Chapter 8: Simulation Analysis

---

Overview

Simulation is the realization of a model for a system in computer executable form. That is, the model of the real-world system has been translated into a computer simulation language. The computer realization provides a vehicle to conduct experiments with the model in order to gain insight into the behavior and makeup of the system or to evaluate alternatives. Simulations, to be effective, require a precise formulation of the system to be studied, correct translation of this formulation into a computer program, and interpretation of the results.

Simulation is usually undertaken because the complexity of most computer systems defies use of simpler mathematical means for realistic performance studies. This complexity may occur from inherent stochastic processes in the system, complex interactions of elements that lack mathematical formulations, or the sheer intractability of mathematical relationships that result from the system's equations and constraints. Because of these constraints and other reasons, simulation is often the tool for evaluation. Simulation provides many potential benefits to the modeler. It makes it possible to experiment and study the myriad complex internal interactions of a particular system, with the complexity left up to the modeler.

Simulation allows for the sensitivity analysis of the system by providing a means to alter the model and observe the effects it has on the system's behavior. Through simulation we can often gain a better understanding of the real system. This is because of the detail of the model and the modeler's need to independently understand the computer system in order to faithfully construct a simulation of it. The process of learning about the system in order to simulate it will often lead to suggestions for change and improvements. The simulation then provides a means to test these hypotheses. Simulation often leads to a better understanding of the importance of various elements of a system and how they interact with each other. It provides a laboratory environment in which we can study and analyze many alternatives and their impact well before a real system even exists or, if one exists, without disturbing or perturbing it. Simulation enables the modeler to study dynamic systems in real, compressed, or expanded time, providing a means to examine details of situations and processes that otherwise could not be performed. Finally, it provides a means to study the effects on an existing system of adding new components, services, and so on without testing them in the system. This provides a means to discover bottlenecks and other problems before we actually expend time and capital to perform the changes.

Simulation has been used for a wide variety of purposes, as can be seen from the diversity of topics covered at annual simulation symposiums. Simulation easily lends itself to many fields, including business, economics, marketing, education, politics, social sciences, behavioral sciences, natural sciences, international relations, transportation, war gaming, law enforcement, urban studies, global systems, space systems, computer design and operations, and myriad others.

Up to this point we have used "system" to describe the intended modeled entity. In the context of simulation, it is used to designate a collection of objects with a well-defined set of interactions between them. A bank teller interacts with the line of customers, and the job the teller does may be considered a system in this context, with the customers and tellers forming the objects and the functions performed by each (deposit, withdrawal) as the set of interactions.

Systems by nature are typically described as being continuous or discrete, where these terms imply the behavior of the variables associated with the system. They provide us, the modelers, with a context in which to place the model and on which to build. In both cases, the typical relation of variables is built around time. In the case of the discrete model, time is assumed to step forward in fixed intervals determined by the events of occurrence versus some formulation, and in the continuous model, the variables change continually as time ticks forward. For example, with the bank scenario, if the variable of interest is the number of customers waiting for service, we have a dependent discrete "counting" sequence. On the other hand, if we are looking at a drive-up bank teller and are interested in the remaining fuel in each vehicle and the average, we could model the gasoline consumption as a continuous variable dependent on the time in line until exiting.

Systems can possess both discrete and continuous variables and still be modeled. In reality, this is frequently the case. Another consideration in defining a system is the nature of its processes. Processes, whether they are discrete or continuous, can have another feature, that of being deterministic or stochastic. A deterministic system is where, given an input x and initial conditions i, you will always derive the same output: y = f (x, i). That is, if we were to perform the same process an infinite number of times, with the same inputs and same initial state of the process, we would always realize the same result.

On the other hand, if the system were stochastic, this would not hold. For the same system with input held at X and initial state held at I, we could have the output Y take on one of many possible outputs. This is based on the random nature of stochastic processes. That is, they will be randomly distributed over the possible outcomes. For example, if the bank teller system is described as a discrete system, we are assuming that the service time of the server is exactly the same and the arrival rate of customers is fixed and nonvarying. However, if the same system is given some reality, we all know that service is random, based on the job the tellers must perform and how they perform it. Likewise customers do not arrive in perfect order; they arrive randomly. In both cases the model will give vastly different results.

---