1,395 research outputs found
Numerical analysis of deterministic and stochastic Petri nets with concurrent deterministic transitions
This paper introduces an efficient numerical algorithm for the steady-state analysis of deterministic and stochastic Petri nets (DSPNs) without structural restrictions on the enabling of deterministic transitions. The method rests on observation, at equidistant time points, of the continuous-time Markov process that records tangible markings of the DSPN and remaining firing times associated with deterministic transitions. This approach results in the analysis of a general state space Markov chain whose system of stationary equations can be transformed into a system of Volterra equations. The techniques of this paper are also applicable to queueing networks, stochastic process algebras, and other discrete-event stochastic systems with an underlying stochastic process which can be represented as a generalized semi-Markov process with exponential and deterministic events
Transient analysis of deterministic and stochastic Petri nets with concurrent deterministic transitions
This paper introduces an efficient numerical algorithm for transient analysis of deterministic and stochastic Petri nets (DSPNs) and other discrete-event stochastic systems with exponential and deterministic events. The proposed approach is based on the analysis of a general state space Markov chain (GSSMC) whose state equations constitute a system of multidimensional Fredholm integral equations. Key contributions of this paper constitute the observations that the transition kernel of this system of Fredholm equations is piece-wise continuous and separable. Due to the exploitation of these properties, the GSSMC approach shows great promise for being effectively applicable for the transient analysis of large DSPNs with concurrent deterministic transitions. Moreover, for DSPNs without concurrent deterministic transitions the proposed GSSMC approach requires three orders of magnitude less computational effort than the previously known approach based on the method of supplementary variables
Petri nets for systems and synthetic biology
We give a description of a Petri net-based framework for
modelling and analysing biochemical pathways, which uni¯es the qualita-
tive, stochastic and continuous paradigms. Each perspective adds its con-
tribution to the understanding of the system, thus the three approaches
do not compete, but complement each other. We illustrate our approach
by applying it to an extended model of the three stage cascade, which
forms the core of the ERK signal transduction pathway. Consequently
our focus is on transient behaviour analysis. We demonstrate how quali-
tative descriptions are abstractions over stochastic or continuous descrip-
tions, and show that the stochastic and continuous models approximate
each other. Although our framework is based on Petri nets, it can be
applied more widely to other formalisms which are used to model and
analyse biochemical networks
CSL model checking of Deterministic and Stochastic Petri Nets
Deterministic and Stochastic Petri Nets (DSPNs) are a widely used high-level formalism for modeling discrete-event systems where events may occur either without consuming time, after a deterministic time, or after an exponentially distributed time. The underlying process dened by DSPNs, under certain restrictions, corresponds to a class of Markov Regenerative Stochastic Processes (MRGP). In this paper, we investigate the use of CSL (Continuous Stochastic Logic) to express probabilistic properties, such a time-bounded until and time-bounded next, at the DSPN level. The verication of such properties requires the solution of the steady-state and transient probabilities of the underlying MRGP. We also address a number of semantic issues regarding the application of CSL on MRGP and provide numerical model checking algorithms for this logic. A prototype model checker, based on SPNica, is also described
Performance Evaluation of CORBA Concurrency Control Service Using Stochastic Petri Nets
The interest in performance evaluation of middleware systems is increasing. Measurement techniques are still predominant among those used to carry out performance evaluation. However, performance models are currently being defined due to their flexibility, precision and facilities to carry out capacity planning activities. This paper presents stochastic Petri net models for performance evaluation of the CORBA Concurrency Control Service (CCS), which mediates concurrent access to objects. In order to validate the proposed models, CCS performance results obtained using those models are then compared against ones obtained through actual measurements.The interest in performance evaluation of middleware systems is increasing. Measurement techniques are still predominant among those used to carry out performance evaluation. However, performance models are currently being defined due to their flexibility, precision and facilities to carry out capacity planning activities. This paper presents stochastic Petri net models for performance evaluation of the CORBA Concurrency Control Service (CCS), which mediates concurrent access to objects. In order to validate the proposed models, CCS performance results obtained using those models are then compared against ones obtained through actual measurements
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
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