Phase-type distributions in stochastic automata networks

Phase-type distributions in stochastic automata networks

Abstract Stochastic Automata Networks (Sans) are high-level formalisms for modeling very large and complex Markov chains in a compact and structured manner. To date, the exponential distribution has been the only distribution used to model the passage of time in the evolution of the different San components. In this paper we show how phase-type distributions may be incorporated into Sans thereb...

Phase Type and Matrix Exponential distributions in stochastic modelling

Since their introduction, properties of Phase Type (PH) distributions have been analyzed and many interesting theoretical results found. Thanks to these results, PH distributions have been profitably used in many modeling contexts where non exponentially distributed behavior is present. Matrix Exponential (ME) distributions are distributions whose matrix representation is structurally similar t...

Stochastic Automata Networks

cient Handling of Phase - type Distributions inGeneralized Stochastic Petri

We study the introduction of transitions with Phase-type distribution ring time in (bounded) generalized stochastic Petri nets. Such transitions produce large increases of both space and time complexity for the computation of the steady state probabilities of the underlying Markov chain. We propose a new approach to limit this phenomenon while keeping full stochastic semantics of previous works...

Classification and properties of acyclic discrete phase-type distributions based on geometric and shifted geometric distributions

Acyclic phase-type distributions form a versatile model, serving as approximations to many probability distributions in various circumstances. They exhibit special properties and characteristics that usually make their applications attractive. Compared to acyclic continuous phase-type (ACPH) distributions, acyclic discrete phase-type (ADPH) distributions and their subclasses (ADPH family) have ...