Open Access
2017 Detecting Markov Chain Instability: A Monte Carlo Approach
M. Mandjes, B. Patch, N. S. Walton
Stoch. Syst. 7(2): 289-314 (2017). DOI: 10.1287/stsy.2017.0003


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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M. Mandjes. B. Patch. N. S. Walton. "Detecting Markov Chain Instability: A Monte Carlo Approach." Stoch. Syst. 7 (2) 289 - 314, 2017.


Received: 1 September 2016; Accepted: 1 July 2017; Published: 2017
First available in Project Euclid: 24 February 2018

zbMATH: 06849803
MathSciNet: MR3741355
Digital Object Identifier: 10.1287/stsy.2017.0003

Primary: 60K25 , 68M20 , 68W40 , 90B22

Keywords: Markov chains , Monte Carlo algorithm , Queueing networks , stability , Stochastic networks

Vol.7 • No. 2 • 2017
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