Compositional Asymmetric Cooperations for Process Algebras with Probabilities, Priorities, and Time

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Process algebra for performance evaluation

This paper surveys the theoretical developments in the field of stochastic process algebras, process algebras where action occurrences may be subject to a delay that is determined by a random variable. A huge class of resource-sharing systems – like large-scale computers, client–server architectures, networks – can accurately be described using such stochastic specification formalisms. The main emphasis of this paper is the treatment of operational semantics, notions of equivalence, and (sound and complete) axiomatisations of these equivalences for different types of Markovian process algebras, where delays are governed by exponential distributions. Starting from a simple actionless algebra for describing time-homogeneous continuous-time Markov chains, we consider the integration of actions and random delays both as a single entity (like in known Markovian process algebras like TIPP, PEPA and EMPA) and as separate entities (like in the timed process algebras timed CSP and TCCS). In total we consider four related calculi and investigate their relationship to existing Markovian process algebras. We also briefly indicate how one can profit from the separation of time and actions when incorporating more general, non-Markovian distributions

P♤ : A process algebra for modeling prioritized stochastic timed systems (extended abstract)

We present P♤, a Stochastic Process Algebra (SPA) that allows for the modeling of timed systems with priorities and urgency. We de ne the semantics of P♤ in terms of Prioritized Stochastic Automata (PSA), an extension of automata with clock events, priorities and probabilistic symbolic transitions. PSAs are symbolic objects that have a concrete semantics on Probabilistic Timed Transition Systems (PTTS). Therefore, P♤ has semantics in two steps in terms of PTTS. We also de ne several operators directly on PTTS. They include parallel composition and a prioritizing operator. We show that this operators applied to PTTS commute (modulo probabilistic bisimulation) with their relatives in P♤ .Eje: Teoría (TEOR)Red de Universidades con Carreras en Informática (RedUNCI

Non-determinism in Probabilistic Timed Systems with General Distributions

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On the use of MTBDDs for performability analysis and verification of stochastic systems

AbstractThis paper describes how to employ multi-terminal binary decision diagrams (MTBDDs) for the construction and analysis of a general class of models that exhibit stochastic, probabilistic and non-deterministic behaviour. It is shown how the notorious problem of state space explosion can be circumvented by compositionally constructing symbolic (i.e. MTBDD-based) representations of complex systems from small-scale components. We emphasise, however, that compactness of the representation can only be achieved if heuristics are applied with insight into the structure of the system under investigation. We report on our experiences concerning compact representation, performance analysis and verification of performability properties

Extensions of Standard Weak Bisimulation Machinery: Finite-state General Processes, Refinable Actions, Maximal-progress and Time

AbstractWe present our work on extending the standard machinery for weak bisimulation to deal with: finite-state processes of calculi with a full signature, including static operators like parallel; semantic action refinement and ST bisimulation; maximal-progress, i.e. priority of standard actions over unprioritized actions; representation of time: discrete real-time and Markovian stochastic time. For every such topic we show that it is possible to resort simply to weak bisimulation and that we can exploit this to obtain, via modifications to the standard machinery: finite-stateness of semantic models when static operators are not replicable by recursion, as for CCS with the standard semantics, thus yielding decidability of equivalence; structural operational semantics for terms; a complete axiomatization for finite-state processes via a modification of the standard theory of standard equation sets and of the normal-form derivation procedure