Simulation Software 1

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Introduction

The features that should be programmed in simulation are: • Generating random numbers from the uniform distribution • Generating random variates from any distribution

• Advancing simulation time

• Determining the next event and passing control to the appropriate block of code

• Adding records to, or deleting records from, a list • Collecting output statistics and reporting them • Detecting error conditions

These common features are programmed using general-purpose

How to simulate a system with a

computer code?

• Planning the study

– Description of the system

– Definitions of the performance measures

• Algorithm

– Flowchart: Process in the system, collection of statistics

to estimate the performance measures, reporting

– Algorithm that corresponds to the flowchart

• Computer code (Matlab, Java, …)

– Data structures (sequential vs linked allocation: in book)

– Random number generation

Simulating a Multi-Teller Bank

• The bank opens its doors at 9 A.M. and closes its doors at 5 

P.M., but operates until all customers still in the bank are 

served. Customer interarrival times are IID and exponential 

with mean 1 minute and services are IID and exponential with 

mean 4.5 minutes. 

• Each teller has a separate queue. An arriving customer joins 

the shortest queue, choosing the leftmost shortest queue if 

there is a tie. Let n

be the number of customers in front of 

teller i. If the completion of service at teller i causes n

> n

+ 1 

for some other teller j, then the customer from the tail of 

queue j jockeys to the tail of queue i. If there are two or more 

such customers, the one from the closest leftmost queue 

joins. 

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Events and state transitions

Events and state transitions:

arrival to a non-empty system

Events and state transitions:

arrival to an empty system

Events and state transitions: departure from

a non-empty system, followed by jockeying

Performance measures

• Expected number in each queue

• Expected waiting time of a customer

• Expected utilization of each server

Flowchart

• Events?



a separate flowchart for each event

– Customer arrival

– Customer departure

– Jockeying

• How to combine them?



main flowchart

Arrival

Flowchart

Function arrive

Schedule the next arrival event

Is a teller idle? Set a delay of 0 for

this customer

Make the teller busy Schedule the departure of this

customer

Find the number of the leftmost shortest

queue (shortest_q) Place the customer at

the end of queue number shortest_q i.e., increase the # in

the queue by 1

Return

Record the arrival time of this customer

Departure

Flowchart

Remove the first customer from this

queue Compute this customer’s delay and

gather statistics

Return

Schedule the departure event for

this customer

Yes No

Jockeying

Flowchart

customer from the tail of his or her current

queue

Return Yes

No

Is the teller who Is the teller who just completed

service now busy?

Compute this customer’s delay and

gather statistics

Make this teller busy Schedule the departure event for

the jockeying customer Place the jockeying

customer at the tail of the queue of the teller who just completed

service

Flowchart

Combining

Departure and

Jockeying

Remove the first customer from this queue

Compute this customer’s delay and gather statistics

Return

Schedule the departure event for this customer

Yes No

Is there a customer to

jockey? Remove this customer from the

tail of his or her current queue Compute this customer’s delay

and gather statistics Make this teller busy Schedule the departure event

for the jockeying customer

Place the jockeying customer at the tail of this

queue

Is there a Is there a customer to

jockey? Make this teller idle

Yes No

Yes

Main

flowchart

•Update current_time: current_time+time_till_next

Yes

Call the function corresponding to the event

Common mistakes in the flowcharts

• Schedule next departure only if you make the

server busy with the next customer.

• Collect the statistics:

– How many customers were waiting between the

previous event and the departure now?

– The waiting time of the customer who just started

service?

– …

How to think to draw a flowchart:

Process

• Departure function is called, when the minimum of the

event times (in this case, departure and

time-to-arrival) corresponds to a departure.

• So we know that a customer is leaving the system, which

means that the server serving that customer is now idle

and has to look for a customer if there is any in the

system.

• Is there any customer to serve for this server? Check:

– The server’s queue – Other queues

• Once the server’s state is determined, check for

jockeying

How to think to draw a flowchart:

Process

• Which event will happen next?

• Events:

– Arrival

– Potentially departure from queue i, i=1,2,…,5

– End of simulation

How to think to draw a flowchart:

Information gathering

• What do you need to know about the queues?

• The number of customers in each queue:

– State variable: (n₁(t),n₂(t),..n₅(t)), where n_i(t) denotes the total number of customers in queue i (including the customer in service).

– Server state?

• What do we need to know about customers?

• For each customer:

– The queue that he/she is waiting for (denote by cust_queue) – His/her position in the cust_queue

– His/her arrival time

How to modify the states?

• Let (n₁(t),n₂(t),..n₅(t)) be our state variable where n_i(t) denotes the total number of customers in queue i (including the customer in service).

• Arrival event:

• If there is at least one n_i(t-) =0.

– Let j be the smallest index of the queue that is empty, then • n_j(t)=n_j(t-)+1

• Else

– Find

argmin

((n

(t),n

(t),..n

(t))

– Let j be the smallest index of the queue has the smallest number of customers, then

• n_j(t)=n_j(t-)+1

How to gather statistics

• Define the variables:

– Cum_delay – Cum_queue – Cum_busy

• At each event epoch, update these variables

How to think to draw a flowchart:

Information gathering

• For example:

• At each event epoch, update these variables

23 t Events Next Event N₁(t) Cum_queue₁ 0 {I₁} I₁ (0.4) 0 0 0.4 {I_2, C₁} I₂ (1.6) 1 0+00.4=0 1.6 {I_3, C_1, C₂ } I₃ (2.1) 1 0+0*(1.6-0.4)=0 2.1 {I_3, C_1, C_2, C₃ } C2 (2.3) 1 0+1*(2.1-1.6)=0.5 …   d N t



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Output

Report

for

Multite

ller

Bank

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Comparison of Simulation Packages

with Programming Languages

Advantages of simulation packages

• They automatically provide most of the features,

requiring less programming time and cost.

• They provide a natural framework for simulation

modeling.

• Models are easier to modify and maintain.

• They provide better error detection because potential

errors are checked for automatically.

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Advantages of general purpose languages

• Most modelers already know a language, but this is often

not the case with a simulation package.

• A simulation model efficiently written in a language may

require less execution time.

• Programming languages may allow greater programming

flexibility.

• Software cost is generally lower, but total project cost

may not be.

Comparison of Simulation Packages

with Programming Languages

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Classification of Simulation Software

• Earlier times: A combination of general purpose

language and simulation concepts such as

Simscript, Siman, or SLAM

• Recently: Simulation software packages

– Easy-to-use

– User friendly graphical model building approach

involving use of modules and icons selected by the

user on screen

– Entities represented by icons with a wide range of

animation capabilities.

29 General-purpose versus application-oriented simulation packages

• A general-purpose simulation package can be used for any application, but might have special features for certain ones (like manufacturing, communications, or business process

reengineering).

• An application-oriented simulation package is designed to be used for a certain class of application (like manufacturing, health-care, or call centers).

30 Modeling approach

• Event-scheduling approach is based on simulating over time by executing the events selected from the event list in increasing order of their time.

• Process approach is based on simulating the time-ordered sequence of processes experienced by a single entity as it flows through the system.

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Prototype

customer-process routine

for a

single-server queueing

system

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Common Modeling Elements

Simulation packages typically include entities, attributes,

resources and queues as part of their modeling framework.

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Desirable Software Features

1. General capabilities

– Modeling flexibility, Ease of use, Hierarchical

modeling, Debugging aids, Fast model execution speed, etc.

2. Hardware and software requirement

– Computer platforms (PC’s, UNIX workstations, Apple’s), RAM requirement, Operating system requirement (Windows, UNIX, Mac OS)

3. Animation and dynamic graphics

– Concurrent and post-processed animation, Vector based and pixel based graphics, Two and three dimensional animation, Dynamic graphics and statistics

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Desirable Software Features

4. Statistical capabilities

– Good random number generation, Theoretical discrete and continuous distributions, Empirical distributions, Independent replications or runs, Performance estimation, Confidence interval determination, Warmup period, Optimization via simulation

5. Customer support and documentation

– Public and customized training – Technical support

– Good documentation

6. Output reports and graphics

– Standart and customized reports

– Descriptive statistics (histograms, time plots, bar chart, pie chart, etc.)

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General-Purpose Simulation Packages

Arena

This is the package we will be using in this course. Modeling is done using modules arranged into a number of templates:

• Basic Process template has modules used in many models for modeling arrivals (create), services (process) and departures (dispose).

• Advanced Process template contains modules to perform very specific logical functions such as choosing a queue when several are available or coordinating the advancement of multiple entities in different areas

• Advanced Transfer template contains modules (like conveyors and transporters) that are used to describe the transfer of entities from one part of the system to another.

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A model is constructed by dragging and dropping modules into the model window, connecting them to indicate the flow of entities through the simulated system, and then detailing the modules using dialog boxes of Arena’s built-in spreadsheet.

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Other General-Purpose Simulation

Packages

 Extend  AweSim  GPSS/H  Micro Saint

 MODSIM III  SES/workbench  SIMPLE++  SIMUL8

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Application-Oriented Simulation

Packages

• Manufacturing: AutoMod, AutoSched AP, Extend + Manufacturing,

Arena Packaging Edition, ProModel, QUEST, Taylor Enterprise Dynamics, WITNESS

• Communication Networks: COMNET, IT DecisionGuru, OPNET

Modeler

• Process Reengineering and Services: Arena Business Edition,

Extend + BPR, ProcessModel, ServiceModel, SIMPROCESS

• Heath Care: MedModel

• Call Centers: Arena Call Center Edition