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Queuing networks with blocking. Exact and approximate solutions. (English) Zbl 0849.90064

Oxford: Oxford Univ. Press. xiii, 288 p. (1994).
A queueing network with blocking is essentially a queueing network with finite capacity nodes. Blocking occurs at a node whenever on service completion a customer is unable to proceed further, as its destination node has reached its capacity. The importance of such network models arises mainly due to its potential application in computer systems, communication systems and flexible manufacturing systems. However, exact closed form solutions for the queue length distribution at equilibrium are not possible except in some simple situations. As a consequence numerical techniques and analytic approximations are employed to study these models. Even then exact numerical methods become cumbersome as the number of servers and buffer sizes increase. This research monograph particularly deals with approximations to various networks with blocking and will be welcome by both researchers and practitioners involved with such network configurations.
The book consists of the following eight chapters. 1. Basic concepts; 2. Numerical methods for queueing networks with blocking; 3. Two-node open queueing networks with blocking; 4. Approximate analysis of open tandem queueing networks with blocking; 5. Approximate analysis of arbitrarily linked open networks with blocking; 6. Closed queueing networks with blocking with product-form solution; 7. Closed queueing networks with blocking with nonproduct-form solution; 8. Applications.
The first chapter contains basic concepts like various blocking mechanisms and a review of phase-type distributions that are required for the rest of the chapters. Chapter 2 presents the various numerical methods that are employed in solving the equations that arise in the study of continuous parameter Markov chains. Chapter 3 to 5 deal with the solutions of open queueing networks with blocking while chapters 6 and 7 present the results for closed queueing networks. The last chapter contains examples which illustrate the applicability of these networks configurations in modelling real-life systems. Each chapter is accompanied by its own specific references and ends with a discussion of these references. In addition, a bibliography containing an extensive list of references is included.

MSC:

90B22 Queues and service in operations research
60K25 Queueing theory (aspects of probability theory)
60K20 Applications of Markov renewal processes (reliability, queueing networks, etc.)
90B18 Communication networks in operations research
90B30 Production models
90-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to operations research and mathematical programming
60-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to probability theory
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