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This is a revised and expanded version of the earlier edition. The new material is on Markov-modulated storage processes arising from queueing and data commu­ nication models. The analysis of these models is based on the fluctuation theory of Markov-additive processes and their discrete time analogues, Markov random walks. The workload and queue length processes, omitted from the earlier edition, are also presented. In addition, many sections have been rewritten, with new re­ sults and proofs, as well as further examples. The mathematical level and style of presentation, however, remain the same. Chapter I contains a comprefensive treatment of the waiting time and related quantities in a single server queue, combining Chapters 1 and 2 of the earlier edition. In Chapter 2 we treat the (continuous time) workload and queue length processes using their semiregenerative properties. Also included are bulk queues omitted from the earlier edition, but included in its Russian translation. The queue MIMIl is presented in Chapter 3. This is the so-called simple queue, but its treat­ ment in most of the literature is far from simple. Our analysis of the queue length process is elementary and yields explicit results for various distributions of interest. are treated in Chapter 4, combining Chapters 3 Continuous time storage models and 4 of the earlier edition. We present extensive new material, omitting much of the old Chapter 4. This has resulted in a streamlined account of this important class of models.

Actuarial mathematics --- Queuing theory. --- Stochastic processes. --- Files d'attente, Théorie des --- Processus stochastiques --- Files d'attente, Théorie des --- Statistics . --- Probabilities. --- Statistics, general. --- Probability Theory and Stochastic Processes. --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Econometrics --- Erlang traffic formula --- Queueing theory --- Theory of queues --- Waiting-line theory --- Production scheduling --- Stochastic processes --- Random processes --- Probabilities

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Actuarial mathematics --- 519.2 --- Probability. Mathematical statistics --- 519.2 Probability. Mathematical statistics --- Files d'attente

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Recent research in probability has been concerned with applications such as data mining and finance models. Some aspects of the foundations of probability theory have receded into the background. Yet, these aspects are very important and have to be brought back into prominence.

Probabilities. --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Stochastic processes

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