Introduction to Modeling

A bank

• Customers arrive at a bank• The inter-arrival time is recorded• Customers wait there turn in the waiting area• Customers are served on the first come first

served basis• When his turn comes, the customer moves to the

teller• The service time is recorded• The customer leaves after he got serviced

Basic Elements

• We need to define the following:– Entity

• Items processed in the system

– Arrival• How often entities arrive

– Location• Places where entities are held or processed

– Resources• Agents used in the processing of entities

– Path• The course of travel for entities and resources in the system

Logic building

• Several choice:– Unified Modeling Language (UML)– Outline process map• Six symbols to represent the process• The symbols can be used to extract further information

Outline Process MapProcess: an action performed on an Entity

Inspection: Revision or test of an Entity

Transportation: Movement of the entity from one location to another

Decision: When there are several choices or options

Handling: movement of an entity using resources

Delay: Some time spent in waiting

Storage: Long time waiting

Outline Process MapCustomers arrive at the bank

Customers wait in the waiting area (queue) for their turn

Customer moves to tellers

Customer gets serviced

Waiting Area Teller Area

Customer Exits

EntitiesCustomers arrive at the bank

Customers wait in the waiting area (queue) for their turn

Customer moves to tellers

Customer gets serviced

Waiting Area Teller Area

Customer Exits

Each line in process map is considered an entity.Entities here are customers.

ArrivalCustomers arrive at the bank

Customers wait in the waiting area (queue) for their turn

Customer moves to tellers

Customer gets serviced

Waiting Area Teller Area

Customer Exits

The rate of arrival of each entity in the system

Stat::fit

Or Insert the data here

Choose file-open then choose files of type data files (*.txt)

Stat::fit

•Choose continuous or discrete•Choose whether the distribution is• Unbounded (no upper or lower limit)• Lower bound• Assigned bound (you specify the lower bound)

Stat::fit

• Choose assigned bound and specify the lower bound as 0.

Stat::fit

LocationsCustomers arrive at the bank

Customers wait in the waiting area (queue) for their turn

Customer moves to tellers

Customer gets serviced

Waiting Area Teller Area

Customer Exits

Two locations:Waiting Area and Teller AreaWaiting area is a QUEUE Specify waiting rule

RecoursesCustomers arrive at the bank

Customers wait in the waiting area (queue) for their turn

Customer moves to tellers

Customer gets serviced

Waiting Area Teller Area

Customer Exits

Resources are the equipments used in handling, or workers used to perform processes on entities.The resources here are the clerks serving customers.

PathsCustomers arrive at the bank

Customers wait in the waiting area (queue) for their turn

Customer moves to tellers

Customer gets serviced

Waiting Area Teller Area

Customer Exits

Only relevant when the transportation time is important.

Modeling

• For each entity, :• From arrival to departure, define the following

for each entity:– What does the entity do at each location?– Then, where does it go?

• Customers arrive at 2 locations– At each location define what they do at the

location– Where to go after the process

Processing

• At Waiting area– What to do:

• Wait his turn

– Where to go:• To the teller

• At the Teller– What to do:

• Get serviced

– Where to go:• Exit the system

The Complete Model• Entities:

– Customer• Locations

– Waiting area (Queue)– Teller desk

• Resources– Clerk(s)

• Networks– Irrelevant as we don’t need to analyze transportation time, otherwise it should be

included• Processing

– Customer @ waiting area does not do any processes• Customer then goes to teller

– Customer @ teller waits until the end of the service• Customer then leaves

Manual SimulationRandom No. Inter-arrival time Random No Service time

0.3 3.6 0.1 8.5

0.9 4.7 0.3 9.2

0.3 3.6 0.6 10.3

0.1 3.1 0.5 10.2

1.0 4.9 0.3 9.2

No customers in bank Clerk is idle First arrival at time 3.2

Event Time Event Type Entity serial Wait in Queue Queue Size Clerk Status Idle Time Wait in system

0 - - - 0 Idle - -

3.6 Arrive and wait 1 - 1 Idle - -

3.6 go to teller and service 1 0 0 Busy 3.6 -

8.3 Arrive and wait 2 - 1 Busy - -

9.1 Exit 1 - 1 Idle - 5.5

9.1 go to teller and service 2 0.8 0 Busy 0 -

11.9 Arrive and wait 3 - 1 Busy - -

15 Arrival and wait 4 - 2 Busy -

15.3 Exit 2 - 2 Idle - 7

15.3 go to teller and service 3 3.4 1 Busy 0 -

20 Arrival and wait 5 - 2 Busy -

22.6 Exit 3 - 2 Idle - 10.7

22.6 go to teller and service 4 7.6 0 Busy 0 -

29.8 Exit 4 - 2 Idle - 14.5

29.8 go to teller and service 5 9.8 0 Busy 0 -

36 Exit 5 - 2 Idle - 16