Petri Box Calculus (PBC) is an algebraicmodel for the description of concurrent systems and sPBC (stochastic Petri Box Calculus) is a Markovian extension of that model. In this paper we add immediate multiactions to sPBC in order to increase the description power of this language. Thus, we both have timed multiactions that follow an exponential distribution, and multiactions that do not require any time and can be immediately executed. The denotational semantics of this model is based on a special class of GSPN (Generalized Stochastic Petri Nets), called gs-boxes .
2
Dostęp do pełnego tekstu na zewnętrznej witrynie WWW
In the last decades, a number of stochastic enrichments of process algebras was constructed to allow one for specification of stochastic processes within the well-developed framework of algebraic calculi. In [], a continuous time stochastic extension of finite Petri box calculus (PBC) was proposed called sPBC. The algebra sPBC has interleaving semantics due to the properties of continuous time distributions. At the same time, PBC has step semantics, and it could be natural to propose its concurrent stochastic enrichment. We construct a discrete time stochastic extension dtsPBC of finite PBC. A step operational semantics is defined in terms of labeled transition systems based on action and inaction rules. A denotational semantics is defined in terms of a subclass of labeled discrete time stochastic Petri nets (LDTSPNs) called discrete time stochastic Petri boxes (dts-boxes). A consistency of both semantics is demonstrated. In addition, we define a variety of probabilistic equivalences that allow one to identify stochastic processes with similar behaviour which are differentiated by too strict notion of the semantic equivalence. The interrelations of all the introduced equivalences are investigated.
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.