Probabilistic true-concurrency models: Markov nets and a Law of large numbers

Samy Abbes (1) , Albert Benveniste (2)

1 PPS - Preuves, Programmes et Systèmes
2 DISTRIBCOM - Distributed and Iterative Algorithms for the Management of Telecommunications Systems

We introduce the model of Markov nets, a probabilistic extension of safe Petri nets under the true-concurrency semantics. This means that traces, not firing sequences, are given a probability. This model builds upon our previous work on probabilistic event structures. We use the notion of branching cell for event structures and show that the latter provides the adequate notion of local state, for nets. We prove a Law of Large Numbers (LLN) for Markov nets, which constitutes the main contribution of the paper. This LLN allows characterizing in a quantitative way the asymptotic behavior of Markov nets.

Keywords: Probabilistic event structures; true-concurrency; probability

Domains: Networking and Internet Architecture [cs.NI]; Probability [math.PR]

Samy Abbes, Albert Benveniste. Probabilistic true-concurrency models: Markov nets and a Law of large numbers. Theoretical Computer Science, 2008, 390, pp.129-170. ⟨10.1016/j.tcs.2007.09.018⟩. ⟨hal-00349209⟩