Objects. The ~ b s t rac t ~ b j ect forms the fundamental base class for the entire design and all other classes are derived from this base class. The Abstract Object class defines and characterizes all the essential properties every class in this 404 OBJECT-ORIENTED SIMULATION

Handbook of Simulation

Statistical models in engineering , Statistical models in engineering , مرکز فناوری اطلاعات و اطلاع رسانی کشاورزی

Statistical Models in Engineering

Queueing models can usefully represent production systems experiencing congestion due to irregular flows, but exact analyses of these queueing models can be difficult. Thus it is natural to seek relatively simple approximations that are suitably accurate for engineering purposes. Here approximations for a basic queueing model are developed and evaluated. The model is the GI/G/m queue, which has m identical servers in parallel, unlimited waiting room, and the first-come first-served queue discipline, with service and interarrival times coming from independent sequences of independent and identically distributed random variables with general distributions. The approximations depend on the general interarrival-time and service-time distributions only through their first two moments. The main focus is on the expected waiting time and the probability of having to wait before beginning service, but approximations are also developed for other congestion measures, including the entire distributions of waiting time, queue-length and number in system. These relatively simple approximations are useful supplements to algorithms for computing the exact values that have been developed in recent years. The simple approximations can serve as starting points for developing approximations for more complicated systems for which exact solutions are not yet available. These approximations are especially useful for incorporating GI/G/m models in larger models, such as queueing networks, wherein the approximations can be components of rapid modeling tools.

APPROXIMATIONS FOR THE GI/G/m QUEUE

1. Introduction to the Modeling of Manufacturing Systems.- 1.1. Typical Decision Problems in Manufacturing Systems.- 1.2. Performance Evaluation.- 1.3. Models of Manufacturing Systems.- 1.4. Design of Manufacturing Systems.- References.- 2. Tools of Probability.- 2.1. Random Variables and Their Distributions.- 2.2. Joint Distributions.- 2.3. Conditional Distributions.- 2.4. Functions of Random Variables.- 2.5. Moments of Random Variables.- 2.6. Special Distributions.- 2.7. Stochastic Processes.- 2.8. Phase-Type Distributions.- Related Bibliography on Phase-Type Distributions.- References.- Problems.- 3. Analysis of Single Work Stations.- 3.1. Introduction.- 3.2. A Simple Work Station.- 3.3. Distribution of the Number in the System.- 3.4. Work Stations Subject to Failures.- 3.5. Distribution of the Number of Jobs in a Work Station Subject to Failures.- 3.6. The Process-Completion Time.- 3.7. Failure-Repair Policies.- 3.8. The Machine Interference Problem.- Related Literature.- References.- Problems.- 4. Analysis of Flow Lines.- 4.1. Introduction.- 4.2. Characteristics of Flow Lines.- 4.3. Analysis of Two-Station Flow Lines.- 4.4. Analysis of Flow Lines With More Than Two Stations.- 4.5. Deterministic Processing Times.- 4.6. Bounds on the Output Rate.- 4.7. Design Problems in Flow Lines.- Related Literature.- References.- Problems.- 5. Analysis of Transfer Lines.- 5.1. Introduction.- 5.2. A Two-Station Line with No Intermediate Buffer: A Regenerative Approach.- 5.3. Transfer Lines with Work-in-Process Buffers.- 5.4. Buffer Clearing Policies in Transfer Lines.- 5.5. Analysis of a Two-Machine Synchronous Line Under BCP1.- 5.6. Operation Under BCP2.- 5.7. Line Behavior and Design Issues.- 5.8. Analysis of Larger Systems.- 5.9. Transfer Lines with No Scrapping.- Related Bibliography.- References.- Problems.- 6. Assembly Systems.- 6.1. Introduction.- 6.2. An Asynchronous Assembly System.- 6.3. Approximate Analysis of the Two-Station Assembly System.- 6.4. Analysis of Larger Systems.- 6.5. Synchronous Assembly Systems.- 6.6. Relaxing the Assembly Assumption.- Related Bibliography.- References.- Problems.- 7. Pull-Type Manufacturing Systems.- 7.1. Introduction.- 7.2. Production Control Policies.- 7.3. Analysis of Single-Stage, Single-Product Systems.- 7.4. A Single-Stage System with Two Products.- 7.5. Multistage Pull-Type Systems.- 7.6. The Generalized Kanban Scheme.- 7.7. Manufacturing Systems with Inventory Procurement.- 7.8. A Two-Stage, MultiProduct System.- 7.9. The Look-Back Policy.- Related Bibliography.- References.- Problems.- Appendix: A Single-Stage P/I System with PH Delay, Set-up, and Processing Times.

Performance analysis of manufacturing systems

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Proceedings of the 1997 winter simulation conference

Algorithms for matching moments to phase-type distributions are evaluated on the basis of their performance in their intended application, queueing models. The moment-matching algorithms under consideration match two moments to a hyperexponential distribution with balanced means and three moments to a mixture of two Erlang distributions of common order. These algorithms are used to approximate an interarrival-time distribution for a queueing model, and the accuracy of associated performance-measure approximations is then used to evaluate the moment-matching algorithms. Three performance measures are considered, and attention is focussed on the steady-state mean queue length (number in system) of theGI/M/1 queue. Performance-measure approximations are compared to three-moment bounds and performance-measure values arising from hypothetical approximated distributions.

An investigation of phase-distribution moment-matching algorithms for use in queueing models

We develop and evaluate procedures for estimating and simulating nonhomogeneous Poisson processes having an exponential rate function, where the exponent may include a polynomial component or some trigonometric components or both. Maximum likelihood estimates of the unknown continuous parameters of the rate function are obtained numerically, and the degree of the polynomial rate component is determined by a likelihood ratio test. The experimental performance evaluation for this estimation procedure involves applying the procedure to 100 independent replications of nine selected point processes that possess up to four trigonometric rate components together with a polynomial rate component whose degree ranges from zero to three. On each replication of each process, the fitting procedure is applied to estimate the parameters of the process; and then the corresponding estimates of the rate and mean-value functions are computed over the observation interval. Evaluation of the fitting procedure is based on plotted tolerance bands for the rate and mean-value functions together with summary statistics for the maximum and average absolute estimation errors in these functions computed over the observation interval. The experimental results provide substantial evidence of the numerical stability and usefulness of the fitting procedure in simulation applications.

Estimating and simulating Poisson processes having trends or multiple periodicities

The GI/PH/1 model (single-server queue with general independent interarrival times and phase-type service times) is used to explore the behavior of phase-type (PH) approximations of interarrival- and service-time distributions. Various PH approximating distributions are considered for five non-PH interarrival-time distributions and two PH service-time distributions. Simple two- and three-moment-matching approximations and, in some cases, approximations obtained by also considering distribution shape are compared. Each approximating distribution is evaluated on the basis of the quality of the corresponding approximations of steady-state measures of the congestion seen by an arriving customer. The traffic intensity and the variability of the distribution (interarrival-or service-time) that is not approximated are shown to have a substantial effect on the accuracy of the queueing approximations. Rules for selecting approximating distributions for queueing applications are suggested

An empirical study of queueing approximations based on phase-type distributions

This paper summarizes an experimental evaluation of a procedure for estimating a nonhomogeneous Poisson process having an exponential rate function, where the exponent may include both polynomial and trigonometric components. Maximum likelihood estimates of the unknown continuous parameters of the rate function are obtained numerically, and the degree of the polynomial rate component is determined by a likelihood ratio test. Our evaluation is limited to the case of a known frequency. To examine the small- and large-sample behavior of the estimation procedure for many types of time-dependent arrival processes encountered in previous work, we performed 100 independent replications of twelve selected Poisson processes over two observation intervals. On each replication of each case, we applied the fitting procedure to estimate the parameters of the target process; and we computed the corresponding estimates of the rate and mean-value functions over the observation interval. Evaluation of the fitting procedur...

Mary A. Johnson

Papers

An investigation of phase-distribution moment-matching algorithms for use in queueing models

Estimating and simulating Poisson processes having trends or multiple periodicities

Estimating and simulating Poisson processes having trends or multiple periodicities

An empirical study of queueing approximations based on phase-type distributions

Experimental Evaluation of a Procedure for Estimating Nonhomogeneous Poisson Processes Having Cyclic Behavior