Synopses & Reviews
This book presents an introductory course in stochastic orderings and dependence and their applications to queues and networks of queues. Readers are assumed to have a firm grounding in Lebesgue measure, conditional expectation, and martingales. Chapter 1 presents a collection of one-dimensional orderings with applications to the theory of queues. Chapter 2 extends these concepts to stochastic orderings in many dimensional spaces and functional spaces. Then results are given on stochastic ordering of networks, replacement policies, and single-server queues associated with Markov renewal processes. Finally, Chapter 3 is devoted to dependence and the relations between dependence and orderings, and it includes applications to queueing networks and point processes.
Synopsis
This book is an introductionary course in stochastic ordering and dependence in the field of applied probability for readers with some background in mathematics. It is based on lectures and senlinars I have been giving for students at Mathematical Institute of Wroclaw University, and on a graduate course a.t Industrial Engineering Department of Texas A&M University, College Station, and addressed to a reader willing to use for example Lebesgue measure, conditional expectations with respect to sigma fields, martingales, or compensators as a common language in this field. In Chapter 1 a selection of one dimensional orderings is presented together with applications in the theory of queues, some parts of this selection are based on the recent literature (not older than five years). In Chapter 2 the material is centered around the strong stochastic ordering in many dimen sional spaces and functional spaces. Necessary facts about conditioning, Markov processes an"d point processes are introduced together with some classical results such as the product formula and Poissonian departure theorem for Jackson networks, or monotonicity results for some re newal processes, then results on stochastic ordering of networks, re ment policies and single server queues connected with Markov renewal processes are given. Chapter 3 is devoted to dependence and relations between dependence and ordering, exem plified by results on queueing networks and point processes among others."
Description
Includes bibliographical references (p. 184-192) and index.