Discrete-Event System Simulation

Introduction

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A simulation is the imitation of the operation of a real-world process or system over time. Whether done by hand or on a computer, simulation involves the generation of an artificial history of a system and the observation of that artificial history to draw inferences concerning the operating characteristics of the real system.

The behavior of a system as it evolves over time is studied by developing a simulation model. This model usually takes the form of a set of assumptions concerning the operation of the system. These assumptions are expressed in mathematical, logical, and symbolic relationships between the entities, or objects of interest, of the system. Once developed and validated, a model can be used to investigate a wide variety of “what if” questions about the real-world system. Potential changes to the system can first be simulated, in order to predict their impact on system performance. Simulation can also be used to study systems in the design stage, before such systems are built. Thus, simulation modeling can be used both as an analysis tool for predicting the effect of changes to existing systems and as a design tool to predict the performance of new systems under varying sets of circumstances.

Simulation Examples in a Spreadsheet

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This chapter uses spreadsheet examples to provide an introduction to simulation. The examples are relatively simple; many can be carried out manually as well as in a spreadsheet. Our main purpose is to introduce and illustrate some of the key concepts in simulation; it is not to teach how to formulate or develop a spreadsheet model, but rather to use a few simple spreadsheet models to illustrate, by example, some of the key elements of any simulation. These key elements range from the components of a model to experimentation with the model.

Although some types of real-world simulation models, such as those for risk analysis, financial analysis, some reliability problems and others, are amenable to a spreadsheet formulation and solution, the spreadsheet has severe limitations for most complex real-world dynamic, event-based simulations. More often, these complex models are developed in a simulation package or general purpose programming language, not in a spreadsheet.

General Principles

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This chapter develops a common framework for the modeling of complex systems by using discreteevent simulation. It covers the basic building blocks of all discrete-event simulation models: entities and attributes, activities, and events. In discrete-event simulation, a system is modeled in terms of its state at each point in time; of the entities that pass through the system and the entities that represen system resources; and of the activities and events that cause the system state to change. Discrete-event models are appropriate for those systems for which changes in system state occur only at discrete points in time.

The discussion in this chapter focuses on the discrete-event concepts and methodologies of simulation languages and software (collectively called simulation packages).

This chapter introduces and explains the fundamental concepts and methodologies underlying al discrete-event simulation packages. These concepts and methodologies are not tied to any particular package. Many of the packages use different terminology from that used here, and most have a number of higher-level constructs designed to make modeling simpler and more straightforward for their application domain. For example, this chapter discusses the fundamental abstract concept of an entity, but not covered are more concrete realizations of entities, such as machines, conveyors, and vehicles that are built into some of the packages to facilitate modeling in the manufacturing, materia handling, or other domains

About this edition

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Simulation Software

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In this chapter, we first discuss the history of simulation software and speculate on its future. Simulation software has a history that is just reaching middle age. We base this history on our collective experience, articles written by Professor Richard Nance, panel discussions at the annual Winter Simulation Conference, and a recent article by one of the co-authors.

Next, we discuss features and attributes of simulation software. If you were about to purchase simulation software, what would concern you? Would it be the cost, the ease of learning, the ease o use, or would it be the power to model the kind of system with which you are concerned? Or would it be the animation capabilities? Following the discussion of features, we discuss other issues and concerns related to the selection of simulation software.

Statistical Models in Simulation

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In modeling real-world phenomena, there are few situations where the actions ofthe entities within the system under study can be predicted completely. The world the model builder sees is probabilistic rather than deterministic. There are many causes of variation. The time it takes a repairperson to fix a broken machine is a function of the complexity of the breakdown, whether the repairperson brought the proper replacement parts and tools to the site, whether another repairperson asks for assistance during the course ofthe repair, whether the machine operator receives a lesson in preventive maintenance, and so on. To the model builder, these variations appear to occur by chance and canno be predicted. However, some statistical model might well describe the time to make a repair.

Queueing Models

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Simulation is often used in the analysis of queueing models. In a simple but typical queueing model, shown in Figure 1, customers arrive from time to time and join a queue (waiting line), are eventually served, and finally leave the system. The term customer refers to any type of entity that can be viewed as requesting service from a system. Therefore, many service facilities, production systems, repair and maintenance facilities, communications and computer systems, and transport and material-handling systems can be viewed as queueing systems.

Queueing models, whether solved mathematically or analyzed through simulation, provide the analyst with a powerful tool for designing and evaluating the performance of queueing systems. Typical measures of system performance include server utilization (percentage of time a server is busy), length of waiting lines, and delays of customers. Quite often, when designing or attempting to improve a queueing system, the analyst (or decision maker) is involved in tradeoffs between server utilization and customer satisfaction in terms of line lengths and delays. Queueing theory and simulation analysis are used to predict these measures of system performance as a function of the input parameters. The input parameters include the arrival rate of customers, the service demands of customers, the rate at which a server works, and the number and arrangement of servers. To a certain degree, some of the input parameters are under management’s direct control. Consequently, the performance measures could be under their indirect control, provided that the relationship between the performance measures and the input parameters is adequately understood for the given system.

Random-Number Generation

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Random numbers are a necessary basic ingredient in the simulation of almost all discrete systems. Most computer languages have a subroutine, object, or function that will generate a random number. Random numbers are used to generate event times and other random variables in simulation languages. In this chapter, the generation of random numbers and their subsequent testing for randomness is described.

1 Properties of Random Numbers

A sequence ofrandom numbers, $R_{1} , R_{2} , \ldots ,$ , must have two important statistical properties: uniformity and independence. Each random number $R_{i}$ must be an independent sample drawn from a continuous uniform distribution between zero and 1—that is, the pdf is given by

Random-Variate Generation

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This chapter deals with procedures for sampling from a variety ofwidely used continuous and discrete distributions. Previous discussions and examples indicated the usefulness of probability distributions in modeling activities that are generally unpredictable or uncertain. For example, interarrival times and service times at queues and demands for a product are quite often unpredictable in nature, a least to a certain extent. Usually, such variables are modeled as random variables with some specified probability distribution, and standard statistical procedures exist for estimating the parameters of the hypothesized distribution and for testing the validity of the assumed statistical model.

In this chapter, it is assumed that a distribution has been completely specified, and ways are sough to generate samples from this distribution to be used as input to a simulation model. The purpose of the chapter is to explain and illustrate some widely used techniques for generating random variates, not to give a state-of-the-art survey of the most efficient techniques. In practice, most simulation modelers will use either existing routines available in programming libraries or the routines built into a simulation language. However, some programming languages do not have built-in routines for all of the regularly used distributions, and some computer installations do not have random-variategeneration libraries; in such cases the modeler must construct an acceptable routine. Even though the chance of this happening is small, it is nevertheless worthwhile to understand how random-variate generation occurs.

Input Modeling

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Input models provide the driving force for a simulation. In the simulation ofa queueing system, typica input models are the distributions of time between arrivals and of service times. For a supply-chain simulation, input models include the distributions of demand and of lead time. For the simulation of a reliability problem, the distribution of time to failure of a component is an example of an input model.

In real-world simulation applications, choosing appropriate distributions for input data is a major task from the standpoint of time and resource requirements. Regardless of the sophistication of the analyst, faulty models of the inputs will lead to outputs whose interpretation could give rise to misleading recommendations.

There are four steps in the development of a useful model of input data:

Verification and Validation of Simulation Models

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One ofthe most important and difficult tasks facing a model developer is the verification and validation of the simulation model. The engineers and analysts who use the model outputs to aid in making design recommendations and the managers who make decisions based on these recommendations— justifiably look upon a model with some degree of skepticism about its validity. It is the job o the model developer to work closely with the end users throughout the period of development and validation to reduce this skepticism and to increase the model’s credibility.

The goal of the validation process is twofold: (a) to produce a model that represents true system behavior closely enough for the model to be used as a substitute for the actual system for the purpose of experimenting with the system, analyzing system behavior, and predicting system performance; and (b) to increase the credibility of the model to an acceptable level, so that the model will be used by managers and other decision makers.

Estimation of Absolute Performance

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Output analysis is the examination of data generated by a simulation. Its purpose is either to predic the performance ofa system or to compare the performance oftwo or more alternative system designs. This chapter deals with estimating absolute performance, by which we mean estimating the value of one or more system performance measures as opposed to the comparison of two or more systems, in other words relative performance.

The need for statistical output analysis is based on the observation that the output data from a simulation exhibits random variability when random-number generators are used to produce the values of the input variables—that is, two different streams or sequences of random numbers wil produce two sets ofoutputs, which (probably) will differ. Ifthe performance ofthe system is measured by a parameter $\theta ,$ the result ofa set ofsimulation experiments will be an estimator θ ofθ. The precision of the estimator $\widehat {\theta}$ can be measured by the standard error of $\widehat {\theta}$ -or by the width of a confidence interva - -for θ. The purpose of the statistical analysis is either to estimate this standard error or confidence interval or to figure out the number of observations required to achieve a standard error or confidence interval of a given size—or both.

Estimation of Relative Performance

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This chapter discusses a few of the many statistical methods that can be used to compare the relative performance of two or more system designs. This is one of the most important uses of simulation. Because the observations of the response variables contain random variation, statistical analysis is needed to discover whether any observed differences are due to differences in design or merely to the random fluctuation inherent in the models.

The comparison of two system designs is easier than the simultaneous comparison of multiple system designs. Section 1 discusses the case of two system designs, using two possible statistica techniques: independent sampling and correlated sampling. Correlated sampling is also known as the common random numbers (CRN) technique; simply put, the same random numbers are used to simulate both alternative system designs. If implemented correctly, CRN usually reduces the variance of the estimated difference of the performance measures and thus can provide, for a given sample size, more precise estimates of the mean difference than can independent sampling. Section 2 extends the statistical techniques of Section 1 to the comparison of multiple (more than two) system designs using simultaneous confidence intervals, screening and selection of the best. These approaches are somewhat limited with respect to the number of system designs that can be considered, so Section 3 describes how a large number of complex system designs can sometimes be represented by a simpler

Simulation of Manufacturing and Material-Handling Systems

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Manufacturing and material-handling systems provide one of the most important applications of simulation. Simulation has been used successfully as an aid in the design of new production facilities, warehouses, and distribution centers. It has also been used to evaluate suggested improvements to existing systems. Engineers and analysts using simulation have found it valuable for evaluating the impact of capital investments in equipment and physical facility and of proposed changes to material handling and layout. They have also found it useful to evaluate staffing and operating rules and proposed rules and algorithms to be incorporated into production control systems, warehousemanagement control software, and material-handling controls. Managers have found simulation useful in providing a “test drive” before making capital investments, without disrupting the existing system with untried changes.