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arXiv · 1608.03257

Detecting Markov Chain Instability: A Monte Carlo Approach

Michel Mandjes·Brendan Patch·Neil Walton
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Abstract

We devise a Monte Carlo based method for detecting whether a non-negative Markov chain is stable for a given set of parameter values. More precisely, for a given subset of the parameter space, we develop an algorithm that is capable of deciding whether the set has a subset of positive Lebesgue measure for which the Markov chain is unstable. The approach is based on a variant of simulated annealing, and consequently only mild assumptions are needed to obtain performance guarantees. The theoretical underpinnings of our algorithm are based on a result stating that the stability of a set of parameters can be phrased in terms of the stability of a single Markov chain that searches the set for unstable parameters. Our framework leads to a procedure that is capable of performing statistically rigorous tests for instability, which has been extensively tested using several examples of standard and non-standard queueing networks.

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Michel Mandjes, Brendan Patch, Neil Walton. 2016-08-10. Detecting Markov Chain Instability: A Monte Carlo Approach. https://arxiv.org/abs/1608.03257

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