Probabilistic non-asymptotic analysis of distributed algorithms

Nicolas Champagnat (1, 2) , René Schott (2, 3) , Denis Villemonais (2, 1)

1 TOSCA - TO Simulate and CAlibrate stochastic models
2 IECL - Institut Élie Cartan de Lorraine
3 LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications

We present a new probabilistic analysis of distributed algorithms. Our approach relies on the theory of quasi-stationary distributions (QSD) recently developped by the first and third authors [4, 5, 6]. We give properties on the deadlock time and the distribution of the model before deadlock, both for discrete and diffusion models. Our results are non-asymptotic since they apply to any finite values of the involved parameters (time, numbers of resources, number of processors, etc.) and reflect the real behavior of these algorithms, with potential applications to deadlock prevention, which are very important for real world applications in computer science.

Mots clés: Distributed algorithms; Deadlock; Quasi-stationary distributions

Domaines: Probabilités [math.PR]; Calcul parallèle, distribué et partagé [cs.DC]

Nicolas Champagnat, René Schott, Denis Villemonais. Probabilistic non-asymptotic analysis of distributed algorithms. 2018. ⟨hal-01710663v1⟩