Markov Nets: Probabilistic Models for distributed and
Albert Benveniste, Éric Fabre, Stefan Haar · 2001
For distributed systems, i.e. large networked complex systems, there is a drastic difference between a local view and knowledge of the system, and its global view. Distributed systems have local state and time, hut do not possess global state and time in the usual sense. In this paper, motivated by the monitoring of distributed systems and in particular of telecommunications networks, we develop Markov nets as an extension of Markov chains and hidden Markov models (HMM) for distributed and concurrent systems. By a concurrent system, we mean a system in which compcnents may evolve independently, with sparse synchrcnizations. We follow a sc-called true concurrency ap proach, in which neither global state nor global linear time are available. Instead, we use only local states in combination with a partial order model of time. Our basic mathematical tool is that of Petri net unfoldings.