Class Of Timed Petri Nets Research Articles

A Clustering Approach to Approximate the Timed Reachability Graph for a Class of Time Petri Nets

Timed extended reachability graphs (TERG) of time Petri nets abstract the temporal specifications and represent the feasible trajectories under the earliest firing policy. One drawback of such graphs is the rapid increase in the number of states with respect to time specifications. For this reason, approximations of TERG that remove some states have been studied in recent works. In this article, we improve the approximation of a TERG. New objects—called vertices—are defined to manipulate the time constraints and algorithms are proposed to cluster nearby vertices. A metric based on the time constraints is defined for this purpose and a cluster TERG of reduced size is obtained.

Analysis of P-time event graphs in (max,+) and (min,+) semirings

In this paper, we investigate the behaviour of P-time event graphs, a class of time Petri nets with non-deterministic timing of places. Our approach is based on combined linear descriptions in both (max,+) and (min,+) semirings, where lower bounds on the state vector are (max,+)-linear and upper bounds are (min,+)-linear. We present necessary and sufficient conditions for the existence of extremal (fastest and slowest) periodic trajectories that are derived from the new description. The results are illustrated by a realistic example of an electroplating process.

State‐Feedback Control for a Class of Timed Petri Nets Subject to Marking Constraints

AbstractThe paper contributes with an original method of designing a control for discrete event systems modeled by a class of timed Petri nets. Precisely, this work deals with the closed loop control of Timed Event Graphs (TEGs) under specifications expressed with linear marking constraints. The objective of the controller is to limit the number of tokens in some places of these TEGs. The behavior of TEGs is represented by a system of difference equations that are linear in Min‐Plus algebra and the constraints are described by a set of inequalities, which are also linear in Min‐Plus algebra. A formal approach to design control laws that guarantee compliance with these marking constraints is proposed. For this, two sufficient conditions for the existence of control laws are proposed. The computed controls are causal feedbacks, which can be represented by a set of marked and timed places. The proposed method is illustrated in two applications: a manufacturing production line and an assembly system.

Flight Rescheduling Problem Induced by Air Traffic Network Capacity Constraints Based on the Binary Decision Diagram Approach

The exponential growth in air traffic and unplanned events on the day of flight schedules such as adverse weather conditions led to initial flight disruptions. In this paper, we propose a decision support framework for flight rescheduling in air traffic management based on ground delay, changing the initial flight and flight canceling. This approach is based on using Time Petri Nets (TPN) to model air traffic networks. We introduce a Binary Decision Diagram based tool to represent the state space of a class of Time Petri Nets. This tool, called Time Reduced Ordered Binary Decision Diagram (T-ROBDD) is able to represent a large state space of a TPN with a small data structure and enable the efficient manipulation of this set. In what follows, we developed a technique to generate all the rescheduling flights plans taking into account the temporal and spatial constraints.

Time-independent Liveness in Time Petri Nets

In this paper we consider a class of Time Petri nets defined by structural restrictions. Each Time Petri net which belongs to this class has the property that their liveness behaviour does not depend on the time. Therefore, the Time Petri net is live when its skeleton is live.

Uma abordagem intervalar para a caracterização de intervalos de disparo em redes de Petri temporais

As redes de Petri temporais são uma das extensões das redes de Petri convencionais para modelagem e análise de sistemas a eventos discretos temporizados. A cada transição da rede é associado um intervalo de tempo, o qual delimita o instante de disparo da transição. A análise das redes de Petri temporais tem sido feita por métodos enumerativos que relacionam todos os estados alcançáveis da rede. Neste artigo, usando recursos da álgebra intervalar e utilizando o conceito de classe de estados, é apresentada uma abordagem para resolver problemas relacionados à caracterização de intervalos de tempo de disparo em redes de Petri temporais. A partir de uma expressão algébrica, desenvolvida para cálculo de intervalos de tempo entre duas classes de estados consecutivas, obtém-se uma equação intervalar que possibilita o cálculo de intervalos de tempo entre duas classes de estados quaisquer. Assim, é possível calcular o intervalo de tempo para ocorrência de uma seqüência de eventos. Utilizando um método de redução da rede, a equação intervalar assume a forma matricial e, com isso, amplia a classe das redes de Petri temporais à qual a equação intervalar é aplicável. Por fim, uma aplicação explorando as potencialidades da equação intervalar no cálculo de medidas características de um sistema a eventos discretos temporizados é apresentada.

Modeling for Systems with Selective Parameters based on Max-plus Algebra

This paper proposes Max-Plus Linear (MPL) systems with selective parameters that can describe a certain class of Timed Petri nets (TPN). In this class, selector and joint places are incorporated with Single-Input and Single-Output Timed Event Graph (SISO TEG) subnets. It is confirmed that the proposed controller effectively works taking into account practical constraints through a numerical example.

Efficient verification of a class of time Petri nets using linear programming

Efficient verification of a class of time Petri nets using linear programming

On Flows in Stochastic Marked Graphs

In this work, the discrete event systems called Stochastic Marked Graphs (SMGs) are investigated from a stability point of view. Being a special class of Timed Petri Nets with stochastic firing times, they are studied under general assumptions of stationarity and ergodicity of the firing times and ergodicity of flows of their free strongly connected components. The values of the flows of tokens in an SMG are specified as functions of the intrinsic rates of its free strongly connected components, and various stability issues are discussed.