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Event coupling and performance sensitivity analysis of generalized semi-Markov processes

Part of: Special processes Stochastic processes

Published online by Cambridge University Press:  01 July 2016

Xi-Ren Cao
Xi-Ren Cao*
Affiliation:
The Hong Kong University of Science and Technology
*
* Postal address: Department of Electrical and Electronic Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong.
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Abstract

We study a fundamental feature of the generalized semi-Markov processes (GSMPs), called event coupling. The event coupling reflects the logical behavior of a GSMP that specifies which events can be affected by any given event. Based on the event-coupling property, GSMPs can be classified into three classes: the strongly coupled, the hierarchically coupled, and the decomposable GSMPs. The event-coupling property on a sample path of a GSMP can be represented by the event-coupling trees. With the event-coupling tree, we can quantify the effect of a single perturbation on a performance measure by using realization factors. A set of equations that specifies the realization factors is derived. We show that the sensitivity of steady-state performance with respect to a parameter of an event lifetime distribution can be obtained by a simple formula based on realization factors and that the sample-path performance sensitivity converges to the sensitivity of the steady-state performance with probability one as the length of the sample path goes to infinity. This generalizes the existing results of perturbation analysis of queueing networks to GSMPs.

Keywords

PERTURBATION ANALYSIS

MSC classification

Primary: 60G20: Generalized stochastic processes
Secondary: 60G17: Sample path properties 60K25: Queueing theory
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 27 , Issue 3 , September 1995 , pp. 741 - 769
Copyright
Copyright © Applied Probability Trust 1995 

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Footnotes

Research supported in part by the grant HKUST 599/94E.

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