Detecting Markov Chain Instability: A Monte Carlo Approach
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.
Cite
@article{arxiv.1608.03257,
title = {Detecting Markov Chain Instability: A Monte Carlo Approach},
author = {Michel Mandjes and Brendan Patch and Neil Walton},
journal= {arXiv preprint arXiv:1608.03257},
year = {2016}
}