Introduction to Modeling and Simulation - AcqNotes

1 Introduction TO Modeling AND SIMULATIONAnu MariaState University of New York at BinghamtonDepartment of Systems Science and Industrial EngineeringBinghamton, NY 13902-6000, introductory tutorial is an overview of simulationmodeling and analysis. Many critical questions areanswered in the paper. What is Modeling ? What issimulation? What is Simulation Modeling and analysis?What types of problems are suitable for Simulation ? Howto select Simulation software? What are the benefits andpitfalls in Modeling and Simulation ? The intendedaudience is those unfamiliar with the area of discreteevent Simulation as well as beginners looking for anoverview of the area. This includes anyone who isinvolved in system design and modification - systemanalysts, management personnel, engineers, militaryplanners, economists, banking analysts, and computerscientists.

2 Familiarity with probability and statistics IS Modeling ? Modeling is the process of producing a model; a modelis a representation of the construction and working ofsome system of interest. A model is similar to butsimpler than the system it represents. One purpose of amodel is to enable the analyst to predict the effect ofchanges to the system. On the one hand, a model shouldbe a close approximation to the real system andincorporate most of its salient features. On the otherhand, it should not be so complex that it is impossible tounderstand and experiment with it. A good model is ajudicious tradeoff between realism and practitioners recommend increasing thecomplexity of a model iteratively. An important issue inmodeling is model validity. Model validation techniquesinclude simulating the model under known inputconditions and comparing model output with , a model intended for a Simulation studyis a mathematical model developed with the help ofsimulation software.

3 Mathematical model classificationsinclude deterministic (input and output variables arefixed values) or stochastic (at least one of the input oroutput variables is probabilistic); static (time is not takeninto account) or dynamic (time-varying interactionsamong variables are taken into account). Typically, Simulation models are stochastic and IS Simulation ?A Simulation of a system is the operation of a model ofthe system. The model can be reconfigured andexperimented with; usually, this is impossible, tooexpensive or impractical to do in the system it operation of the model can be studied, and hence,properties concerning the behavior of the actual systemor its subsystem can be inferred. In its broadest sense, Simulation is a tool to evaluate the performance of asystem, existing or proposed, under differentconfigurations of interest and over long periods of is used before an existing system isaltered or a new system built, to reduce the chances offailure to meet specifications, to eliminate unforeseenbottlenecks, to prevent under or over-utilization ofresources, and to optimize system performance.

4 Forinstance, Simulation can be used to answer questionslike: What is the best design for a newtelecommunications network? What are the associatedresource requirements? How will a telecommunicationnetwork perform when the traffic load increases by 50%?How will a new routing algorithm affect itsperformance? Which network protocol optimizesnetwork performance? What will be the impact of a linkfailure?The subject of this tutorial is discrete eventsimulation in which the central assumption is that thesystem changes instantaneously in response to certaindiscrete events. For instance, in an M/M/1 queue - asingle server queuing process in which time betweenarrivals and service time are exponential - an arrivalcauses the system to change instantaneously.

5 On theother hand, continuous simulators, like flight simulatorsand weather simulators, attempt to quantify the changesin a system continuously over time in response tocontrols. Discrete event Simulation is less detailed(coarser in its smallest time unit) than continuoussimulation but it is much simpler to implement, andhence, is used in a wide variety of 1 is a schematic of a Simulation study. Theiterative nature of the process is indicated by the systemunder study becoming the altered system which thenbecomes the system under study and the cycle repeats. Ina Simulation study, human decision making is required atall stages, namely, model development, experimentdesign, output analysis, conclusion formulation, andmaking decisions to alter the system under study.

6 Theonly stage where human intervention is not required isthe running of the simulations, which most simulationsoftware packages perform efficiently. The importantpoint is that powerful Simulation software is merely ahygiene factor - its absence can hurt a Simulation studybut its presence will not ensure success. Experiencedproblem formulators and Simulation modelers andanalysts are indispensable for a successful 1: Simulation Study SchematicThe steps involved in developing a simulationmodel, designing a Simulation experiment, andperforming Simulation analysis are:Step 1. Identify the 2. Formulate the 3. Collect and process real system 4. Formulate and develop a 5. Validate the 6. Document model for future 7. Select appropriate experimental 8. Establish experimental conditions for 9.

7 Perform Simulation 10. Interpret and present 11. Recommend further course of this is a logical ordering of steps in asimulation study, many iterations at various sub-stagesmay be required before the objectives of a simulationstudy are achieved. Not all the steps may be possibleand/or required. On the other hand, additional steps mayhave to be performed. The next three sections describethese steps in TO DEVELOP A SIMULATIONMODEL? Simulation models consist of the following components:system entities, input variables, performance measures,and functional relationships. For instance in a simulationmodel of an M/M/1 queue, the server and the queue aresystem entities, arrival rate and service rate are inputvariables, mean wait time and maximum queue lengthare performance measures, and 'time in system = waittime + service time' is an example of a functionalrelationship.

8 Almost all Simulation software packagesprovide constructs to model each of the abovecomponents. Modeling is arguably the most importantpart of a Simulation study. Indeed, a Simulation study isas good as the Simulation model. Simulation modelingcomprises the following steps:Step 1. Identify the problem. Enumerate problemswith an existing system. Produce requirements for aproposed 2. Formulate the problem. Select the boundsof the system, the problem or a part thereof, to bestudied. Define overall objective of the study and a fewspecific issues to be addressed. Define performancemeasures - quantitative criteria on the basis of whichdifferent system configurations will be compared andranked. Identify, briefly at this stage, the configurationsof interest and formulate hypotheses about systemperformance.

9 Decide the time frame of the study, ,will the model be used for a one-time decision ( ,capital expenditure) or over a period of time on a regularbasis ( , air traffic scheduling). Identify the end userof the Simulation model, , corporate managementversus a production supervisor. Problems must beformulated as precisely as 3. Collect and process real system data on system specifications ( , bandwidth fora communication network), input variables, as well asAlteredSystemSystemUnderStudySimulatio nModelRealWorldSimulationStudySimulation ExperimentSimulationAnalysisConclusions8 Mariaperformance of the existing system. Identify sources ofrandomness in the system, , the stochastic inputvariables. Select an appropriate input probabilitydistribution for each stochastic input variable andestimate corresponding parameter(s).

10 Software packages for distribution fitting andselection include ExpertFit, BestFit, and add-ons in somestandard statistical packages. These aids combinegoodness-of-fit tests, , 2 test, Kolmogorov-Smirnovtest, and Anderson-Darling test, and parameterestimation in a user friendly distributions, , exponential, Poisson,normal, hyperexponential, etc., are easy to model andsimulate. Although most Simulation software packagesinclude many distributions as a standard feature, issuesrelating to random number generators and generatingrandom variates from various distributions are pertinentand should be looked into. Empirical distributions areused when standard distributions are not appropriate ordo not fit the available system data. Triangular, uniformor normal distribution is used as a first guess when nodata are available.