Praise for the Third Edition: "This is one of the best books available. Its excellent organizational structure allows quick reference to specific models and its clear presentation . . . solidifies the understanding of the concepts being presented."IIE Transactions on Operations EngineeringThoroughly revised and expanded to reflect the latest developments in the field, Fundamentals of Queueing Theory, Fourth Edition continues to present the basic statistical principles that are necessary to analyze the probabilistic nature of queues. Rather than presenting a narrow focus on the subject, this update illustrates the wide-reaching, fundamental concepts in queueing theory and its applications to diverse areas such as computer science, engineering, business, and operations research.This update takes a numerical approach to understanding and making probable estimations relating to queues, with a comprehensive outline of simple and more advanced queueing models. Newly featured topics of the Fourth Edition include:Retrial queuesApproximations for queueing networksNumerical inversion of transformsDetermining the appropriate number of servers to balance quality and cost of serviceEach chapter provides a self-contained presentation of key concepts and formulae, allowing readers to work with each section independently, while a summary table at the end of the book outlines the types of queues that have been discussed and their results. In addition, two new appendices have been added, discussing transforms and generating functions as well as the fundamentals of differential and difference equations. New examples are now included along with problems that incorporate QtsPlus software, which is freely available via the book's related Web site.With its accessible style and wealth of real-world examples, Fundamentals of Queueing Theory, Fourth Edition is an ideal book for courses on queueing theory at the upper-undergraduate and graduate levels. It is also a valuable resource for researchers and practitioners who analyze congestion in the fields of telecommunications, transportation, aviation, and management science.

Fundamentals of Queueing Theory

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

This article explores possibilities for designing and executing simulation models with specific analysis goals in mind, and shows that a tight coupling of the modeling and analysis phases in a simulation project can lead to dramatic improvements in the study results. Suggestions are made for how simulation analysis, considered in the explicit context of discrete-event simulation models, can create new opportunities for meaningful research and more efficient modeling. Modeling decisions can play a significant role in the performance of analytical procedures. How a simulation model is designed can enable, inhibit, or even invalidate analytical procedures and methodology research results.

Simulation modeling for analysis

This paper discusses a method for placing confidence limits on the steady state mean of an output sequence generated by a discrete event simulation. An estimate of the variance is obtained by estimating the spectral density at zero frequency. This estimation is accomplished through a regression analysis of the logarithm of the averaged periodogram. By batching the output sequence the storage and computational requirements of the method remain low. A run length control procedure is developed that uses the relative width of the generated confidence interval as a stopping criterion. Experimental results for several queueing models of an interactive computer system are reported.

A spectral method for confidence interval generation and run length control in simulations

We propose and analyze a generic mathematical model for dynamic, stochastic vehicle routing problems, the dynamic traveling repairman problem (DTRP). The model is motivated by applications in which the objective is to minimize the wait for service in a stochastic and dynamically changing environment. This is a departure from classical vehicle routing problems where one seeks to minimize total travel time in a static, deterministic environment. Potential areas of application include repair, inventory, emergency service and scheduling problems. The DTRP is defined as follows: Demands for service arrive in time according to a Poisson process, are independent and uniformly distributed in a Euclidean service region, and require an independent and identically distributed amount of on-site service by a vehicle. The problem is to find a policy for routing the service vehicle that minimizes the average time demands spent in the system. We propose and analyze several policies for the DTRP. We find a provably optima...

/pdf/a-stochastic-and-dynamic-vehicle-routing-problem-in-the-4kkc6tmjgl.pdf

A stochastic and dynamic vehicle routing problem in the Euclidean plane

We consider the efficient estimation of mean delay in queue, d, mean wait in system, w, time average number in queue, Q, and time average number in system, L, for simulated queueing systems. We prove for the GI/G/s queue that it is more efficient to estimate w, Q, and L from an estimate of d than it is to estimate them directly. This generalizes previous results for the M/G/l queue and also confirms empirical studies on other GI/G/s queues.

Conservation equations and variance reduction in queueing simulations

We correct some errors in Spira’s algorithm for the all-pairs shortest-path problem, and empirically compare his algorithm (with two distinct sorting, routines) to Dijkstra’s procedure. The results show that Spira’s algorithm is only efficient for “large” networks. Furthermore, it is seen that the asymptotic number of additions and comparisons required by two algorithms may be a very poor indicator of their relative running times.

A Note on Spira’s Algorithm for the All-Pairs Shortest-Path Problem

We discuss a general concept of natural stratification in simulation, and present an approach to estimating mean performance measures in stationary simulations which possess a natural stratification.

Methods for stratified estimation in nonregenerative simulations

A common problem faced by simulators is that of constructing a confidence interval for the steady-state mean of a stochastic process. We have reviewed the existing procedures for this problem and found that all but one either produce confidence intervals with coverages which may be considerably lower than desired or have not been adequately tested. Thus, in many cases simulators will have more confidence in their results than is justified. In this paper we present a new sequential procedure based on the method of batch means for constructing a confidence interval with coverage close to the desired level. The procedure has the advantage that it does not explicitly require a stochastic process to have regeneration points. Empirical results for a large number of stochastic systems indicate that the new procedure performs quite well.

A Sequential Procedure for Determining the Length of a Steady-State Simulation

We consider the efficient estimation of mean delay in queue, d, mean wait in system, w, time average number in queue, Q, time average number in system, L, and time average amount of work in system, V, for simulated queueing systems. We prove for the regenerative GI/G/s queue that it is more efficient to estimate w, Q, L, and V from an estimate of d than it is to estimate them directly. This generalizes previous results for the M/G/1 queue and also confirms empirical studies on other GI/G/s queues.

/pdf/conservation-equations-and-variance-reduction-in-queueing-1wiymp0jix.pdf

Conservation Equations and Variance Reduction in Queueing Simulations

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