Stochastic Monotonicity and Queueing Applications of Birth-Death Processes

Erik Van Doorn

ISBN 10: 0387905472 / ISBN 13: 9780387905471

Published by Springer New York, Springer US Feb 1981, 1981

About this Item

This item is printed on demand - Print on Demand Titel. Neuware -A stochastic process {X(t): 0 S tSpringer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 124 pp. Englisch.

Seller Inventory # 9780387905471

Bibliographic Details

• Title: Stochastic Monotonicity and Queueing Applications of Birth-Death Processes
• Publisher: Springer New York, Springer US Feb 1981
• Publication Date: 1981
• Language: English
• ISBN 10: 0387905472
• ISBN 13: 9780387905471
• Binding: Taschenbuch
• Condition: Neu

About this title

Synopsis

A stochastic process {X(t): 0 S t < =} with discrete state space S c ~ is said to be stochastically increasing (decreasing) on an interval T if the probabilities Pr{X(t) > i}, i E S, are increasing (decreasing) with t on T. Stochastic monotonicity is a basic structural property for process behaviour. It gives rise to meaningful bounds for various quantities such as the moments of the process, and provides the mathematical groundwork for approximation algorithms. Obviously, stochastic monotonicity becomes a more tractable subject for analysis if the processes under consideration are such that stochastic mono tonicity on an inter­ val 0 < t < E implies stochastic monotonicity on the entire time axis. DALEY (1968) was the first to discuss a similar property in the context of discrete time Markov chains. Unfortunately, he called this property "stochastic monotonicity", it is more appropriate, however, to speak of processes with monotone transition operators. KEILSON and KESTER (1977) have demonstrated the prevalence of this phenomenon in discrete and continuous time Markov processes. They (and others) have also given a necessary and sufficient condition for a (temporally homogeneous) Markov process to have monotone transition operators. Whether or not such processes will be stochas­ tically monotone as defined above, now depends on the initial state distribution. Conditions on this distribution for stochastic mono tonicity on the entire time axis to prevail were given too by KEILSON and KESTER (1977).