On Markov Chains with Uncertain Data

CentER Discussion Paper Series No. 2008-50

20 Pages Posted: 28 May 2008

See all articles by Hans Blanc

Hans Blanc

Tilburg University - Tilburg University School of Economics and Management

Dick den Hertog

Tilburg University - Department of Econometrics & Operations Research

Date Written: May 1, 2008

Abstract

this paper, a general method is described to determine uncertainty intervals for performance measures of Markov chains given an uncertainty region for the parameters of the Markov chains. We investigate the effects of uncertainties in the transition probabilities on the limiting distributions, on the state probabilities after n steps, on mean sojourn times in transient states, and on absorption probabilities for absorbing states. We show that the uncertainty effects can be calculated by solving linear programming problems in the case of interval uncertainty for the transition probabilities, and by second order cone optimization in the case of ellipsoidal uncertainty. Many examples are given, especially Markovian queueing examples, to illustrate the theory.

Keywords: Markov chain, Interval uncertainty, Ellipsoidal uncertainty, Linear Programming, Second Order Cone Optimization

JEL Classification: C61

Suggested Citation

Blanc, Hans and den Hertog, Dick, On Markov Chains with Uncertain Data (May 1, 2008). Available at SSRN: https://ssrn.com/abstract=1138144 or http://dx.doi.org/10.2139/ssrn.1138144

Hans Blanc (Contact Author)

Tilburg University - Tilburg University School of Economics and Management ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands

Dick Den Hertog

Tilburg University - Department of Econometrics & Operations Research ( email )

Tilburg, 5000 LE
Netherlands

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