Simulation Concepts
Dr. Jason Merrick
Randomness in Simulation
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The above was just one “replication” -- a sample of size one (not
worth much)
We will do multiple replications:
Replication
Average time in queue
Average number in queue
Machine utilization
Number of samples
1
0.19
0.27
0.85
5
2
1.12
0.3
0.91
Lower
0.98
0.31
0.69
Upper
1.59
0.41
0.32
3
3.72
0.99
1
4
0
0
0.32
5
0
0
0.37
Average
1.01
0.31
0.69
Std Dev
1.59
0.41
0.32
Confidence Interval
Average time in queue
Average number in queue
Machine utilization
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Confidence intervals on expectations
– e.g., 95% c.i. on E(avg. time in queue):
What about your replications?
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X  tn ,
s
n
C3/2
Simulation Replications
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Inter-arrival Times
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9.84, 0.44,
2.39, 2.63, 4.82, 3.98
2.90, 2.54, 1.96, 3.29
0.32, 3.54, 3.98, 0.49
4.79, 1.45
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Service Times
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8.72, 3.05
1.98, 1.60, 8.79, 16.23
2.03, 10.46, 4.15, 0.90
3.11, 1.42, 0.62, 3.70
2.67, 2.77
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Comparing Alternatives
• Usually, simulation is used for more than just a
single model “configuration”
• Often want to compare alternatives, select or
search for the best (via some criterion)
• Simple processing system:
What would happen
if the arrival rate were to double?
– Cut inter-arrival times in half
– Rerun the model for double-time arrivals
– Make five replications
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C3/4
Results:
Original vs. Double-Time Arrivals
Original Model
1
Double-Time Model
1
0
1
2
Total Production
3
4
Original Model
1
Double-Time Model
1
1
0
2
3
Average Time in Queue
4
5
Original Model
1
Double-Time Model
1
3
4
5
6
7
8
Average Flowtime
9
10
11
Original Model
1
Double-Time Model
1
1
0
2
3
Average Number in Queue
4
Original Model
1
1
0.4
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0.6
0.8
Machine Utilization
Double-Time Model
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Note variability
Danger of making
decisions based on
one (first) replication
Hard to see if there are
really differences
Need: Statistical
analysis of simulation
output data
1.0
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C3/5
Scheduling Dynamics:
The Event-Scheduling World
View
• Identify characteristic events—change state
• Decide on logic to: effect state changes for
each event type, observe statistics
• Keep a simulation clock, future event calendar
• Jump from one event to the next, process,
observe statistics, update event calendar
• Stopping rule
• Usually done with general-purpose
programming language (C, FORTRAN, etc.)
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C3/6
Events for our
Simple Processing System
Arrival of
a new part
Departure of
completed part
Update time
persistent statistics
Mark arrival time
Increment number produced
Compute & tally flowtime
Update time-persistent stats
Machine
busy?
Queue
Empty
No
Start processing
Make machine busy
Tally time in queue
Yes
Go to end of queue
Increase queue length
No
Start processing next part
Tally time in queue
Schedule departure event
Yes
Make machine idle
Schedule
next arrival
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C3/7
Events for
Simple Processing System (cont’d.)
• The End
– Update time-persistent statistics (to end of the simulation)
– Compute final output performance measures using current
values of statistical accumulators
• After each event, the event calendar’s top record
is removed to see what time it is, what to do
• Also must initialize everything
• This is not the only way to view a simulation
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C3/8
Simulation Dynamics:
The Process-Interaction World View
• Identify characteristic entities in the system
• Tell a “story” about what happens to a “typical”
entity
– Multiple copies of entities co-exist, interact, compete
– “Code” is non-procedural
• Usually requires special simulation software
• This is the view normally taken by Arena
• Underneath, still SIMAN executes the simulation
using event-scheduling
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C3/9
Process View of the
Simple Processing System
Stay in queue
Yes
Entity enters
the system
• Mark arrival time
Entity goes to
end of queue
Is the server
busy?
• Increment queue length
• Mark arrival time at queue
No
Entity leaves
the system
When service time
is finished release
the server
Start processing
Seize the machine
• Mark departure time
• Decrement queue length
• Calculate flow time
• Calculate time in queue
• Increment total production
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Process View
• Used in most simulation languages
• Much easier to think about
• Do not have to define separate event logic for
each possible event
• Similar to flow charting in business process
analysis
• Leaves the complicated event programming to
the simulation software designer
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Simulation as a Tool
• Simulation can be used for
– Comparison
• To compare system alternatives and their performance measures
across various factors (decision variables) with respect to some
objectives
– Prediction
• To predict the behavior of the system at some future point in time.
– Investigation
• To learn about and gain insight into the behavior of the system given
various inputs.
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Objectives of the
Simulation Study
• These are given in the "To" + "Action verb" +
"Qualifiers" format.
• The objectives will assist in identifying decision
variables, output measures, and presentation
requirements.
• Examples
– To investigate how to improve system throughput. (rather
loose)
– To compare the cost and throughput changes given an
increase from 2 to 3 machines available.
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Complex Systems
• A system is
– a group of interacting elements functioning as a complex
whole (American Heritage Dictionary)
– a group of objects that are joined together in some regular
interaction or interdependence towards the
accomplishment of some purpose (B,C&N)
• Must decide on an artificial boundary for the
system
• The system state is the collection of variables
that “describe” the system at any given time
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System Description
• A verbal and/or pictorial representation of the
major elements of the system under study
– Especially the flow characteristics of entities passing
through the systems.
• Distill the system description down to a "text
book" word problem for performing the study.
– Graphical descriptions, flow charts, etc..
• Get buy in for the system description from
– system experts
– management
– decision makers
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Simulation as a
Decision Making Tool
• Input variables
– List all input data and its form
– e.g. if it needs to be extracted from a file in a certain format.
– Pay close attention to the probability distributions and their parameters.
• Output variables
– A formal listing and description of the outputs required including all
statistical measures to be observed.
• Decision variables
– List the factors and their levels which are to be varied during the
experiments.
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Overview of a Simulation Study
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Understand the system
– It is not possible to model a system without first observing and
understanding it
– Visit the system and observe
– Go to experts with a deep understanding of the system
– ask them how the system works
Be clear about the goals
– What are the project objectives?
– What do you want to get out of this study?
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understanding the system
testing alternative configurations
– The simulation you build cannot do everything - time and money
constraints
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– Tell management what Simulation
you with
will
deliver ahead of time
C3/17
Overview of a Simulation Study
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Formulate the model representation
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What level of detail is required for the project objectives
What needs to be modeled in detail?
What can be modeled at a higher level?
What is the system boundary?
What are the entities, attributes, global variables, output variables,
decision variables of interest?
– Make the management/decision makers aware of the modeling
assumptions before building the model
– To get buy in you will need to speak in English, not mathematics
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Overview of a Simulation Study
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Translate into modeling software
– Represent the modeling assumptions in the simulation software
– If there are difficulties, talk about them
– It is often beneficial to go back and check how the system really works
to get past implementation problems
– Show system experts an animation of the simulation as you go along
Verify “program”
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Try obvious inputs and look for the obvious outputs
Test extreme inputs to see what happens
Walk through the program logic
Structure any code to avoid confusion
Output your inputs to ensure they follow your assumed input processes
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Overview of a Simulation Study
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Validate model
– Does model adequately represent real world system?
– Are model generated behavioral data characteristic of real world
system's behavioral data?
– Does the model's user have confidence in model's results? (credibility)
– Turing Test - people knowledgeable about the system are asked to
examine one or more sets of system data as well as sets of model data
without knowing which sets are which, (can they tell the difference)
Design experiments
– What input variables do you want to test the effect of?
– What decision variables do you want to test the effect of?
– What alternative configurations of the system do you want to test?
Make runs
– Go get a cup of coffee
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Overview of a Simulation Study
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Analyze
– Carry out statistical analysis to make accurate and precise statement
about the results
Get insight
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Can you understand the results at a gut feeling level?
Can you explain the logic behind your results?
Remember there is a world outside your model
Be sensitive to the implications of what you are saying
Document results
– You cannot present your analysis to all interested parties
– Good documentation is readable by a non-simulation expert
– Put the technical stuff in appendices
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