Stochastic comparison of Markov processes through coupling by mapping functions

Hind Castel-Taleb (1, 2, 3, 4) , Idriss Ismael Aouled (2, 5, 3, 4)

1 METHODES-SAMOVAR - Méthodes et modèles pour les réseaux
2 TSP - RST - Département Réseaux et Services de Télécommunications
3 SAMOVAR - Services répartis, Architectures, MOdélisation, Validation, Administration des Réseaux
4 CNRS - Centre National de la Recherche Scientifique
5 LACL - Laboratoire d'Algorithmique Complexité et Logique

We consider large queueing networks for which transient and stationary probability distributions are very difficult or impossible to obtain due to the state space explosion. We apply the coupling by mapping functions in order to compare large size multidimensional Markov chains with smaller ones, generating bounds on stationary and transient performance measures. When the processes have many transitions due to several events, the coupling is not easy to apply. The goal of this work is to provide a general algorithm for the comparison using the coupling by mapping functions. This algorithm can be applied for the generation of aggregated bounding processes

Domaines: Performance et fiabilité [cs.PF]

Hind Castel-Taleb, Idriss Ismael Aouled. Stochastic comparison of Markov processes through coupling by mapping functions. QEST 2011 : 8th International Conference on Quantitative Evaluation of Systems, Sep 2011, Aachen Germany. ⟨hal-01303048⟩