N.U. Prabhu - Böcker

Covering both theory and applications, this collection of eleven contributed papers surveys the role of probabilistic models and statistical techniques in image analysis and processing, develops likelihood methods for inference about parameters that determine the drift and the jump mechanism of a di

This monograph gives a self-contained treatment of stochastic processes arising from models for queues, insurance risk, and dams and data communication, using their sample function properties. The approach is based on the fluctuation theory of random walks, L vy processes, and Markov-additive processes, in which Wiener-Hopf factorization plays a central role. The second edition includes results for the virtual waiting time and queue length in single server queues. The treatment of continuous time storage processes is thoroughly revised and simplified. Markov- modulated storage processes are inlcuded in Part III with application to data communication models. The book can be used as a text for an advanced course on applied probability models. The prerequisite is a graduate-level course in probability and stochastic processes.

This work examines the foundations of queueing theory and is intended as an advanced text for courses on queueing theory, as well as a professional reference to queueing research. The results of queueing theory are established within the context of the book's instructional framework. The central results of queueing theory are stated in the form of theorems for accessibility and reading ease. Current research has shown the need to pay more attention to the basic concepts and techniques of queueing theory. These include the busy period, imbedded chains, regeneration points, Wiener-Hopf technique, time-reversibility, output, vector Markov processes, remaining workload and completion times. The use of these concepts and techniques considerably simplifies the analysis of models involving last come, first served queue discipline, priorities, networks, set-up times and server vacations. It is these conceptional techniques that form the foundations of queueing theory.

Covering both theory and applications, this collection of eleven contributed papers surveys the role of probabilistic models and statistical techniques in image analysis and processing, develops likelihood methods for inference about parameters that determine the drift and the jump mechanism of a di

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.