Distributed Markov Processes

Samy Abbes (1)

1 PPS - Preuves, Programmes et Systèmes

This paper introduces the model of Distributed Markov Processes (DMP), a probabilistic model of a system with distributed state over n>1 sites. The definition of DMP being given, the notion of stopping time in the distributed context is introduced, and a Strong Markov Property is derived. DMP are then characterized by their characteristic coefficients. These play a role similar to the coefficients of the transition matrix of discrete Markov chains, excepted that normalization conditions sufficient to define a DMP are not given here. The characteristic coefficients of a DMP are shown to satisfy the concurrency equations. The main result of the paper is the proof of the existence of DMP on n sites, n>1. The proof makes use of the tools introduced, especially the notion of stopping times. The case n=2 has been extensively studied in a previous note.

Mots clés: Markov processes; concurrency; distributed system

Domaines: Probabilités [math.PR]; Modélisation et simulation; Réseaux et télécommunications [cs.NI]

Samy Abbes. Distributed Markov Processes. 2011. ⟨hal-00631501⟩