Overview of Systems Simulation
Introduction
Uses, Popularity of Simulation
One of the most popular, widely used of all scientific Techniques
Historical Roadblocks
Hard to write code for large, complicated models: Now have very good
software—improving all the time
Requires too much computer time: Marginal cost of computing decreases
all the time.
Many simulations (stochastic) don’t give exact “answers”—only estimates:
True, but with one is able to increase the precision of the estimate.
Modeling
System: Physical facility or process, usually evolving through time it may
or may not exist. Usually want to study its performance
Model: An abstraction/simplification of the system used as a proxy
Physical (iconic), Mathematical—quantitative and logical assumptions,
Numerical and simulation.
Relative advantages of studying the model vs. system: May be impractical
or impossible to perform experiments on the real system.
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Methods of Studying a System
SYSTEM
Experiment
with the
actual system
Experiment
with a model
of the system
Physical
model
Mathematical
model
Analytical
solution
2
Simulation
Types of Models
Useful dimensions of classification with regard to design/analysis:
Dynamic vs. Static, Stochastic vs. Deterministic, Discrete vs.
Continuous
Some examples:
Deterministic
No randomness
Inputs are exact, no
uncertainty
One model needs only
one run
Static
No time
element
Use fitted regression
model for unobserved
independent-variable
combinations
Financial scenarios
Dynamic
Stochastic
Random inputs—
uncertain
Inputs are from known
distributions
One model needs more
than one run
“Monte Carlo” simulation
Estimate an intractable
integral
Get empirical distribution
of a new test statistic
for some null
hypothesis
Passage Differential-equation
Queueing models
of time is
models of population
representing
important
growth and decay
manufacturing,
part of
computer, or
Deterministic forecasting
model
communications
over time
systems
Dynamic macroeconomic
Inventory models
models
Compute (exactly)
desired output
quantities
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Can only estimate desired
output quantities
Advantages and Disadvantages of Simulation
Compared to experimenting with the actual system:

Validity uncertainty with simulation (as with all models)

Much more flexibility in simulation to try things out

Can control the uncontrollable in simulation

Can study the physically impossible or non-existent
Compared to exact analytical models:

Don’t have to make as many simplifying assumptions—get more
flexible models that can be more valid

Don’t get simple formulas from which insight can be gained

Don’t get exact answers—only estimates, maybe uncertain—calls
for careful design and analysis of simulation experiments (our
concern)
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Steps in a Simulation Model
Formulate problem
and plan the study
Collect data and
define a model
Valid?
No
Yes
Construct a computer
program and verify
Make pilot runs
Valid?
Yes
Design experiments
Make production runs
Analyze output data
Document, present, and
implement results
5
No
Simulation Modeling, Input, Output, and
Experiments
Modeling
The modeling process: two distinct but related activities
Structural modeling
Physical/logical relationships among components
Topology/layout of machines
Possible routings for part flows
Feedback/failure loops
Closed vs. open structure in model of a computer system
Quantitative modeling
Specific numerical/distributional assumptions composing model
How many machines at each workcenter?
Probabilities for branch points on routing decisions?
Cycle times of part type 3 on a machine in group 5 are random
variates drawn from what distribution? With what parameters?
Run model for one hour? One year? Until 5000 parts have been
produced?
Building “good” simulation models:
Verification—Code (in whatever language or product) is correct
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Validation—Model (as expressed in the verified code) faithfully mimics
the system to study; can use model/code as surrogate for system to
make decisions
Credibility—The valid model is accepted by decision makers; critical for
implementation success
Elements of both structural and quantitative components can become
variables (or factors) in the design of simulation experiments
Structural factors:
Try a different layout of machines
What if part-flow routings changed due to technology?
What if rework were just scrapped instead (no feedback loops)?
What if the computer system went from open (batch jobs) to closed
(interactive)?
Quantitative factors:
What if we added a machine somewhere?
What if quality improvement changed pass/fail branching probabilities?
How effective would it be to reduce cycle times on the bottleneck work
center?
How long will the model operate before becoming unduly congested?
“Machine” View of What a Simulation Does:
Inputs –
Structural
Quantitative
Model
and
code
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Outputs –
Performance
measures
A Brief History
1733
Buffon needle problem—estimate 
1920s, 1930s
Random-number schemes used by applied statisticians
Physical methods of generating random numbers (tables)
1940s
Manhattan project, used to estimate multiple integrals and
solutions to systems of differential equations
Electronic random-number generators (more tables)
1950s
Early language development (GPSS, SIMSCRIPT)
Recognition of simulation for complex queueing models
First algorithmic random-number generators
1960s
Early work on probabilistic/statistical methodology
Recognition of need to do analysis of simulation results
Variance reduction for static simulations
Algorithms for variate and process generation
1970s
Advances in probabilistic/statistical methodology
Variance reduction for dynamic simulation
Use of stochastic processes for rigorous output analysis
Simulation languages widened, improved (GASP, SLAM)
1980s
Continued advances in rigorous output analysis
Initialization/termination methods
Adaptation of ranking/selection methods to dynamic
simulation
Languages continue to improve (SIMAN)
Implementation on microcomputers
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Current
Estimating derivatives and gradients of simulated
response
Optimizing simulated systems
Refined, strengthened-output analysis methods
Hybrid analytical/simulation methods
Technology transfer of probabilistic/statistical
methodology to practitioners, languages
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