1847:50 - 7:54 157 102 1367:55 - 7:59 185 163 1098:00 - 8:04 196 198 1528:05 - 8:09 108 169 1868:10 - 8:14 95 116 1568:15 - 8:19 85 94 1168:20 - 8:24 187 168 1198:25 - 8:29 96 77 948:30 - 8:34 99 99 828:35 - 8:39 99 93 738:40 - 8:44 100 78 838:45 - 8:49 78 89 978:50 - 8:54 67 90 898:55 - 8:59 91 82 85Total 2652 2596 2497Average 111 108 104

Average arrival rate for three consecutive days is (111 + 108 + 104)/3 =

107.67 per 5min

Which is λ = (107.67)/(5 x 60) = 0.2265 per sec

Utilization factor ,

= 4.261 x 0.2265 = 0.965

Average time spent waiting in the system

19

= (0.965 x 4.261)/(1 – 0.965) = 117.482s

Average number in queue

N = 0.965/ (1 – 0.965) = 27.57 passengers

II. Ketu Bus Terminal


The data table for server service time is in appendix B for Ketu table:


day is (3.35 + 3.3 + 3.35)min/3 = 3.33min


Ketu Bus Terminalstart time Number of passengers

Day 1 Day 2 Day37:00 - 7:04 71 78 957:05 - 7:09 66 70 1027:10 - 7:14 108 81 897:15 - 7:19 94 116 1177:20 - 7:24 97 74 867:25 - 7:29 69 106 1097:30 - 7:34 108 115 737:35 - 7:39 91 115 1027:40 - 7:44 97 80 1057:45 - 7:49 162 198 1707:50 - 7:54 98 147 90

20

7:55 - 7:59 137 118 1968:00 - 8:04 164 78 1618:05 - 8:09 113 122 698:10 - 8:14 196 128 1598:15 - 8:19 154 194 868:20 - 8:24 116 73 1728:25 - 8:29 95 66 888:30 - 8:34 85 70 798:35 - 8:39 75 68 658:40 - 8:44 85 90 718:45 - 8:49 92 96 1008:50 - 8:54 73 80 958:55 - 8:59 65 98 83Total 2510 2462 2561Average 105 103 107

Average arrival rate for three consecutive days is (105 + 103 + 107)/3 = 105

per 5min



= 4.348 x 0.2187= 0.951


= (0.951 x 4.348)/(1 – 0.951) = 84.39s


21

N = 0.951/ (1 – 0.951) = 19.408 passengers

III. Ojota Bus Terminal


The data table for server service time is in appendix B for Ojota table:


day is (3.3 + 3.3 + 3.35)min/3 = 3.32min


Ojota 12 Bus Terminalstart time Number of passengers

Day 1 Day 2 Day37:00 - 7:04 66 69 687:05 - 7:09 92 84 757:10 - 7:14 73 71 1107:15 - 7:19 72 68 957:20 - 7:24 94 66 857:25 - 7:29 100 117 1187:30 - 7:34 84 109 697:35 - 7:39 93 84 1177:40 - 7:44 102 86 857:45 - 7:49 168 147 1497:50 - 7:54 73 102 827:55 - 7:59 151 167 1268:00 - 8:04 190 116 1968:05 - 8:09 120 118 808:10 - 8:14 75 140 798:15 - 8:19 164 66 1538:20 - 8:24 114 88 1688:25 - 8:29 77 77 888:30 - 8:34 99 70 988:35 - 8:39 70 82 828:40 - 8:44 96 70 838:45 - 8:49 67 78 998:50 - 8:54 85 96 718:55 - 8:59 75 68 85Total 2401 2238 2461

22

Average 100 93 103

Average arrival rate for three consecutive days is (105 + 103 + 107)/3 = 105

per 5min



= 4.326 x 0.227= 0.982


= (0.982 x 4.326)/(1 – 0.982) = 236.007s


N = 0.951/ (1 – 0.951) = 54.56 passengers

IV. Fadeyi Bus Terminal

Peak Period (6:00pm to 8:00pm)

The data table for server service time is in appendix B for Fadeyi table:


day is (3.3 + 3.3 + 3.03)min/3 = 3.21min

23


Fadeyi 12 Bus Terminalstart time Number of passengers

Day 1 Day 2 Day36:00 - 6:04 109 108 1036:05 - 6:09 108 91 1086:10 - 6:14 115 116 676:15 - 6:19 106 82 796:20 - 6:24 84 91 716:25 - 6:29 102 73 1086:30 - 6:34 72 116 1096:35 - 6:39 104 97 916:40 - 6:44 117 86 1116:45 - 6:49 136 150 1946:50 - 6:54 167 118 956:55 - 6:59 158 101 2097:00 - 7:04 181 96 1737:05 - 7:09 92 80 1457:10 - 7:14 98 94 967:15 - 7:19 203 83 1667:20 - 7:24 139 71 1187:25 - 7:29 69 78 807:30 - 7:34 94 71 677:35 - 7:39 68 68 727:40 - 7:44 98 80 787:45 - 7:49 73 87 777:50 - 7:54 69 84 817:55 - 7:59 92 82 92Total 2651 2201 2590Average 110 92 108

Average arrival rate for three consecutive days is (110 + 92 + 108)/3 = 103.3

per 5min

Which is λ = (103.3)/(5 x 60) = 0. 2362per sec


= 4.187 x 0.2362= 0.989

24


= (0.989 x 4.187)/(1 – 0.989) = 376.449s


N = 0.951/ (1 – 0.951) = 89.909 passengers

V. Leventis Bus Terminal


The data table for server service time is in appendix B for Leventis table:


day is (3.35 + 3.35 + 3.3)min/3 = 3.33min


Leventis 12 Bus Terminalstart time Number of passengers

Day 1 Day 2 Day36:00 - 6:04 67 82 906:05 - 6:09 69 67 786:10 - 6:14 107 76 886:15 - 6:19 118 90 956:20 - 6:24 118 84 996:25 - 6:29 78 102 916:30 - 6:34 115 74 796:35 - 6:39 97 100 1056:40 - 6:44 75 116 108

25

6:45 - 6:49 111 89 926:50 - 6:54 126 170 1546:55 - 6:59 72 166 1537:00 - 7:04 81 69 1297:05 - 7:09 100 111 1727:10 - 7:14 182 149 1407:15 - 7:19 74 133 887:20 - 7:24 67 68 847:25 - 7:29 95 88 777:30 - 7:34 65 84 947:35 - 7:39 73 73 807:40 - 7:44 90 93 777:45 - 7:49 82 79 827:50 - 7:54 80 98 1007:55 - 7:59 67 84 85Total 2211 2345 2439Average 92 98 102

Average arrival rate for three consecutive days is (92 + 98 + 102)/3 = 97.3

per 5min

Which is λ = (97.3)/(5 x 60) = 0. 2278per sec


= 4.348 x 0.2278= 0.991


= (0.991 x 4.348)/(1 – 0.991) = 478.763s


26

N = 0.951/ (1 – 0.951) = 110.11 passengers

VI. TBS Bus Terminal


The data table for server service time is in appendix B for TBS table:


day is (3.4 + 3.35 + 3.3)min/3 = 3.35min


TBS 12 Bus Terminalstart time Number of passengers

Day 1 Day 2 Day36:00 - 6:04 102 113 1036:05 - 6:09 69 115 1196:10 - 6:14 90 65 996:15 - 6:19 91 91 856:20 - 6:24 65 114 1146:25 - 6:29 116 92 1026:30 - 6:34 108 75 676:35 - 6:39 101 80 1096:40 - 6:44 105 90 1186:45 - 6:49 68 70 836:50 - 6:54 113 196 826:55 - 6:59 189 73 1077:00 - 7:04 156 151 1957:05 - 7:09 177 196 1337:10 - 7:14 170 90 1197:15 - 7:19 93 145 1647:20 - 7:24 82 68 947:25 - 7:29 81 84 957:30 - 7:34 66 98 797:35 - 7:39 75 80 96

27

7:40 - 7:44 90 96 957:45 - 7:49 92 89 767:50 - 7:54 69 97 817:55 - 7:59 68 76 95Total 2437 2446 2511Average 102 102 105

Average arrival rate for three consecutive days is (102 +102 + 105)/3 = 103

per 5min

Which is λ = (103)/(5 x 60) = 0. 2277per sec


= 4.370 x 0.2277= 0.995


= (0.995 x 4.370)/(1 – 0.995) = 869.63s


N = 0.995/ (1 – 0.995) = 199 passengers

3.6 Interpretation

28

The time unit for the calculation is in seconds. All the data collected in minute

were all converted to seconds for consistence and for the purpose of interpretation

will be converted back to minute. The model for the queue analysis for each BRT

used for this study is M/M/1.

1. Queue situation in Mile 12 BRT terminal

From the result of the data analysis, average server service rate per

passenger is 3.27min, arrival rate is 0.2265 per second, the utilization factor

is 0.965 (=96.5%), average time spent waiting in the system is 117.482s,

average number of commuters in the queue is 27.57. These simply mean that

at Mile 12 BRT terminal, a commuter is service in 4.261s where on the

average the 13.59 commuters join the queue every minute making the server

(Bus attendant) work 96.5% of his/her strength. And the average waiting

time of commuters is 1.958min and average number of commuters in the

queue during the peak period/hours (7:00am to 9:00am) is approximately 28.

2. Queue situation at Ketu BRT terminal




average number of commuters in the queue is 19.408. These simply mean

that at Ketu terminal, a commuter is service in 4.348s where on the average

105 commuters join the queue every 5 minute making the server (Bus

attendant) work 95.1% of his/her strength. And the average waiting time of

commuters is 1.4065min and average number of commuters in the queue

during the peak period/hours (7:00am to 9:00am) is approximately 19.

3. Queue situation at Ojota BRT terminal

29


passenger is 3.32min, arrival rate is 4.326 per second, the utilization factor is

0.982 (=98.2%), average time spent waiting in the system is 236.007s,

average number of commuters in the queue is 54.56. These simply mean that

at Ojota BRT terminal, a commuter is service in 4.326s where on the

average 105 commuters join the queue every 5 minute making the server




4. Queue situation at Fadeyi BRT terminal





that at Fadeyi BRT terminal, a commuter is service in 4.187 where on the

average 103 commuters join the queue every 5 minute making the server




5. Queue situation at Leventis BRT terminal





that at Leventis BRT terminal, a commuter is service in 4.348s where on the

average 97 commuters join the queue every 5 minute making the server (Bus


30



6. Queue Situation at TBS BRT terminal




average number of commuters in the queue is 119. These simply mean that

at TBS BRT terminal, a commuter is service in 4.370s where on the average

103 commuters join the queue every 5 minute making the server (Bus




31

Chapter Four

4.1 SummaryThe BRT (Bus Rapid Transit) system was initiated in other to solve transportation

problems in Lagos, Nigeria. That is why any problem or challenges that can make

service delivery ineffective needs to be identified and solved. The Queue model is

used to analyze the long queue that is experienced by passengers/commuters at

each major BRT terminal at their respective peak hours so that the management

will have a clear picture of what commuters experience on daily basis. The queue

situation at the six (Mile 12, Ketu, Ojota, Fadeyi, Leventis and TBS (Tafawa

Balewa Square)) major BRT terminals was analyzed by using analytical method of

queue analysis. Utilization factor of the servers shows that the servers are working

at their highest capacity.

4.2 ConclusionIn conclusion, the queue intensity result at each of the six (Mile 12, Ketu, Ojota,

Leventis and TBS (Tafawa Balewa Square)) terminals shows that the amount of

queue is high, which requires urgent attention by the BRT managements in order to

ease passengers’ delay at the peak periods. Ketu, Fadeyi, Leventis and TBS bus

terminals have the highest queue intensity shown in the analysis result with 99.5 to

99.6. The result of this study cannot be used to justify other transportation system

other than LAMATA BRT commuters on Mile 12 to TBS route.

32

4.3 RecommendationWhat is initiated to remove the commuters’ traffic situation in Lagos is expected to

compound their problems through delays in queue at the terminals. Looking at the

problems identified at the BRT terminals, I recommend that the BRT management

must find a way to increase the number of servers to minimum of two during the

passengers/commuters’ peak periods and make the servers (bus officers) speed up

there service at the BRT terminals in order to improve service delivery.

33

References NumberBose S.J., (2002). Chapter 1 - An Introduction to Queueing Systems,

Kluwer/Plenum Publishers

Flood, J.E. (1998). Telecommunications Switching, Traffic and Networks, Chapter

4: Telecommunications Traffic, New York: Prentice-Hall.

Giulianoa, G., & O’Brien, T. (2007). Reducing port-related truck emissions: The

terminal gate appointment system at the Ports of Los Angeles and Long Beach.

Transportation Research Part D , Volume 12, pp.460–473.

Huynh, N., & Walton, C. M. (2011). Improving Efficiency of Drayage Operations

at Seaport Container Terminals Through the Use of an Appointment System. In J.

W. Böse, Handbook of Terminal Planning (pp. 323-344). New York: Springer.

Ingolfsson, A., Campello, F., Wu, X., & Cabral, E. (2010). Combining integer

programming and the randomization method to schedule employees. European

Journal of Operational Research , Volume 202,Pages 153-163.

Jim Fawcett (2002). CSE681/791– Software Modeling and Analysis, Queue

Analysis version 2.1, Brenda Press.

34

K. S. Trivedi, Probability and Statistics with Reliability, Queueing and Computer

Science Applications. Jonh Wiley & Sons, 2001.

L. Kleinrock, (1976). Queueing Systems Volume II: Computer Applications, Wiley

Interscience.

Lawrence W. Dowdy, Virgilio A.F. Almeida, Daniel A. Menasce (2004),

Performance by Design: Computer Capacity Planning By Example, pp. 480.

Lazowska, Edward D.; John Zahorjan, G. Scott Graham, Kenneth C. Sevcik

(1984). Quantitative System Performance: Computer System Analysis Using

Queueing Network Models. Prentice-Hall, Inc.

Mayhew, Les; Smith, David (2006). "Using queuing theory to analyse completion

times in accident and emergency departments in the light of the Government 4-

hour target". Cass Business School, Retrieved 2008-05-20.

Morais, P., & Lord, E. (2006). Terminal appointment system study. Transport

Canada.

Penttinen A. (2009). Chapter 8 – Queueing Systems, Lecture Notes: S-38.145 -

Introduction to Teletraffic Theory.

Schlechter, Kira (2009), "Hershey Medical Center to open redesigned emergency

room", The Patriot-News

Tijms, H.C, (2003). “Algorithmic Analysis of Queues", Chapter 9 in a First Course

in Stochastic Models, Wiley, Chichester, 2003

35

http://www.pennlive.com/midstate/index.ssf/2009/03/hershey_med_to_open_redesigned.html

http://www.pennlive.com/midstate/index.ssf/2009/03/hershey_med_to_open_redesigned.html

http://en.wikipedia.org/wiki/Cass_Business_School

http://www.cass.city.ac.uk/media/stories/story_96_105659_69284.html



http://www.cs.washington.edu/homes/lazowska/qsp/

http://www.cs.washington.edu/homes/lazowska/qsp/

http://www.cs.gmu.edu/~menasce/perfbyd/

Zukermam M. (2005). An Introduction to Queueing Theory and Stochastic

Teletraffic Models, Jonh Wiley & Sons.

Appendix AThis shows the graph of number of customer (passengers/commuters) against time

in seconds. Where the red lines mean confidence limits and the blue line is the

simulation result true result.

Line diagram for Mile 12 Bus Terminal queue nature

Line diagram for Ketu Bus Terminal queue nature

36

http://www.ee.unimelb.edu.au/staff/mzu/classnotes.pdf

http://www.ee.unimelb.edu.au/staff/mzu/classnotes.pdf

Line diagram for Ojota Bus Terminal queue nature

Line diagram for Fadeyi Bus Terminal queue nature

37

Line diagram for Leventis Bus Terminal queue nature

Line diagram for TBS Bus Terminal queue nature

38

Appendix B

Mile 12 Bus Terminal Day 1 Peak Period is 7:00 - 9:00AM

S/N

Bus No Arrival Time

Start Time

Finish time Service Time No of Passengers

1 284 7:01 7:01 7:04:00 0:03:00 46

2 427 7:03 7:06 7:09 0:03:00 46

3 371 7:07 7:09 7:13 0:04:00 46

4 341 7:14 7:15 7:18 0:03:00 46

5 291 7:15 7:18 7:21 0:03:00 46

6 481 7:17 7:21 7:25 0:04:00 46

7 502 7:26 7:26 7:29 0:03:00 46

8 11 7:32 7:32 7:35 0:03:00 46

9 382 7:33 7:36 7:39 0:03:00 46

10 356 7:36 7:40 7:43 0:03:00 46

11 316 7:41 7:44 7:47 0:03:00 46

12 423 7:43 7:47 7:50 0:03:00 46

13 351 7:49 7:51 7:54 0:03:00 46

39

14 375 8:08 8:08 8:11 0:03:00 46

15 204 8:10 8:12 8:15 0:03:00 46

16 441 8:11 8:16 8:19 0:03:00 46

17 404 8:15 8:19 8:23 0:04:00 46

18 352 8:23 8:24 8:27 0:03:00 46

19 20 8:31 8:31 8:34 0:03:00 46

20 40 8:33 8:35 8:38 0:03:00 46

Mile 12 Bus Terminal Day 2Peak Period is 7:00 - 9:00AM

Sitting

S/NBus No

Arrival Time Start Time Finish time

Service Time

No of Passengers

1 396 7:04 7:04 7:07 0:03 46

2 273 7:06 7:08 7:11 0:03 46

3 324 7:08 7:15 7:18 0:03 46

4 134 7:09 7:18 7:22 0:04 46

5 173 7:13 7:22 7:25 0:03 46

6 44 7:20 7:26 7:29 0:03 46

7 473 7:22 7:29 7:32 0:03 46

8 271 7:23 7:32 7:35 0:03 46

9 132 7:27 7:35 7:39 0:04 46

10 21 7:35 7:39 7:42 0:03 46

11 270 7:38 7:38 7:41 0:03 46

12 275 7:48 7:48 7:51 0:03 46

13 497 7:49 7:52 7:57 0:05 46

14 377 7:49 7:57 8:00 0:03 46

15 483 7:53 8:01 8:04 0:03 46

16 109 7:57 8:04 8:07 0:03 46

17 431 8:01 8:07 8:11 0:04 46

18 308 8:03 8:12 8:15 0:03 46

19 78 8:04 8:15 8:18 0:03 46

20 48 8:08 8:18 8:21 0:03 46

Mile 12 Bus Terminal

Sitting

S/NBus No


Service Time

No of Passengers

1 125 7:00 7:00 7:03:00 0:03 46

2 443 7:02 7:03 7:06:00 0:03 46

3 214 7:09 7:09 7:12:00 0:03 46

4 184 7:13 7:13 7:17:00 0:04 46

5 519 7:14 7:18 7:21:00 0:03 46

6 413 7:16 7:22 7:25:00 0:03 46

7 461 7:24 7:25 7:28:00 0:03 46

40

8 294 7:27 7:29 7:32:00 0:03 46

9 199 7:30 7:32 7:36:00 0:04 46

10 460 7:34 7:36 7:41:00 0:05 46

11 99 7:35 7:42 7:45:00 0:03 46

12 460 7:39 7:45 7:49:00 0:04 46

13 391 7:45 7:49 7:52:00 0:03 46

14 165 7:51 7:52 7:55:00 0:03 46

15 252 7:53 7:56 7:59:00 0:03 46

16 216 7:54 8:00 8:05:00 0:05 46

17 397 7:59 8:06 8:09:00 0:03 46

18 437 8:04 8:10 8:13:00 0:03 46

19 453 8:11 8:13 8:17:00 0:04 46

20 515 8:15 8:18 8:21:00 0:03 46

Ketu Bus Terminal

Sitting

S/NBus No


Service Time

No of Passengers

1 230 7:04 7:05 7:09 0:04 46

2 463 7:06 7:10 7:13 0:03 46

3 202 7:13 7:14 7:17 0:03 46

4 60 7:16 7:18 7:22 0:04 46

5 382 7:18 7:24 7:27 0:03 46

6 257 7:25 7:27 7:30 0:03 46

7 370 7:26 7:31 7:35 0:04 46

8 249 7:28 7:42 7:45 0:03 46

9 428 7:31 7:46 7:50 0:04 46

10 351 7:42 7:51 7:54 0:03 46

11 490 7:46 7:55 7:58 0:03 46

12 15 7:48 7:59 8:02 0:03 46

13 313 7:51 8:02 8:07 0:05 46

14 423 7:58 8:07 8:10 0:03 46

15 360 8:01 8:11 8:14 0:03 46

16 337 8:02 8:15 8:18 0:03 46

17 199 8:12 8:19 8:23 0:04 46

18 117 8:19 8:23 8:26 0:03 46

19 27 8:25 8:27 8:30 0:03 46

20 280 8:26 8:31 8:34 0:03 46

Ketu Bus Terminal

Sitting

S/NBus No


Service Time

No of Passengers

1 472 7:02 7:03 7:06 0:03 46

41

2 425 7:05 7:07 7:10 0:03 46

3 278 7:09 7:10 7:13 0:03 46

4 452 7:15 7:14 7:18 0:04 46

5 491 7:16 7:18 7:21 0:03 46

6 465 7:17 7:21 7:24 0:03 46

7 445 7:24 7:24 7:28 0:04 46

8 517 7:29 7:29 7:32 0:03 46

9 468 7:30 7:33 7:37 0:04 46

10 343 7:34 7:38 7:41 0:03 46

11 205 7:38 7:41 7:44 0:03 46

12 77 7:38 7:44 7:47 0:03 46

13 167 7:41 7:48 7:53 0:05 46

14 322 7:48 7:53 7:56 0:03 46

15 518 7:51 7:57 8:00 0:03 46

16 507 7:58 8:01 8:04 0:03 46

17 354 8:13 8:05 8:09 0:04 46

18 296 8:14 8:10 8:13 0:03 46

19 91 8:20 8:13 8:16 0:03 46

20 204 8:25 8:17 8:20 0:03 46

Ketu Bus Terminal

Sitting

S/NBus No


Service Time

No of Passengers

1 355 7:01 7:01 7:04:00 0:03 46

2 400 7:02 7:05 7:08:00 0:03 46

3 126 7:08 7:09 7:12:00 0:03 46

4 153 7:12 7:13 7:17:00 0:04 46

5 533 7:15 7:18 7:21:00 0:03 46

6 470 7:20 7:22 7:25:00 0:03 46

7 55 7:21 7:26 7:29:00 0:03 46

8 170 7:22 7:30 7:33:00 0:03 46

9 234 7:23 7:33 7:37:00 0:04 46

10 63 7:31 7:38 7:43:00 0:05 46

11 413 7:36 7:44 7:47:00 0:03 46

12 450 7:41 7:48 7:52:00 0:04 46

13 452 7:43 7:53 7:56:00 0:03 46

14 160 7:46 7:57 8:00:00 0:03 46

15 485 7:51 8:01 8:04:00 0:03 46

16 471 7:55 8:05 8:09:00 0:04 46

17 271 7:57 8:11 8:14:00 0:03 46

18 380 7:58 8:15 8:18:00 0:03 46

19 378 8:05 8:18 8:22:00 0:04 46

42

20 446 8:06 8:23 8:26:00 0:03 46

Ojota Bus Terminal

Sitting

S/NBus No


Service Time

No of Passengers

1 408 7:02 7:03 7:06 0:03 46

2 174 7:03 7:06 7:10 0:04 46

3 275 7:04 7:11 7:14 0:03 46

4 97 7:09 7:15 7:18 0:03 46

5 110 7:12 7:19 7:22 0:03 46

6 13 7:15 7:23 7:28 0:05 46

7 145 7:24 7:28 7:31 0:03 46

8 347 7:30 7:32 7:35 0:03 46

9 129 7:34 7:45 7:48 0:03 46

10 198 7:38 7:49 7:52 0:03 46

11 131 7:45 7:53 7:56 0:03 46

12 42 7:47 7:56 7:59 0:03 46

13 66 7:50 8:00 8:04 0:04 46

14 268 7:55 8:04 8:07 0:03 46

15 125 7:58 8:08 8:11 0:03 46

16 280 7:59 8:12 8:15 0:03 46

17 240 8:05 8:16 8:21 0:05 46

18 336 8:08 8:22 8:25 0:03 46

19 264 8:11 8:25 8:28 0:03 46

20 210 8:18 8:30 8:33 0:03 46

Ojota Bus Terminal

Sitting

S/NBus No


Service Time

No of Passengers

1 483 7:01 7:02 7:05 0:03 46

2 228 7:03 7:06 7:09 0:03 46

3 257 7:07 7:10 7:13 0:03 46

4 69 7:10 7:13 7:17 0:04 46

5 112 7:18 7:18 7:21 0:03 46

6 182 7:27 7:27 7:30 0:03 46

7 46 7:35 7:35 7:39 0:04 46

8 25 7:36 7:40 7:43 0:03 46

9 200 7:42 7:43 7:47 0:04 46

10 423 7:46 7:48 7:51 0:03 46

11 63 7:47 7:52 7:55 0:03 46

12 388 7:48 7:55 7:58 0:03 46

43

13 138 7:51 7:59 8:04 0:05 46

14 259 7:52 8:05 8:08 0:03 46

15 208 7:52 8:08 8:11 0:03 46

16 134 7:57 8:12 8:15 0:03 46

17 46 7:59 8:16 8:20 0:04 46

18 352 8:04 8:20 8:23 0:03 46

19 295 8:12 8:24 8:27 0:03 46

20 109 8:13 8:28 8:31 0:03 46

Ojota Bus Terminal

Sitting

S/NBus No


Service Time

No of Passengers

1 186 7:00 7:00 7:03:00 0:03 46

2 177 7:03 7:04 7:07:00 0:03 46

3 85 7:03 7:08 7:11:00 0:03 46

4 328 7:07 7:11 7:15:00 0:04 46

5 64 7:15 7:16 7:19:00 0:03 46

6 329 7:16 7:20 7:23:00 0:03 46

7 304 7:26 7:26 7:29:00 0:03 46

8 522 7:27 7:30 7:33:00 0:03 46

9 225 7:38 7:38 7:42:00 0:04 46

10 368 7:41 7:42 7:47:00 0:05 46

11 455 7:46 7:48 7:51:00 0:03 46

12 99 7:48 7:52 7:56:00 0:04 46

13 433 7:52 7:57 8:00:00 0:03 46

14 238 7:55 8:01 8:04:00 0:03 46

15 213 7:59 8:04 8:07:00 0:03 46

16 336 8:03 8:08 8:12:00 0:04 46

17 364 8:05 8:13 8:16:00 0:03 46

18 414 8:09 8:17 8:20:00 0:03 46

19 291 8:15 8:20 8:24:00 0:04 46

20 219 8:19 8:25 8:28:00 0:03 46

Fadeyi Bus Terminal

Sitting

S/NBus No


Service Time

No of Passengers

1 511 6:02 6:03 6:06 0:03 46

2 450 6:03 6:06 6:10 0:04 46

3 196 6:04 6:11 6:14 0:03 46

4 374 6:09 6:15 6:18 0:03 46

44

5 446 6:12 6:19 6:22 0:03 46

6 377 6:15 6:23 6:28 0:05 46

7 20 6:24 6:28 6:31 0:03 46

8 31 6:30 6:32 6:35 0:03 46

9 84 6:34 6:45 6:48 0:03 46

10 436 6:38 6:49 6:52 0:03 46

11 79 6:45 6:53 6:56 0:03 46

12 361 6:47 6:56 6:59 0:03 46

13 519 6:50 7:00 7:04 0:04 46

14 274 6:55 7:04 7:07 0:03 46

15 238 6:58 7:08 7:11 0:03 46

16 272 6:59 7:12 7:15 0:03 46

17 199 7:05 7:16 7:21 0:05 46

18 15 7:08 7:22 7:25 0:03 46

19 276 7:11 7:25 7:28 0:03 46

20 127 7:18 7:30 7:33 0:03 46

Fadeyi Bus Terminal

Sitting

S/NBus No


Service Time

No of Passengers

1 397 6:01 6:02 6:05 0:03 46

2 47 6:03 6:06 6:09 0:03 46

3 477 6:07 6:10 6:13 0:03 46

4 294 6:10 6:13 6:17 0:04 46

5 233 6:18 6:18 6:21 0:03 46

6 108 6:27 6:27 6:30 0:03 46

7 531 6:35 6:35 6:39 0:04 46

8 191 6:36 6:40 6:43 0:03 46

9 470 6:42 6:43 6:47 0:04 46

10 241 6:46 6:48 6:51 0:03 46

11 470 6:47 6:52 6:55 0:03 46

12 412 6:48 6:55 6:58 0:03 46

13 94 6:51 6:59 7:04 0:05 46

14 226 6:52 7:05 7:08 0:03 46

15 448 6:52 7:08 7:11 0:03 46

16 128 6:57 7:12 7:15 0:03 46

17 154 6:59 7:16 7:20 0:04 46

18 235 7:04 7:20 7:23 0:03 46

19 151 7:12 7:24 7:27 0:03 46

20 313 7:13 7:28 7:31 0:03 46

45

Fadeyi Bus Terminal

Sitting

S/NBus No


Service Time

No of Passengers

1 123 6:00 6:00 6:03:00 0:03 46

2 78 6:03 6:04 6:07:00 0:03 46

3 404 6:03 6:08 6:11:00 0:03 46

4 109 6:07 6:11 6:15:00 0:04 46

5 423 6:15 6:16 6:19:00 0:03 46

6 172 6:16 6:20 6:23:00 0:03 46

7 12 6:26 6:26 6:29:00 0:03 46

8 148 6:27 6:30 6:33:00 0:03 46

9 325 6:38 6:38 6:42:00 0:04 46

10 503 6:41 6:42 6:47:00 0:05 46

11 517 6:46 6:48 6:51:00 0:03 46

12 316 6:48 6:52 6:56:00 0:04 46

13 93 6:52 6:57 7:00:00 0:03 46

14 249 6:55 7:01 7:04:00 0:03 46

15 99 6:59 7:04 7:07:00 0:03 46

16 352 7:03 7:08 7:12:00 0:04 46

17 169 7:05 7:13 7:16:00 0:03 46

18 279 7:09 7:17 7:20:00 0:03 46

19 452 7:15 7:20 7:24:00 0:04 46

20 119 7:19 7:25 7:28:00 0:03 46

Leventis Bus Terminal

Sitting

S/NBus No


Service Time

No of Passengers

1 31 6:04 6:05 6:09 0:04 46

2 173 6:06 6:10 6:13 0:03 46

3 395 6:13 6:14 6:17 0:03 46

4 264 6:16 6:18 6:22 0:04 46

5 34 6:18 6:24 6:27 0:03 46

6 156 6:25 6:27 6:30 0:03 46

7 430 6:26 6:31 6:35 0:04 46

8 69 6:28 6:42 6:45 0:03 46

9 211 6:31 6:46 6:50 0:04 46

10 166 6:42 6:51 6:54 0:03 46

11 96 6:46 6:55 6:58 0:03 46

12 183 6:48 6:59 7:02 0:03 46

13 14 6:51 7:02 7:07 0:05 46

14 241 6:58 7:07 7:10 0:03 46

15 517 7:01 7:11 7:14 0:03 46

16 56 7:02 7:15 7:18 0:03 46

46

17 299 7:12 7:19 7:23 0:04 46

18 216 7:19 7:23 7:26 0:03 46

19 233 7:25 7:27 7:30 0:03 46

20 370 7:26 7:31 7:34 0:03 46


Sitting

S/NBus No


Service Time

No of Passengers

1 110 6:01 6:01 6:04:00 0:03 46

2 252 6:02 6:05 6:08:00 0:03 46

3 144 6:08 6:09 6:12:00 0:03 46

4 108 6:12 6:13 6:17:00 0:04 46

5 195 6:15 6:18 6:21:00 0:03 46

6 341 6:20 6:22 6:25:00 0:03 46

7 125 6:21 6:26 6:29:00 0:03 46

8 141 6:22 6:30 6:33:00 0:03 46

9 357 6:23 6:33 6:37:00 0:04 46

10 288 6:31 6:38 6:43:00 0:05 46

11 180 6:36 6:44 6:47:00 0:03 46

12 533 6:41 6:48 6:52:00 0:04 46

13 384 6:43 6:53 6:56:00 0:03 46

14 222 6:46 6:57 7:00:00 0:03 46

15 403 6:51 7:01 7:04:00 0:03 46

16 228 6:55 7:05 7:09:00 0:04 46

17 71 6:57 7:11 7:14:00 0:03 46

18 458 6:58 7:15 7:18:00 0:03 46

19 340 7:05 7:18 7:22:00 0:04 46

20 431 7:06 7:23 7:26:00 0:03 46


Sitting

S/NBus No


Service Time

No of Passengers

1 163 6:02 6:03 6:06 0:03 46

2 504 6:05 6:07 6:10 0:03 46

3 181 6:09 6:10 6:13 0:03 46

4 485 6:15 6:14 6:18 0:04 46

5 402 6:16 6:18 6:21 0:03 46

6 375 6:17 6:21 6:24 0:03 46

7 84 6:24 6:24 6:28 0:04 46

8 154 6:29 6:29 6:32 0:03 46

9 192 6:30 6:33 6:37 0:04 46

10 167 6:34 6:38 6:41 0:03 46

47

11 173 6:38 6:41 6:44 0:03 46

12 149 6:38 6:44 6:47 0:03 46

13 392 6:41 6:48 6:53 0:05 46

14 226 6:48 6:53 6:56 0:03 46

15 124 6:51 6:57 7:00 0:03 46

16 479 6:58 7:01 7:04 0:03 46

17 57 7:13 7:05 7:09 0:04 46

18 281 7:14 7:10 7:13 0:03 46

19 256 7:20 7:13 7:16 0:03 46

20 84 7:25 7:17 7:20 0:03 46

TBS Bus Terminal

Sitting

S/NBus No


Service Time

No of Passengers

1 190 6:00 6:00 6:03:00 0:03 46

2 370 6:02 6:03 6:06:00 0:03 46

3 330 6:09 6:09 6:12:00 0:03 46

4 446 6:13 6:13 6:17:00 0:04 46

5 365 6:14 6:18 6:21:00 0:03 46

6 273 6:16 6:22 6:25:00 0:03 46

7 494 6:24 6:25 6:28:00 0:03 46

8 416 6:27 6:29 6:32:00 0:03 46

9 393 6:30 6:32 6:36:00 0:04 46

10 293 6:34 6:36 6:41:00 0:05 46

11 474 6:35 6:42 6:45:00 0:03 46

12 184 6:39 6:45 6:49:00 0:04 46

13 374 6:45 6:49 6:52:00 0:03 46

14 390 6:51 6:52 6:55:00 0:03 46

15 305 6:53 6:56 6:59:00 0:03 46

16 195 6:54 7:00 7:05:00 0:05 46

17 243 6:59 7:06 7:09:00 0:03 46

18 176 7:04 7:10 7:13:00 0:03 46

19 348 7:11 7:13 7:17:00 0:04 46

20 258 7:15 7:18 7:21:00 0:03 46

TBS Bus Terminal

Sitting

S/NBus No


Service Time

No of Passengers

48

1 112 6:04 6:05 6:09 0:04 46

2 223 6:06 6:10 6:13 0:03 46

3 444 6:13 6:14 6:17 0:03 46

4 28 6:16 6:18 6:22 0:04 46

5 78 6:18 6:24 6:27 0:03 46

6 16 6:25 6:27 6:30 0:03 46

7 208 6:26 6:31 6:35 0:04 46

8 189 6:28 6:42 6:45 0:03 46

9 377 6:31 6:46 6:50 0:04 46

10 81 6:42 6:51 6:54 0:03 46

11 128 6:46 6:55 6:58 0:03 46

12 493 6:48 6:59 7:02 0:03 46

13 179 6:51 7:02 7:07 0:05 46

14 31 6:58 7:07 7:10 0:03 46

15 520 7:01 7:11 7:14 0:03 46

16 376 7:02 7:15 7:18 0:03 46

17 119 7:12 7:19 7:23 0:04 46

18 255 7:19 7:23 7:26 0:03 46

19 432 7:25 7:27 7:30 0:03 46

20 247 7:26 7:31 7:34 0:03 46

TBS Bus Terminal

Sitting

S/NBus No


Service Time

No of Passengers

1 115 6:02 6:03 6:06 0:03 46

2 38 6:05 6:07 6:10 0:03 46

3 346 6:09 6:10 6:13 0:03 46

4 151 6:15 6:14 6:18 0:04 46

5 411 6:16 6:18 6:21 0:03 46

6 241 6:17 6:21 6:24 0:03 46

7 317 6:24 6:24 6:28 0:04 46

8 32 6:29 6:29 6:32 0:03 46

9 64 6:30 6:33 6:37 0:04 46

10 405 6:34 6:38 6:41 0:03 46

11 47 6:38 6:41 6:44 0:03 46

12 210 6:38 6:44 6:47 0:03 46

13 355 6:41 6:48 6:53 0:05 46

14 529 6:48 6:53 6:56 0:03 46

15 270 6:51 6:57 7:00 0:03 46

16 225 6:58 7:01 7:04 0:03 46

17 246 7:13 7:05 7:09 0:04 46

18 132 7:14 7:10 7:13 0:03 46

19 531 7:20 7:13 7:16 0:03 46

20 107 7:25 7:17 7:20 0:03 46

49

Project Report New

Documents

Transcript of Project Report New