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Sensitivity analysis for Markov reward structures until entrance times

Part of: Stochastic processes Markov processes Operations research and management science

Published online by Cambridge University Press:  14 July 2016

N. M. van Dijk  and
H. Korezlioglu
N. M. van Dijk*
Affiliation:
University of Amsterdam
H. Korezlioglu*
Affiliation:
Ecole Nationale Supérieure des Télécommunications
*
∗Postal address: Department of Econometrics, University of Amsterdam, Roeterstraat 11, 1018 WB, Amsterdam, The Netherlands
∗∗Postal address: Ecole Nationale Supérieure des Télécommunications, 46 rue Barrault, 75634 Paris Cedex 13, France. Email address: [email protected]
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Abstract

This work presents an estimate of the error on a cumulative reward function until the entrance time of a continuous-time Markov chain into a set, when the infinitesimal generator of this chain is perturbed. The derivation of an error bound constitutes the first part of the paper while the second part deals with an application where the time until saturation is considered for a circuit switched network which starts from an empty state and which is also subject to possible failures.

Keywords

Continuous-time Markov chaincumulative rewardentrance timeparameter sensitivityerror boundbias termsuniformization

MSC classification

Primary: 60J27: Continuous-time Markov processes on discrete state spaces 60G40: Stopping times; optimal stopping problems; gambling theory
Secondary: 90B22: Queues and service 90B25: Reliability, availability, maintenance, inspection
Type
Research Papers
Information
Journal of Applied Probability , Volume 37 , Issue 1 , March 2000 , pp. 45 - 63
Copyright
Copyright © 2000 by The Applied Probability Trust 

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