Stochastic Petri nets (SPNs) with generally distributed firing times can model a large class of systems, but simulation is the only feasible approach for their solution. We explore a hierarchy of SPN classes where modeling power is reduced in exchange for an increasingly efficient solution. Generalized stochastic Petri nets (GSPNs), deterministic and stochastic Petri nets (DSPNs), semi-Markovia...

Stochastic Petri nets generalize the notion of queueing systems and are a useful model in performance evaluation of parallel and distributed systems. We give necessary and sufficient conditions for the boundedness of a stochastic process related to these nets. A.M.S. Classification : 60 G 40, 68 M 20, 60 K 25 Research partially supported by project PA86-0028 of the Spanish Comisión Interministe...

We consider equivalence relations for Fluid Stochastic Petri Nets (FSPNs). Based on equivalence relations for Stochastic Petri Nets (SPNs), which are derived from lumpability for Markov Chains, and from lumpability for certain classes of differential equations, we define an equivalence relation for FSPNs. Lumpability for the differential equations is based on a finite discretization approach an...

We present SPNP, a powerful GSPN package developed at Duke University. SPNP allows the modeling of complex system behaviors. Advanced constructs are available, such as markingdependent arc multiplicities, enabling functions, arrays of places or transitions, and subnets; in addition, the full expressive power of the C programming language is available to increase the flexibility of the net descr...

A MATLAB toolbox has been developed to handle the basic problems of discrete event dynamical systems that are modeled by Petri nets. In the Petri Net Toolbox five types of Petri nets (untimed, transition-timed, place-timed, stochastic and generalized stochastic), with finite or infinite capacity, can be used. A user-friendly graphical interface allows activating three simulation modes (accompan...

Petri nets have been widely used to model and analyze biochemical reaction networks. This chapter gives an overview of di↵erent types of Petri nets within a unifying Petri net framework that comprises the qualitative, stochastic, continuous and hybrid paradigms at both uncolored and colored levels. The Petri net framework permits to investigate one and the same biological reaction network with ...

High availability constraints ensure a high level of operational performance that must be maintained during a contractual measurement period. Such constraints must be satisfied, particularly, for critical systems related to global security and human safety. High availability often results from material redundancies and lead to large stochastic discrete event models with numerous states. Markov ...

Stochastic performance models are widely used to analyse the performance of systems that process customers and resources. However, the construction of such models is traditionally manual and therefore expensive, intrusive and prone to human error. In this paper we introduce PEPERCORN, a Petri Net Performance Model (PNPM) construction tool, which, given a dataset of raw location tracking traces ...

This paper addresses the computation of upper bounds for the steady-state throughput of stochastic Petri net systems with immediate and generally distributed timed transitions. It is achieved through the use of a kind of decomposition of the whole net system. Results are obtained deeply bridging stochastic Petri net theory to untimed Petri net and queueing network theories. Previous results are...

Biological systems are often very complex so that an appropriate formalism is needed for modeling their behavior. Hybrid Petri nets, consisting of timediscrete as well as continuous Petri net elements, have proven to be ideal. This formalism was implemented based on the Modelica language. Several Petri net components are structured within an advanced Petri net library. A special sub-library con...