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Insensitivity and product-form decomposability of reallocatable GSMP

Part of: Special processes Markov processes

Published online by Cambridge University Press:  01 July 2016

Masakiyo Miyazawa
Masakiyo Miyazawa*
Affiliation:
Science University of Tokyo
*
∗Postal address: Department of Information Science, Science University of Tokyo, Noda, Chiba 278, Japan.
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Abstract

A stochastic process, called reallocatable GSMP (RGSMP for short), is introduced in order to study insensitivity of its stationary distribution. RGSMP extends GSMP with interruptions, and is applicable to a wide range of queues, from the standard models such as BCMP and Kelly's network queues to new ones such as their modifications with interruptions and Serfozo's (1989) non-product form network queues, and can be used to study their insensitivity in a unified way. We prove that RGSMP supplemented by the remaining lifetimes is product-form decomposable, i.e. its stationary distribution splits into independent components if and only if a version of the local balance equations hold, which implies insensitivity of the RGSMP scheme in a certain extended sense. Various examples of insensitive queues are given, which include new results. Our proofs are based on the characterization of a stationary distribution for SCJP (self-clocking jump process) of Miyazawa (1991).

Keywords

INTERRUPTIONSSYMMETRIC QUEUENETWORK QUEUENEGATIVE CUSTOMERSTATE DEPENDENT ROUTINGSTATIONARY DISTRIBUTION

MSC classification

Primary: 60K25: Queueing theory
Secondary: 60J75: Jump processes

Information

Type
Research Article
Information
Advances in Applied Probability , Volume 25 , Issue 2 , June 1993 , pp. 415 - 437
Copyright
Copyright © Applied Probability Trust 1993 

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