Experiment Design and Analysis
The purpose of simulation, at least in this book, is to estimate the values of performance measures of a stochastic system by conducting a statistical experiment on a computer model of it. This chapter describes principles and methods for the design and a
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Experiment Design and Analysis
The purpose of simulation, at least in this book, is to estimate the values of performance measures of a stochastic system by conducting a statistical experiment on a computer model of it. This chapter describes principles and methods for the design and analysis of that experiment. We have considered several different performance measures, including means, probabilities and quantiles, sometimes for systems with a natural time horizon, and sometimes for steady-state systems (as time goes to infinity). For this initial overview, let θ (x) denote a generic performance measure for scenario x. A “scenario” defines a specific instance of a more general system. For example, the scenario variable x could be a vector of cardinal values (e.g., x = (15, 9, 6, 3) denotes the number Entry Agents and Specialists assigned before and after noon, respectively, in the fax center simulation of Sect. 4.6) or nominal values (e.g., x = 2 denotes the system design for the hospital reception of Sect. 4.3 that employs an electronic kiosk, while x = 1 denotes the current design with a human receptionist). What we call the scenario variable is sometimes called a decision variable, and having it will be useful when we consider comparing system designs to answer questions such as “What is the probability of a special fax being entered in less than 10 minutes when we use a staff of x = (15, 9, 6, 3) agents?” The reason for conducting a simulation experiment is to produce an estimator of θ (x), denoted by θ(x; T, n, U), which is a function of x and up to three additional quantities: Stopping time T : The stopping time is the simulation clock time at which a replication ends; it can be a fixed time (“simulate 8 hours, from 8 AM to 4 PM”) or a random time (“simulate until the stochastic activity network completes” or “simulate until the system fails”). In some contexts T is called runlength. See also the Remark at the end of this section. Number of replications n: The number of independent and identically distributed replications of the simulation may also be fixed (n = 30) or random (“simulate until the width of the confidence interval for θ (x) is less than 3 minutes”).
B.L. Nelson, Foundations and Methods of Stochastic Simulation: A First Course, International Series in Operations Research & Management Science 187, DOI 10.1007/978-1-4614-6160-9 8, © Springer Science+Business Media New York 2013
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8 Experiment Design and Analysis
(Pseudo)random numbers U: The estimator θ(x; T, n, U) is a random variable because we treat U as random numbers. Of course, we will actually use pseudorandom numbers; therefore, we may also think of U as a fixed set of numbers, say u1 , that can be reused by fixing the starting seed or stream. Experiment design consists of selecting the scenarios x to simulate, controlling the number of replications n to obtain, assigning the pseudorandom numbers U to drive the simulations and, in steady-state simulation, setting the stopping time T . Notice that whether or not T is part o
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