Title: Strong and weak stochastic bounds for multidimensional Markov chains


Author: Hind Castel-Taleb; Nihal Pekergin


Institute Telecom SudParis, 9 rue Charles Fourier, 91011 Evry Cedex, France
University of Paris-Est Créteil-Val de Marne, LACL, 61 avenue Général de Gaulle, 94010, Créteil, France


Journal: Int. J. of Critical Computer-Based Systems, 2014 Vol.5, No.1/2, pp.148 - 168


Abstract: We study queueing networks similar to Jackson networks, modelled by a multidimensional Markov chain. The performance analysis may be very difficult or intractable, if there is no specific solution form. We explain how stochastic comparisons of Markov chains can be used to overcome this problem. We build new queueing which are easier to analyse and providing stochastic bounds (upper or lower) for the original model. In this paper, we propose different queueing systems in the sense of the strong and weak stochastic ordering for a general queueing network model in order to compute performance measure bounds as blocking probabilities. We discuss the accuracy of the bounds under different input parameter values.


Keywords: queueing networks; stochastic comparisons; weak ordering; strong ordering; blocking probabilities; stochastic bounds; multidimensional Markov chains; modelling.


DOI: http://dx.doi.org/10.1504/IJCCBS.2014.059592


Available online 02 Mar 2014



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