Simulation Software
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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
languages like FORTRAN, C or C++ to develop simulation packages.
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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
– Coding the algorithm
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 ni be the number of customers in front of
teller i. If the completion of service at teller i causes nj > ni + 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.
Multiteller Bank with Jockeying
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Events and state transitions
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Events and state transitions:
arrival to a non-empty system
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Events and state transitions:
arrival to an empty system
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Events and state transitions: departure from
a non-empty system, followed by jockeying
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Performance measures
• Expected number in each queue
• Expected waiting time of a customer
• Expected utilization of each server
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Flowchart
• Events?
 a separate flowchart for each event
– Customer arrival
– Customer departure
– Jockeying
• How to combine them?
 main flowchart
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Function
arrive
Arrival
Flowchart
Schedule the next
arrival event
Yes
Is a
teller
idle?
No
Find the number of
the leftmost shortest
queue (shortest_q)
Set a delay of 0 for
this customer
Place the customer at
the end of queue
number shortest_q
i.e., increase the # in
the queue by 1
Make the teller busy
Schedule the
departure of this
customer
Record the arrival
time of this customer
Return
Function
depart
Departure
Flowchart
Yes
Is the
queue for
this teller
empty?
No
Remove the first
customer from this
queue
Make this teller idle
Compute this
customer’s delay and
gather statistics
Schedule the
departure event for
this customer
Call function Jockey
Return
Function
jockey
Jockeying
Flowchart
Is there a
customer to
jockey?
Yes
Remove this
customer from the tail
of his or her current
queue
Yes
Place the jockeying
customer at the tail of
the queue of the teller
who just completed
service
Is the teller who
just completed
service now
busy?
No
No
Compute this
customer’s delay and
gather statistics
Make this teller busy
Schedule the
departure event for
the jockeying
customer
Return
Flowchart
Combining
Departure and
Jockeying
Yes
Is there a
customer to
jockey?
Remove this customer from the
tail of his or her current queue
Function
depart
Is the
queue for
this teller
empty?
Yes
No
Remove the first customer
from this queue
Compute this customer’s
delay and gather statistics
No
Make this teller idle
Compute this customer’s delay
and gather statistics
Schedule the departure
event for this customer
Yes
Make this teller busy
Is there a
customer to
jockey?
Place the jockeying
customer at the tail of this
queue
Schedule the departure event
for the jockeying customer
No
Return
Start
Main
flowchart
Initialization
Yes
•Find the next event
•Update current_time:
current_time+time_till_next
Is
current_time
< finish_time
No
Report
Call the function
corresponding to the event
Stop
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?
–…
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How to think to draw a flowchart:
Process
• Departure function is called, when the minimum of the
event times (in this case, time-to-departure and time-toarrival) 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
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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
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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 ni(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
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How to modify the states?
• Let (n1(t),n2(t),..n5(t)) be our state variable where ni(t) denotes the
total number of customers in queue i (including the customer in
service).
• Arrival event:
• If there is at least one ni(t-) =0.
– Let j be the smallest index of the queue that is empty, then
• nj(t)=nj(t-)+1
• Else
– Find argminj((n1(t),n2(t),..n5(t))
– Let j be the smallest index of the queue has the smallest number
of customers, then
• nj(t)=nj(t-)+1
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How to gather statistics
• Define the variables:
– Cum_delay
– Cum_queue
– Cum_busy
• At each event epoch, update these variables
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How to think to draw a flowchart:
Information gathering
• For example: Cum_queue
Inter-arrival times: A1 = 0.4, A2 = 1.2, A3 = 0.5, A4 = 1.7, A5 = 0.2, A6 = 1.6, A7 =
0.2, A8 = 1.4, A9 = 1.9
Processing times: S1 = 2.0, S2 = 0.7, S3 = 0.4, S4 = 1.1, S5 = 3.7, S6 = 0.6
• At each event epoch, update these variables
t
Events
Next
Event
N1(t)
Cum_queue1
t
 N ( )d
1
0
0
{I1}
I1 (0.4)
0
0
0.4
{I2, C1}
I2 (1.6)
1
0+00.4=0
1.6
{I3, C1, C2 }
I3 (2.1)
2
0+0*(1.6-0.4)=0
2.1
{I4, C1, C2 }
C2 (2.3)
3
0+0*(2.1-1.6)=0
2.3
{I4, C1, C3}
C1(2.4)
2
0+1*(2.3-2.1)=0.2
…
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Output
Report
for
Multite
ller
Bank
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Output Report for Multiteller 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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Comparison of Simulation Packages
with Programming Languages
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.
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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.
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Classification of Simulation Software
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, healthcare, or call centers).
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Classification of Simulation Software
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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Process Approach
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Prototype
customerprocess routine
for a singleserver 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.
2.
3.
General capabilities
– Modeling flexibility, Ease of use, Hierarchical
modeling, Debugging aids, Fast model execution
speed, etc.
Hardware and software requirement
– Computer platforms (PC’s, UNIX workstations,
Apple’s), RAM requirement, Operating system
requirement (Windows, UNIX, Mac OS)
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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Arena
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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Arena
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Arena
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Arena
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Arena
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Arena
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Other General-Purpose Simulation
Packages

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Extend
GPSS/H
MODSIM III
SIMPLE++
SLX

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AweSim
Micro Saint
SES/workbench
SIMUL8
Taylor Enterprise Dynamics
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Application-Oriented Simulation
Packages
•
Manufacturing: AutoMod, AutoSched AP, Extend + Manufacturing,
Arena Packaging Edition, ProModel, QUEST, Taylor Enterprise
Dynamics, WITNESS
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Communication Networks: COMNET, IT DecisionGuru, OPNET
Modeler
•
Process Reengineering and Services: Arena Business Edition,
Extend + BPR, ProcessModel, ServiceModel, SIMPROCESS
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Heath Care: MedModel
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Call Centers: Arena Call Center Edition
•
Animation: Proof Animation
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