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This paper presents results of experimentation aimed at identifying suitable starting rules for discrete event simulations. A starting rule is a decision rule that tells a simulation analyst when to begin collecting data that are relatively free of the initial conditions of a simulation. The starting rules described here rely for decision making on a comparison between a priori information on interarrival and service times and corresponding sample quantities computed during the course of a simulation. Testing of the first proposed rule on a single-server queueing simulation with exponential interarrival and serice times revealed a serious inadequacy. However, an examination of just how this inadequacy arose led to a second proposal for a starting rule. When tested in a parallel simulation the second rule produced considerably more favorable results. In addition, a perusal of the distribution of starting time for 1000 replications suggests a direction for future research aimed at reducing this starting time. (Author)

This paper discusses a procedure for interval estimation of the mean theta of a correlated binary (0,1) sequence. The method assumes that the sequence is strictly stationary and that a particular string of m binary digits is a recurrent event in the sequence, where mor = to 1 is unknown. Of the 2 m squared choices for the possible recurrent events, the strings of all zeros and of all ones are examined.

This paper describes a method of sampling from the binomial distribution beta(n,p) that appears less costly than the beta method recently suggested by Relles and Ahrens and Dieter. The method uses the acceptance-rejection technique together with an efficient sampling algorithm for the Poisson distribution.

This paper presents results of applying the runs up and down test, the chi-square goodness-of-fit test and the serial test to streams of pseudorandom numbers generated by the pseudorandom number generators implemented in the IBM version of SIMSCRIPT II.5, in SIMPL/1 and using their default seeds. Although this limited testing prevents general conclusions, the results presented here do identify several areas of concern.

This paper describes a method of generating gamma variates that appears to be less costly than other methods. For large shape parameter alpha the cost of computation is proportional to square root of alpha, whereas the other method is proportional to alpha. Experimentation also indicates that for small alpha the method suggested here also dominates other recently suggested methods, albeit those methods dominate for large alpha. The method suggested here uses the rejection technique.

This paper illustrates the use of continuous time Markov processes as a basis for analyzing the results of discrete event digital simulations. In particular, the paper describes how judicious use of bit packing enables a user to write an otherwise lengthy state description in concise form for convenient use within an ongoing program. It also describes a procedure for selecting which among the many possible regeneration states allows a user to collect data most efficiently for analysis.

This paper extends the use of the regenerative property of queueing systems in the analysis of simulation output. In particular, it describes a sequential estimation method which when used with the regenerative property allows results to be obtained with specified statistical accuracy. This method includes a test to check the normality assumption on which the sequential procedure relies. The paper illustrates the method using the empty and idle state as the regenerative states. A second example then describes how using the most frequently entered state as the regenerative state reduces the chance of making a costly error in a preliminary simulation run. The paper also describes how a variance reduction method can be used to obtain a specified accuracy with considerably fewer job completions than are required when no variance reduction technique is applied., Report on Curriculum in Operations Research and Systems Analysis.

Sensitivity analysis, which represents an integral part of virtually every study of system reliability, measures variation in this quantity in response to changes in component reliabilities or in system design. Replacing old components with new ones with higher reliabilities affects system reliability. As time elapses, system reliability deteriorates when a non replacement policy for components all affect system reliability. Sampling variation in component reliability estimates induce sampling variation in the corresponding system reliability estimate. Having access to a model that accurately predicts these changes in system behavior allows one to make considerably more well informed decisions for maintaining or enhancing performance. This paper presents a method for estimating variation in system reliability in response to variation in component reliabilities. It describes a Monte Carlo sampling plan that on each of w sets of distinct component reliabilities. It describes a Monte Carlo sampling plan that on each replication provides sample data that contribute to the estimation of system reliability for each w sets of distinct component reliabilities. The sets may represent alternative component replacement plans, deteriorating component reliabilities at a succession of time points or extremal points of simultaneous component reliability interval estimates (Fishman 1987). For purposes of exposition, we focus on s-t reliability but emphasize that the concepts discussed here also apply to other definitions of system reliability. Keywords: Coefficients; Polynomials; Confidence intervals.

This paper studies how sampling variation in component reliability estimates affects the computation of system reliability that uses these estimates as input. Results show that relative bias in system reliability grows quadratically with the number of components for which each component reliability estimate is used whereas the corresponding coefficient of variation grows linearly with this number of components. If these components are in parallel they lead to an understatement of system reliability. In series, they lead to an overstatement. The paper describes resampling schemes that eliminate bias without increasing the dominant variance term. (Keywords: operations research; systems analysis; statistical accuracy).

The computation of system reliability from component reliabilities presents a host of non-trivial problems for systems of varying sizes. These include the functional relationship between the time required to compute system reliability and system size. A second problem concerns how system reliability varies as component reliabilities vary. A third problem concerns how statistical errors in estimating component reliabilities affect the accuracy of the system reliability computation. This paper describes Monte Carlo techniques which provide useful answers to the first two problems and presents an analysis which establishes the potential seriousness of the third problem in practice.

This paper describes a new procedure for estimating parameters of a stochastic activity network of N arcs. The parameters include the probability that path m is the longest path, the probability that path m is the shortest path, the probability that arc i is on the longest path and the probability that arc i is on the shortest path.

This paper describes a numerical method based on quasirandom points for estimating the probability g(s,t) that vertices s and t are connected in an undirected network G=(V,M) with V perfect vertices and M randomly and independently failing edges.

This paper describes an algorithm and a FORTRAN subprogram, CHAIN, for simulating the behavior of an (n+1) state Markov chain using a variance reducing technique called rotation sampling. The simulation of k microreplications is carried out in parallel at a mean cost or = O(1n k) and with variances of sample quantities of interest or = O((1n k squared)/k squared). The program allows for independent macroreplications, each of k microreplications, in order to faciliate estimation of the variances of sample quantities of interest. The paper describes theoretical results that underlie the algorithm and program in Section 1 and presents applications of interest for first passage time and steady-state distributions in Section 2. Section 3 describes the algorithm and CHAIN and an example in Section 4 illustrates how CHAIN works in practice. Section 5 describes the options available for restarting the simulation. (Author)

The purpose of this paper is to review five alternative methods of generating a Poisson distributed random variable on a digital computer.

This paper describes a cutpoint method for sampling from an n-point discrete distribution that preserves the monotone relationship between a uniform deviate and the random variate it generates. This property is useful when developing a sampling plan to reduce variance in a Monte Carlo or simulation study. The alias sampling method generally lacks this property and requires 2n storage locations while the proposed cutpoint sampling method requires m+n storage locations, where m donotes the number of cutpoints. The expected number of comparisons with this method is derived and shown to be bounded above by (m + n - 1/n. The paper describes an algorithm to implement the proposed method as well as two modifications for cases in which n is large and possibly infinite. (Author)

The paper presents two methods for modeling cyclic inputs to a congested system in a discrete event digital simulation. Specifically, it is assumed that the interarrival times follow a probability distribution whose parameters are functions of time. Assuming that the conditional interarrival times follow a given underlying distribution, the mean or a function of the mean is expressed as a linear combination of harmonic components whose coefficients can be determined by stepwise regression. The results can in turn be used in generating the desired inputs for simulations. Examples based on sample data are used to illustrate the two models and to evaluate their goodness of fit. (Author)

The document discusses an algorithm for automatically estimating and collecting the sample size required for statistical precision in a computer simulation experiment while the simulation is running. The algorithm, which would be incorporated directly into the computer routines, would relieve an investigator of the burden of first estimating the variance of the sample mean from a data sample obtained from a trial run, then estimating the sample size necessary for the specified confidence interval, and finally collecting that many more observations in a successive simulation run. The underlying probability model is autoregressive: it would depend on an autoregressive representation of the sequence that considers each observation as a linear combination of past observations plus an uncorrelated random residual. This approach need not require more than 4 or 5 autocovariance computations to estimate the variance of the sample mean. A flowchart is included to aid in building the technique into simulation programs.

The components of the variance of price are analyzed. In the models considered, a price process is assumed to be evolving through time. It is composed of fluctuations of different lengths of time. The relative importance of these fluctuations in shaping the over-all process may show how well a particular model leads to the price behavior commonly observed. This elaboration will extend the traditional synthesis by means of the theory of stationary time series, or more precisely, the spectral representation of such series. Questions to be answered are, for example: What is the relative importance of fluctuations of different lengths of time in the price process. How will reducing the production period affect price. How influential are price expectations on price. Attention is restricted to situations wherein temporary shifts in economic phenomena are dominant over permanent changes in the economic structure. This focus precludes any change in the equilibrium price and, therefore, simplicity dictates that deviation from equilibrium only be considered.

The paper describes three alternative methods for performing a statistical analysis on the output of queueing simulations. One method makes use of the renewal property of certain queueing systems. The second makes use of the periodic sampling of the processes of interest in the simulation and the third relies on the job completion times to indicate when the processes should be sampled. The paper describes each methods's benefits and disadvantages. In particular it is shown that a priori information regarding interarrival and service times can be incorporated into all three method to reduce significantly the amount of data needed to estimate a substantial number of system descriptors. (Author)

The paper presents methods for computing point and interval estimates of descriptors of simulated queueing systems. The methods, which rely on the renewal process representation of certain queueing models, extend the results of previous papers. In particular, two suggested procedures combine sample state times and job completion counts data to produce estimates with desirable statistical properties. One procedure uses linear combinations of the data to derive minimum length interval estimates. The other derives the maximum likelihood estimates of three system descriptors, transformations of which can be used to give maximum likelihood estimates of a variety of other system descriptors. The paper also describes how to extend the results here to other queueing systems and illustrates the approach on a queueing system with finite waiting room. (Author)

The paper studies the effects of using correlated random number streams in replications of a simulation experiment in which output is to be related to input by linear and quadratic response surfaces. For the linear case, it is shown that either positively or negatively correlated streams produce a smaller generalized variance for the least-squares estimates that occur when the streams are independent. Although the prediction variance is small with negatively correlated steams, positively correlated streams produce a smaller variance for the estimated slope. In the quadratic case it is shown that of twenty seven possible input correlation designs only six guarantee a smaller generalized variance. Only one of these produces a smaller prediction variance. However, no plan will guarantee a smaller slope variance. In the quadratic case one often wants the slope variance to be as small as possible since the objective of the study may be to determine where the maximum or minimum response occurs in terms of the input. (Author)

The paper examines alternative techniques for generating random variables from the Poisson, geometric, negative binomial and binomial distributions on a digital computer. A fourfold criterion is used to evaluate these techniques. The criterion is based on the CPU time needed to generate a variate, the sensitivity of this time to changing parameter values, numerical roundoff error and extent to which cost-saving distributional approximations can be used. One conclusion of the study is that in many cases the inverse transformation method appears more attractive than alternative techniques specific to particular distributions. (Author)

The study concerns the relative efficiency of the least-squares estimator of the mean of a covariance stationary sequence that has a constant mean and an autoregressive representation of order p. The results augment those of Chipman, et al. who studied this topic for the case p = 1. Relative efficiency is defined as the ratio of the variance of the best linear unbiased estimator (BLUE) of the mean and the variance of the least-squares estimator (LSE) of the mean. Section 2 presents the problem definition and principal results. Graphical results for the first-order scheme (p = 1) in Sec. 3 imply that the relative desirability of the LSE should be based on variance as well as relative efficiency considerations.

The paper gives a description of improved methods for forecasting depot maintenance manpower requirements and depot item repair levels to facilitate effective long-term depot logistics planning. These methods improve on those currently used by making better use of available data and by being more responsive to specialized needs such as providing item forecasts for a single weapon system when the item is common to more than one weapon system. Flowcharts and computing algorithms are provided to assist in implementing the suggestions without a major revamping of the present system. The study concludes with a suggestion for comparing the present method with the proposed method based on real-life data.

Procedures for determining the result of a change in inputs to a system simulation. The study discusses the reliability of an experimental result and describes methods of estimating it. The method recommended uses a single replication and makes use of the covariance stationarity of the underlying stochastic process. The comparative reliability of results for different experiments is also discussed. For comparing experiments, it is suggested that reliability based on equal ratios is often preferable. A procedure for graphical analysis is presented, including a list of transformations of the dependent variable that help to reveal the correct form of the relationship between input and output. The generalized least-squares method for estimating the parameters of the identified form takes into consideration the varying reliabilities of the different results and leads to more efficient estimates than those obtained by the unweighted least-squares method. A procedure is given for predicting the computer time needed for a given input and a specified reliability. (Author)

This study applies spectral analysis to the study of time series generated by simulated stochastic models. As these data are autocorrelated, analysis by methods applicable to independent observations is precluded. Mathematical models known as covariance stationary stochastic processes are useful representations of autocorrelated time series. The increased publication of literature describing stochastic processes and spectral analysis, in particular, is making these ideas available to an increasing audience. Section I presents a rationale for our interest in time series models and spectral analysis. Section II describes the basic notions of covariance stationary processes. It emphasizes the equivalence of looking at these processes in both the time and frequency domains; the compactness of frequency domain analysis seemingly recommends it over correlation analysis. Section III provides a heuristic background for understanding statistical spectral analysis. Simple frequency-domain statistical properties are emphasized and compared with the rather involved sampling properties of estimated correlograms. Several relevant statistical tests are described. Three simulated experiments are used as examples of how to apply spectral analysis. These are described in Sec. IV.

The purpose of this paper has been to acquaint economists with the use of spectral analysis as an aid in identifying short-run demand and supply from market data. It has been shown that the seasonal and purely random components of price and quantity series can allow us to distinguish short-run demand from supply providing that at least one of the components results in a cross-spectral representation whose sign is opposite to those of the remaining components' representations. Our short-run schedules are actually linear combinations of independent processes. In this sense, our analysis of demand and supply differs from the traditional approach in which long-run phenomena are removed and the aggregate remainders are used to estimate short-run demand and supply. Disaggregating the price and quantity processes allows us to take advantage of the greater certainties in prediction associated with the regularly recurring seasonal patterns, as compared with the purely random processes whose means are the best estimates to be used in preduction. (Author)

After perusal of sample data, the observation often made about demand is that the variance is large compared to the mean. Periodicities of the sort uncovered here explain this phenomenon. For example, a demand process may be at the peak of a cycle one day and at the trough on another. Personnel at Beale argue that schedules for take-offs and landings determine when an aircraft is available for maintenance, and there fore determine the pattern of removals and replacements. The author is of the opinion that institutional maintenance procedures are indeed responsible for many of the uncovered character istics of demand. The primary contribution of this paper to demand prediction '4 been to show the diverse behavior of demand patterns that may actually exist. Wherever attempts at ex plaining these patterns have been made, it has been done on a purely conjectural basis and, hence, they are really ''food for thought'' rather than ''gospel truths.'' Future research ers in demand prediction should take account of these apparent diversities in demand. Hopefully they will find appropriate characterizations of the demand patterns then under scrutiny from pilot spectral analyses such as this one. (Author)