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

Preface to the revised edition Remarks on notation 1. Basic examples 2. Characterization and existence 3. Stable processes and their extensions 4. The Levy-Ito decomposition of sample functions 5. Distributional properties of Levy processes 6. Subordination and density transformation 7. Recurrence and transience 8. Potential theory for Levy processes 9. Wiener-Hopf factorizations 10. More distributional properties Supplement Solutions to exercises References and author index Subject index.

Lévy processes and infinitely divisible distributions

Real and Complex Analysis

Probability and Measure

Convergence Of Probability Measures

Under a Bayesian framework, we formulate the fully sequential sampling and selection decision in statistical ranking and selection as a stochastic control problem, and derive the associated Bellman equation. Using a value function approximation, we derive an approximately optimal allocation policy. We show that this policy is not only computationally efficient but also possesses both one-step-ahead and asymptotic optimality for independent normal sampling distributions. Moreover, the proposed allocation policy is easily generalizable in the approximate dynamic programming paradigm.

Ranking and Selection as Stochastic Control

In this paper, we propose a new unbiased stochastic derivative estimator in a framework that can handle discontinuous sample performances with structural parameters. This work extends the three most popular unbiased stochastic derivative estimators: (1) infinitesimal perturbation analysis (IPA), (2) the likelihood ratio (LR) method, and (3) the weak derivative method, to a setting where they did not previously apply. Examples in probability constraints, control charts, and financial derivatives demonstrate the broad applicability of the proposed framework. The new estimator preserves the single-run efficiency of the classic IPA-LR estimators in applications, which is substantiated by numerical experiments. The online appendix is available at https://doi.org/10.1287/opre.2017.1674.

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A New Unbiased Stochastic Derivative Estimator for Discontinuous Sample Performances with Structural Parameters

We formulate the statistical selection problem in a general dynamic framework comprising fully sequential sampling allocation and optimal design selection. Because the traditional probability of correct selection measure is not sufficient to capture both aspects in this more general framework, we introduce the integrated probability of correct selection to better characterize the objective. As a result, the usual selection policy of choosing the design with the largest sample mean as the estimate of the best is no longer necessarily optimal. Rather, the optimal selection policy is to choose the design that maximizes the posterior integrated probability of correct selection, which is a function of the posterior mean and the correlation structure induced by the posterior variance. Because determining the optimal selection policy is generally intractable, we also devise an approximation scheme to efficiently approximate the optimal selection policy. For the allocation policy, we study an asymptotic policy ca...

Dynamic Sampling Allocation and Design Selection

In this note, we consider the statistical ranking and selection problem of finding the best alternative when the performances of each alternative must be estimated by sampling. We provide a myopic allocation policy that asymptotically achieves the sampling ratios given by the optimal computing budget allocation, an approximate solution of the optimal large deviations rate for the decreasing probability of false selection. We analyze the asymptotic sampling ratio for both known variances and unknown variances under a Bayesian framework. Numerical results substantiate the theoretical results.

Myopic Allocation Policy With Asymptotically Optimal Sampling Rate

Under a Bayesian framework, we formulate the fully sequential sampling and selection decision in statistical ranking and selection as a stochastic control problem, and derive the associated Bellman equation. Using value function approximation, we derive an approximately optimal allocation policy. We show that this policy is not only computationally efficient but also possesses both one-step-ahead and asymptotic optimality for independent normal sampling distributions. Moreover, the proposed allocation policy is easily generalizable in the approximate dynamic programming paradigm.

Yijie Peng

Papers

Ranking and Selection as Stochastic Control

A New Unbiased Stochastic Derivative Estimator for Discontinuous Sample Performances with Structural Parameters

Dynamic Sampling Allocation and Design Selection

Myopic Allocation Policy With Asymptotically Optimal Sampling Rate

Ranking and Selection as Stochastic Control