A. Law, D. Kelton, "Simulation modeling & analysis", McGraw-Hill series in industrial engineering and management science, second edition, 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....in T1X1.3. A general treatment of these topics at a basic level is given in Volume 1 of [5] A more advanced treatment is given in [6] A survey of traffic models is given in [7] 2. 1 Types of models In this contribution, we refer to continuous time, discrete time, and discrete event models (see [8] for a more complete discussion) In a continuous time model, the state can change at any instant of time. Usually the state changes are continuous. In a discrete time model, the state can change only at discrete instants of time. These instants are pre defined, and are usually equally spaced. ....

....mean of 0.5 s. Therefore, the utilization of each queue is 0.5. All of the random time intervals (in fact, all random samples in extend) are generated by first generating a pseudo random number that is uniformly distributed between 0 and 1, and then applying an appropriate transformation (see [8] for a discussion of this) The blocks supplied with Extend are constructed such that each instance of a block requires its own seed. This is unfortunate, as it is then extremely difficult to guarantee that the streams produced by the different blocks will not eventually overlap. In the worst ....

Averill M. Law and W. David Kelton, Simulation Modeling & Analysis, McGraw-Hill, New York, 1991.

....with p. Note that the above complexity measures all concern worst case scenarios. It is undoubtedly that an average case analysis would be more appealing for the evaluation. However, due to the dynamic nature of the problem, an averagecase analysis is extremely complicated. Simulation studies [6] are therefore encouraged to provide some insight into the average case behavior of a proposed solution. 3 A Straightforward Decentralized Solution Recall that in Ricart and Agrawala s algorithm [10] for n process mutual exclusion, a process requiring entry to the critical section multicasts a ....

A. M. Law and W. D. Kelton. Simulation modeling & analysis. McGraw-Hill, 1991.

....This often manifests in varying volumes of incoming requests, varying uses of communication channels, varying processing times and varying abort rates. Therefore many stochastic effects have to be taken into consideration and stochastic discrete event simulation seems to be an obvious tool [Law and Kelton 1991]. Simulation can be used to evaluate the performance of specific organizational designs under given environmental factors and allows the selection of the best design for a given purpose [Zapf and Heinzl 2000] Nevertheless there are critical success factors for putting simulation into practice. ....

Law, A.M.; W.D. Kelton. 1991. Simulation Modeling & Analysis. New York et al.

....of the sciences associated with simulation studies is the application of the appropriate statistical techniques when analysing simulation output. After a model has been created and validated, there are a multitude of decisions that need to be made before a study can proceed. Experimental design [84] is concerned with determining which scenarios are going to be simulated and how each of the scenarios will be simulated in a simulation study. For each scenario in a simulation study one needs to decide how many simulations will be run, how long the simulations will be, and how each scenario will ....

....the purpose of the simulation study may be to locate the parameters that have the most impact on a particular performance measure or to locate important parameters in the system. Sensitivity analysis [77] investigates how extreme values of parameters a#ect performance measures. Gradient estimation [84], on the other hand, is used to examine how small changes in numerical parameters a#ect the performance of the system. Optimisation [3] is often just a sophisticated form of comparing alternative configurations, in that it is a systematic method for trying di#erent combinations of parameters in ....

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A. M. Law and W. D. Kelton. Simulation Modeling & Analysis. McGrawHill, 3rd edition, 2000.

....intent is to make the students think about what are the issues with creating and using a simulator since several of them would have most probably to create some kind of simulator in their first few years in industry. The manual includes for a brief description of Discrete Event Simulation (DES) [3], generation of exponential random variables from uniform random variable, and basic input output analysis. Students are expected to use a general purpose language, e.g. C C in our case, together with the DES framework, to build a simulator and illustrate the behavior of the communication ....

Law, A. M., and Kelton, W. D., Simulation Modeling & Analysis, McGraw-Hill, 1991.

....that some messages might be best represented by probability distributions and others might be best represented as a table lookup. Since the Exponential Distribution is often used to represent inter arrival times of customers and messages, this distribution is supported in the prototype system [8]. In addition, the Normal distribution is supported. The current implementation only supports these two distributions, but a wide variety of distributions can be allowed with minimal effort, including Weibull, Gamma, Uniform, Lognormal, various Pearson distributions, and Triangular. Figure 3: ....

Law, A. M. and Kelton, W. D., Simulation Modeling & Analysis, McGraw-Hill, Inc., New York, 1991.

....which they are capable to measure fab utilization. 3.1 CONWIP CONWIP (CONstant WIP) is a classical closed loop lot release control mechanism [4] Its basic idea is to cap cycle times by capping WIP. The origin of this approach is Little s theorem: average WIP = release rate x average cycle time [6]. This theorem holds for arbitrary systems with a utilization of less than 100 . The mechanism requires a WIP threshold for each product. As soon as this threshold is met, new lots from the order pool are only allowed to enter the fab as soon as lots of the same type left the fab. The mechanism ....

Law, A. and W. Kelton. 1991. Simulation Modeling & Analysis. McGraw-Hill, New York, 2 nd edition.

....The strategies are #relatively # easy to implement. # Usage of the assignment as calculated by the linear optimization or the practical #rule of thumb# one. These four parameters are analysed using a 2 k factorial design, giving 16 design points #for description of experimental design, see #Law and Kelton, 1992#, #Box et al. 1978##. The coding chart is shown in table 2. Factor j Parameter 1 N p 2 4 2 # p 45 55 3 # r 35 45 4 assignment thumb LP Table 2: Coding chart For each design point, 5 replications are made, the results are shown in #gure 2. A steady state is reached after a simulation ....

Law, A. M. and Kelton, W. D. #1992#. Simulation Modeling & Analysis. McGraw-Hill.

....4, we present a validation experience, while Section 5 summarizes the paper. 2 VALIDATION Validation is generally defined as the act of determining whether a simulation model reasonably represents or approximates the real system for its intended use (Fishman and Kiviat 1968, Sargent 1982, Law and Kelton 1991). Validation is a purpose specific task. Balci and Sargent (1981) argue that a simulation model should be developed for a specific purpose or application and its adequacy or validity should be evaluated only in terms of that purpose with regard to the relevant experimental frame(s) Moreover, ....

.... frame(s) Moreover, since increasing the validity of a model beyond a certain level may be quite expensive (e.g. more data collection may be required) it is more cost effective for a simulation model to be validated relative to those MOE s that will actually be used for decision making (Law and Kelton 1991). Thus, the purpose of the model determines what aspects of the model to validate and their levels of detail. Determining the validity of a simulation model is not a binary decision in which the model is simply deemed valid or invalid; rather, validity should be considered one of degree depending ....

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Law, A.M., and W.D. Kelton. Simulation Modeling & Analysis, 2nd edition, McGraw-Hill, Inc., 1991.

.... elementary tutorials on selection procedures, the reader should see Goldsman and Nelson (1998ab) some implementation issues are discussed in Goldsman, et al. 1999) and more advanced treatments are given in Gibbons, Olkin, and Sobel (1977) and Bechhofer, Santner, and Goldsman (BSG) 1995) Law and Kelton (1991) describe a number of selection procedures that have proven useful in simulation applications. This paper concerns the use of Rinott s (1978) twostage selection procedure in the simulation environment. Perhaps the key to Rinott s procedure is that it uses its first stage to estimate the ....

Law, A. M., and W. D. Kelton. 1991. Simulation Modeling & Analysis. 2nd ed. New York: McGraw-Hill, Inc.

....criteria for a well known selection problem. 1 INTRODUCTION This paper considers the problem of comparing a small number of systems, say 2 to 20, in terms of the expected value of some given stochastic performance measure. The performance of each system is estimated by a simulation experiment (Law and Kelton 1991; Banks, Carson, and Nelson 1996) and the goal is to efficiently identify the best system, where best is defined as having the maximum expected performance. The performance of each system must be estimated with a finite number of simulation replications, so it is impossible to guarantee that ....

....better than the other systems. Most relevant research assumes that the simulation output is independent. On the other hand, common random numbers (CRN) is a variance reduction technique that can be used to sharpen comparisons by inducing a positive correlation between the output of each system (Law and Kelton 1991; Banks, Carson, and Nelson 1996) CRN can be implemented, for example, by causing the j th simulation replication of each system to observe the same demand patterns. Clark and Yang (1986) and Nelson and Matejcik (1995) are exceptions that present procedures for selecting the best system when CRN ....

Law, A. M. and W. D. Kelton. 1991. Simulation Modeling & Analysis (2nd ed.). New York: McGraw-Hill, Inc.

.... and Nelson (1994) provide an excellent survey of ranking, selection, and multiple comparison techniques for selecting 360 An Asymptotic Allocation for Simultaneous Simulation Experiments the best system (e.g. Gupta and Panchapakesan 1979, Kleijnen 1987, Goldsman, Nelson, and Schmeiser 1991, and Law and Kelton 1991). In addition, Bechhofer, Santner, and Goldsman (1995) give a systematic and more detailed discussion on this issue. These approaches are mainly suitable for problems having a small number of competing designs. However, for large scale industrial problems, the number of designs can rapidly grow ....

Law, A. M. and W. D. Kelton, 1991. Simulation Modeling & Analysis. McGraw-Hill, Inc.

....for service in queues. In addition, delays between state changes are usually represented by statistical distributions. 2.1. 1 Components of Discrete Event Simulation Researchers have identified several components common to all discrete event simulation in the past several decades (Kreutzer, 1986; Law, Kelton, 1991; Watkins, 1993) 1. Model structuring and execution facilities. As stated previously, a model is a collection of entities interacting with each other. Object oriented languages, such as C (Stroustrup, 1991) and Java (Flanagan, 1996; Naughton, 1996) allow us to represent entities as objects, ....

....called LCGRandom. The recursive formula for LCG is: Z i = aZ i Gamma1 m (4.3) where the multiplier a is 7 5 and the modulus m 2 31 Gamma 1. The LCG random number generator has a very long period, and it has been statistically proven that it provides good inter sample independence (Law, Kelton, 1991). It produces random numbers in the range of (0, 1) The Variate class serves a base class for all other variate generators. It uses the LCGRandom random number generator. However, users of this simulation library can easily change to use some other random number generator, such as Java s Random ....

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Law, A.M., & Kelton, W.D. (1991). Simulation modeling & analysis (2nd ed.). New York: McGraw-Hill.

....long uniformly distributed sequence [Tausworthe 1965; Saarinen et al. 1991; Barel 1983] Such a sequence can be converted to any other distribution by a table lookup and interpolation. For example, the alias method can be used to generate any discrete random variate having a finite range of values [Law and Kelton 1991; Walker 1977; Kronmal and Peterson 1979] The local memory of each traffic generator module can be used for storing the necessary lookup tables. More complex traffic models, for example a video stream, that can be modeled using Markov chains can be synthesized by implementing the Markov chain in ....

Law, A. and Kelton, W. 1991. Simulation Modeling & Analysis. Mc-Graw Hill, Inc.

.... organizes the definition of attributes, methods and general characteristics of each system component without going so far as to ascribe dynamics to components. The next four model types reflect an orientation to system construction; a system may be constructed as a Petri net [7] queuing model [8] or as a cellular automaton [9] for instance. The last model type (multimodel) permits the integration of basic model types to create a model composed of component models [10] 11] where each component model represents a level of abstraction for the system. 2 IEEE TRANSACTIONS ON SYSTEMS, MAN ....

Law, Averill M. and Kelton, David W., Simulation Modeling & Analysis, McGraw Hill, 1991, Second edition.

....the different architectures scale, that is how they behave when the number of nodes increases. All our testruns were conducted on SGIs, using the operating system IRIS 5.3. 4.1. 3 Confidence Interval We use the confidence interval as a statistical analysis for terminating the simulation runs [LK91] For each experiment, we make n independent replications of a simulation. The independence of the replications is accomplished by using different random number seeds for the generation of the transactions. Each test run results in a throughput X i , 1 = i = n. We calculate X(n) as a point ....

....of the throughput lies with a probability of 100(1 Gamma ff) within this interval. The confidence interval for is given by X(n) Sigma t n Gamma1;1 Gammaff=2 s S 2 (n) n where t n Gamma1;1 Gammaff=2 are called upper critical points and can be looked up in tables (e.g. Table T. 1 of [LK91] Our simulation runs with record locking achieved very stable results. With less than five test runs we achieved a 90 confidence interval for the mean of the throughput that did not vary more than 1 from the mean. That means, if, for example X(n) 3000, then the exact mean lies with a ....

A. M. Law and W. D. Kelton. Simulation Modeling & Analysis, chapter 4,9. McGraw-Hill, 1991.

....of covariance stationarity. Equation (1) provides a basis for computing a confidence interval for ff based on ff(n) if an estimator for oe 2 can be computed. Several estimators for oe 2 have been proposed in the literature; see chapter 3 of Bratley, Fox and Schrage (1987) or chapter 8 of Law and Kelton (1991) for an overview. In selecting an estimator V (n) for oe 2 , one typically takes into account the properties of X (e.g. is it easy to define regeneration epochs for X ) Of course, one should also take into account the computational effort involved in computing V (n) as the following analysis ....

Law, A. M. and W. D. Kelton. 1991. Simulation Modeling & Analysis, 2nd edition. McGraw Hill, New York.

....(12) is asymptotically given by n Gamma1 kp Uk 2 4 =n Gamma1 (p U) 0 (p U) 13) Standard control variate methodology suggests that one could estimate the covariance matrix (or U 0 U ) and then choose to minimize the vector norm (13) 16, p. 640] However, as cautioned in [16], there is the danger of a variance increase associated with the additional estimation of the covariance matrix. The loss factor is discussed in [15] and [23] for terminating simulations, and in [18] for steady state simulation. The loss 16 factor can become an issue when many control variables ....

Law, A. M. and W. D. Kelton. (1991). Simulation Modeling & Analysis, 2nd ed. McGraw Hill, New York.

....on a regular basis or not. The probability distributions that drive the model can be obtained in different ways. If we have data from a real system, we can use the data directly (trace driven) or we can define an empirical distribution, or we can fit the data onto a theoretical distribution [1]. If we do not have real data, we need to choose a theoretical distributionthat matches our intuition. A sensible distribution to choose (when requests are generated independently) is a Poisson distribution for event inter arrival times [5] We summarize the model parameters in Figure 3. The ....

W. David Kelton Averill M. Law. Simulation Modeling & Analysis. McGraw-Hill, 1991.

....fS (U n )g appears smoother than the underlying fU n g. Moreover, all S ; 0 1, preserve uniformity [25] i.e. S (U n ) is also distributed uniformly on [0; 1) The outer transformation, F Gamma1 , is the inverse of some distribution function F . Notice that by the inversion method [3, 17], each X n in (2.4) has marginal distribution F . Consequently, distortions of the form D(x) F Gamma1 (S (x) x 2 [0; 1] allow us to generate foreground sequences with any prescribed marginal distribution F . In particular, we can match any empirical distribution function H, obtained from ....

A.M. Law and W.D. Kelton. Simulation Modeling & Analysis, (second edition). McGraw-Hill, 1991. 14

....of steady state behaviors. In order to get statically significant simulation results, the determination of how to drive the effects of initial bias to be negligible should be carefully managed. For the purpose of accounting for the initial transient phase, we employ the initial data deletion method[4,5] in that this technique is the most often suggested and accepted for dealing with the initial transient. The idea is to delete a certain number of observations, considered to be insignificant, from the beginning of a run and to use only the remaining observations to estimate the steady state mean. ....

....behavior due to initial transient behaviors. The issue of the initial transient phase is how to choose the warmup period l reasonably. In this paper, we use the graphical procedure [6] to determine l since this has been generally accepted as a proper method to estimate the initial transient phase [5]. The transient phase, of course, does not end at a particular point, but the idea of Welch s procedure is to test the convergence of the mean of the distribution by way of plotting the sequence of the mean in a graph. In order to utilize that procedure, we executed preliminary independent 10 ....

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A. Law, and W. Kelton, "Simulation Modeling & Analysis," Second Edition, McGraw-Hill, 1991.

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A. Law, D. Kelton, "Simulation modeling & analysis", McGraw-Hill series in industrial engineering and management science, second edition, 1991.

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Law, A. M. and W. D. Kelton, 1991. Simulation Modeling & Analysis. McGraw-Hill, Inc.

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Law, A.M. and Kelton, W.D. (1991) Simulation Modeling & Analysis, (second edition), McGraw-Hill.

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In preparation. Law, A. M. and W. D. Kelton. 1991. Simulation Modeling & Analysis, 2nd ed. McGraw Hill, New York.

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