Petri net

About: Petri net is a research topic. Over the lifetime, 25039 publications have been published within this topic receiving 406994 citations.

Stochastic Petri nets: an elementary introduction

Abstract: Petri nets in which random firing delays are associated with transitions whose firing is an atomic operation are known under the name “stochastic Petri nets” These models are discussed, with the purpose of explaining why they were proposed in the performance evaluation field, why random delays with negative exponential probability density functions are mainly used, and what are their strong and weak points An effort is made to summarize the lines of research that are currently being pursued, and to explain what new results would be regarded as breakthroughs and have the most impact on the use of this modeling technique in the application field

Performance evaluation of job-shop systems using timed event-graphs

Abstract: Timed event-graphs, a special class of timed Petri nets, are used for modelling and analyzing job-shop systems. The modelling allows the steady-state performance of the system to be evaluated under a deterministic and cyclic production process. Given any fixed processing times, the productivity (i.e., production rate) of the system can be determined from the initial state. It is shown in particular that, given any desired product mix, it is possible to start the system with enough jobs in process so that some machines will be fully utilized in steady-state. These machines are called bottleneck machines, since they limit the throughput of the system. In that case, the system works at the maximal rate and the productivity is optimal. The minimal number of jobs in process allowing optimal functioning of the system is further specified as an integer linear programming problem. An efficient heuristic algorithm is developed to obtain a near-optimal solution. >

A technique of state space search based on unfolding

Abstract: Unfoldings of Petri nets provide a method of searching the state space of concurrent systems without considering all possible interleavings of concurrent events. A procedure is given for constructing the unfolding of a Petri net, terminating the construction when it is sufficient to represent all reachable markings. This procedure is applied to hazard and deadlock detection in asynchronous circuits. Examples are given of scalable systems with exponential size state spaces, but polynomial size unfoldings, including a distributed mutual exclusion ring circuit.

From UML sequence diagrams and statecharts to analysable petri net models

Abstract: In this paper we study the use of Sequence Diagrams and Statecharts of the Unified Modeling Language (UML) for the validation and the performance evaluation of systems. We assume that the system is specified as a set of Statecharts and that Sequence Diagrams are used to represent "executions of interest". UML lacks a formal semantics and hence it is not possible to apply, directly, mathematical techniques on UML models for system validation. To reach this goal we propose an automatic translation of Statecharts and Sequence Diagrams into Generalized Stochastic Petri Nets, and a composition of the resulting net models suitable for reaching a given analysis goal. The translation into Petri nets is based on the abstract syntax of the UML Collaborations and of the State Machines packages (from which Sequence Diagrams and Statecharts are derived) and the construction of the complete model heavily uses compositionality.