Transient calculations on process algebra derived Markov chains

Transient calculations on process algebra derived Markov chains

The process of obtaining transient measures from a Markov chain as implemented in the software, ipclib is described. The software accepts models written in PEPA, Bio-PEPA or as a Petri net. In the case of the process algebras, a rich query specification language particularly well suited for the derivation of passage-time quantiles is provided. Such measurements are obtained from the derived Mar...

Process Algebra and Markov Chains

This paper surveys and relates the basic concepts of process algebra and the modelling of continuous time Markov chains. It provides basic introductions to both fields, where we also study the Markov chains from an algebraic perspective, viz. that of Markov chain algebra. We then proceed to study the interrelation of reactive processes and Markov chains in this setting, and introduce the algebr...

Performance Evaluation : = (Process Algebra + Model Checking) × Markov Chains

Markov chains are widely used in practice to determine system performance and reliability characteristics. The vast majority of applications considers continuous-time Markov chains (CTMCs). This tutorial paper shows how successful model specification and analysis techniques from concurrency theory can be applied to performance evaluation. The specification of CTMCs is supported by a stochastic ...

Linear Algebra Application~ Markov Chains

Zeon Algebra, Fock Space, and Markov Chains

Fock spaces over zeons are introduced. Trace identities and a noncommutative “integration-by-parts” formula are developed. As an application, we find a new criterion, without involving powers of the transition matrix, for a Markov chain to be ergodic.