Stochastic bisimulation and performance evaluation in discrete time stochastic and deterministic Petri box calculus dtsdPBC
Résumé
We propose dtsdPBC, an extension with deterministically timed multiactions of discrete time stochastic
and immediate Petri box calculus (dtsiPBC), previously presented by I.V. Tarasyuk, H. Maci`a and V. Valero.
In dtsdPBC, non-negative integers specify deterministic multiactions with fixed (including zero) time delays.
The step operational semantics is constructed via labeled probabilistic transition systems. The Petri net
denotational semantics is defined via dtsd-boxes, a subclass of labeled discrete time stochastic Petri nets
with deterministic transitions. We also define step stochastic bisimulation equivalence of the process expres-
sions, which is used to compare the qualitative and quantitative behaviour of the specified processes. The
consistency of the operational and denotational semantics of dtsdPBC up to that equivalence is established.
In order to evaluate performance in dtsdPBC, the underlying semi-Markov chains (SMCs) and (reduced)
discrete time Markov chains (DTMCs and RDTMCs) of the process expressions are analyzed. We explain
how step stochastic bisimulation equivalence of the expressions can be used for quotienting their transition
systems and Markov chains, as well as to compare the stationary behaviour and residence time properties.
We prove that the equivalence guarantees coincidence of the functional and performance characteristics and
therefore can be used to simplify performance analysis of the algebraic processes. In a case study, a method
of modeling, performance evaluation and behaviour reduction for concurrent systems with discrete fixed and
stochastic delays is applied to the generalized shared memory system with maintenance. We also determine
the main advantages of dtsdPBC by comparing it with other well-known or similar SPAs.
Mots clés
stochastic process algebra
stochastic Petri net
Petri box calculus
discrete time
stochastic multiaction
deterministic multiaction
transition system
operational semantics
stochastic transition
deterministic transition
dtsd-box
denotational semantics
Markov chain
performance evaluation
reduction
stochastic bisimulation
quotient
shared memory system
Domaines
Logique en informatique [cs.LO]
Origine : Fichiers produits par l'(les) auteur(s)