Modern Simulation Analysis



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.

Methods of Studying a System

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Types of Models

Useful dimensions of classification with regard to design/analysis: Dynamic vs. Static, Stochastic vs. Deterministic, Discrete vs. Continuous

Some examples:

| | |Deterministic |Stochastic |

| | |No randomness |Random inputs—uncertain |

| | |Inputs are exact, no uncertainty |Inputs are from known distributions |

| | |One model needs only one run |One model needs more than one run |

|Static |No time element |Use fitted regression model for unobserved |“Monte Carlo” simulation |

| | |independent-variable combinations |Estimate an intractable integral |

| | |Financial scenarios |Get empirical distribution of a new test statistic for |

| | | |some null hypothesis |

|Dynamic |Passage of time is |Differential-equation models of population growth and|Queueing models representing manufacturing, computer, |

| |important part of |decay |or communications systems |

| |model |Deterministic forecasting over time |Inventory models |

| | |Dynamic macroeconomic models | |

| | |Compute (exactly) desired output quantities |Can only estimate desired output quantities |

Advantages and Disadvantages of Simulation

Compared to experimenting with the actual system:

6 Validity uncertainty with simulation (as with all models)

4 Much more flexibility in simulation to try things out

4 Can control the uncontrollable in simulation

4 Can study the physically impossible or non-existent

Compared to exact analytical models:

4 Don’t have to make as many simplifying assumptions—get more flexible models that can be more valid

6 Don’t get simple formulas from which insight can be gained

6 Don’t get exact answers—only estimates, maybe uncertain—calls for careful design and analysis of simulation experiments (our concern)

Steps in a Simulation Model

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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

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:

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A Brief History

|1733 |Buffon needle problem—estimate π |

|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 |

|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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