P-time Petri Nets Research Articles

Two-staged approach for estimation of sequences in partially observable P-time Petri nets on a sliding horizon with schedulability analysis

In this paper, we consider the on-line estimation of current subsequences for Partially Observable P-time Petri Nets and their starting markings on a sliding horizon composed of steps defined by two successive occurrences of observable transition firings. We propose a general strategy composed of two phases: Phase 1 exploits a simplification of the P-time Petri net under the form of a Timed Petri net; considering a candidate count vector and the relevant starting marking proposed at Phase 1, Phase 2 makes a schedulability analysis by building a system of relations which can be represented by an acyclic conflict-free computation graph. The complete approach avoids the generation of sets which is generally time and space consuming, and provides an optimal solution for each subproblem by using efficient standard tools.

Petri-Net-Based Scheduling of Flexible Manufacturing Systems Using an Estimate Function

In this paper, a novel admissible estimate function is proposed to schedule flexible manufacturing systems (FMSs) by using heuristic search. The FMSs to be scheduled are modeled by P-timed Petri nets. The problem is to make the system evolve from the initial marking to a given final marking by firing a sequence of transitions. The structure of jobs in an FMS is always symmetrical to utilize the shared resources, but the processing time of each job is asymmetrical to reduce the global process time. By utilizing the structural symmetry of a Petri net model of an FMS, a partial reachability graph is generated such that the notorious state explosion problem is mitigated. For each generated marking, the proposed estimate function is used to provide an estimated cost for firing the transition sequence. Then, we can select the marking with the smallest cost from the generated markings and compute its successors. This process is continued until the system reaches the final marking. With the proposed method, the performance is evaluated in terms of the cost of the obtained transition firing sequence and the number of the expanded markings. The cost provided by the proposed estimate function is closer to the optimal cost than the previous work, i.e., the proposed method can find a transition firing sequence with less expanded markings and minimal process time from a marking to the final marking. Experimental results are used to demonstrate and evaluate the proposed approach.

Robust control strategies facing disturbances in Railway Transport Networks

Objectives: The key objective of this present article is the presentation of a control strategy which consists to compensate the disturbance as soon as it is observed. The main purpose of the proposed control strategy is to guarantee the respect of railway scheduling. The novel strategy allows compensating temporal disruption as soon as it is observed in order to avoid the time constraint violation and to respect planned scheduling. Methods: An algorithm that amends the measured disturbances by compensating the disruption along the mono-synchronized paths is presented. The proposed algorithm allows computing the available control margin for every controllable place. Findings: The main impartial is to compensate partially or totally the disturbance so as to avoid time constraint violation in railway transport networks. In these networks, time may be a significant parameter because it encompasses constraints to avoid adverse events. The temporal constraints which will arise on the railway network may degrade the planed schedules and consequently affect the availability of transportation systems. This leads to many problems in the decision and optimization of the studied transport systems. Novelty/Applications: This paper is devoted to the modeling and robust control of the Tunisian railway network. In this context, a novel robustness strategy is developed to compensate the time disruption in railway networks and to preserve the planned schedule. Keywords: robustness; control; temporal disturbances; railway networks; Ptime Petri Nets

Static Integration Based on Stochastic P-Time Petri Nets of Maintenance Scheduling for Railway Transport Equipment

In transport systems, all equipment requires maintenance, which directly affects the machine’s availability and consequently the planned transport schedule. The purpose of this paper is to carry out a method for integrating recovery jobs in railway systems. The proposed method allows the insertion of preventive and corrective maintenance operations when the transport equipment is available in order to minimize periods of inactivity, avoid catastrophic scenarios, and maintain stability and safety of the studied networks. A computing algorithm, allowing insertion of the planned recovery tasks in periods of metro availability, without changing the initial scheduling solution, is established. Finally, we illustrate the implementation of the proposed approach on Tunisian Sahel railway transport networks.

Decision Tools Regarding Time Constraints Violation in Manufacturing Workshops

This paper is dedicated to the study of constraints violation in manufacturing workshops with time constraints. In such systems, every operation duration is included between minimal and maximal values. P-time Petri nets are used for modeling. A new theorem is introduced, constituting a decision tool about the occurrence of constraints violation at the level of a synchronization transition when various types of time disturbances occur. It shows the robustness properties of a manufacturing system on a range that may include delay and advance disturbances. The theoretical result is illustrated step by step on a given workshop. Two other lemmas are elaborated contributing to the study of the constraints violation problem. The final goal is to generalize the robustness property towards simultaneous occurrence of two delays at two points of the system, each having its own robustness range.

A Monitoring Approach Based on Fuzzy Stochastic P-Timed Petri Nets of a Railway Transport Network

This paper proposes a monitoring approach based on stochastic fuzzy Petri nets (SFPNs) for railway transport networks. In railway transport, the time factor is a critical parameter as it includes constraints to avoid overlaps, delays, and collisions between trains. The temporal uncertainties and constraints that may arise on the railway network may degrade the planned schedules and consequently affect the availability of the transportation system. This leads to many problems in the decision and optimization of the railway transport systems. In this context, we propose a new fuzzy stochastic Petri nets for monitoring (SFPNM). The main goal of the proposed supervision approach is to allow an early detection of traffic disturbance to avoid catastrophic scenarios and preserve stability and security of the studied railway networks. Finally, to demonstrate the effectiveness and accuracy of the approach, an application to the case study of the Tunisian railway network is outlined.

Distributed Monitoring Based on P-Time Petri Nets and Chronicle Recognition of the Tunisian Railway Network

This paper falls under the problems of the monitoring of a Discrete Event System (DES) with time constraints. Among the various techniques used for online and distributed monitoring, we are interested in the chronicle recognition. Chronicles are temporal patterns that represent the system’s possible evolutions. The proposed models are based on P-time Petri nets that are suitable to represent with accuracy and modularity the Tunisian railway network. These models are scalable and may be used to represent a large variety of railway networks. Then, monitoring is based on the generation of chronicles that are suitable to detect and isolate traffic incidents in a distributed setting. Consequently, the proposed approach is tractable for large networks. Finally, to demonstrate the effectiveness and accuracy of the approach, an application to the case study of the Tunisian railway network is outlined.

Modeling of safe time Petri nets by interval weighted automata

Abstract Weighted automata with weights (multiplicities) in the product semirings can be viewed as alternative models for timed systems, where concurrent time behaviors are modeled using nondeterminism, while in timed automata using multiple clocks. It is known that safe timed Petri nets can be modeled by means of (max,+) automata, i.e. weighted automata in the (max,+) semiring. We present here a direct way of deriving interval weighted automata with weights in two different product semirings from both safe P-time and safe T-time Petri nets. It is well known that these two classes of time Petri nets are not comparable as opposed to timed Petri nets with deterministic timing of transitions. In terms of weighted automata we need to consider different underlying semirings, namely the product of (max,+) and (min,+) semirings for P-time Petri nets and the product of (max,+) semiring with itself for T-time Petri nets.

Corrigendum to “Modeling and Robustness Study of Railway Transport Networks Using P-Timed Petri Nets”

Corrigendum to “Modeling and Robustness Study of Railway Transport Networks Using P-Timed Petri Nets”

Robust control for railway transport networks based on stochastic P-timed Petri net models

This article is devoted to the modeling, performance evaluation and robust control of the railway transport network in Sahel Tunisia. The regular increase in the number of passengers makes the management of transportation systems more and more complex. Railway transport requires specific needs. Indeed, many decision and optimization problems occur from the planning phase to the implementation phase. Railway transport networks can be considered as discrete event systems with time constraints. The time factor is a critical parameter, since it includes schedules to be respected in order to avoid overlaps, delays and collisions between trains. The uncertainties affect the service and the availability of transportation resources and, consequently, the transport scheduling plan. Petri nets have been recognized as powerful modeling and analysis tools for discrete event systems with time constraints. Consequently, they are suitable for railway transport systems. In this article, stochastic P-time Petri nets are used for the railway transport networks in Sahel Tunisia. A global model is first detailed. Then, this model is used to analyze the network traffic and evaluate the performance of the system. Robustness again disturbances is introduced and a control strategy is developed to reduce the consequences of the disturbances in order to maintain the expected schedule.

Modeling and Robustness Study of Railway Transport Networks Using P-Timed Petri Nets

The importance of public transport systems continues to grow. These systems must respond to an increasing demand for population mobility and traffic disturbances. Rail transport networks can be considered as Discrete Event Systems (DES) with time constraints. The time factor is a critical parameter, since it includes dates to be respected in order to avoid overlaps, delays, and collisions between trains. P-time Petri Nets have been recognized as powerful modeling and analysis tools for railway transport systems. Temporal disturbances in these systems include railway infrastructure, traffic management, and disturbances (weather, obstacles on the tracks, malice, social movement, etc.). The developments presented in this paper are devoted to the modeling and the study of the robustness of the railway transport systems in order to evaluate the stability and the efficiency of these networks. In this study two robust control strategies towards time disturbances are presented. The first one consists of compensating the disturbance as soon as it is observed in order to avoid constraints violation. The second one allows generating, by the control, a temporal lag identical to the disturbance in order to avoid the death of marks on the levels of synchronization transitions of the P-time Petri net model.

Optimization of Total Energy Consumption in Flexible Manufacturing Systems Using Weighted P-Timed Petri Nets and Dynamic Programming

Schedule optimization is crucial to reduce energy consumption of flexible manufacturing systems (FMSs) with shared resources and route flexibility. Based on the weighted p-timed Petri Net (WTPN) models of FMS, this paper considers a scheduling problem which minimizes both productive and idle energy consumption subjected to general production constraints. The considered problem is proven to be a nonconvex mixed integer nonlinear program (MINLP). A new reachability graph (RG)-based discrete dynamic programming (DP) approach is proposed for generating near energy-optimal schedules within adequate computational time. The nonconvex MINLP is sampled, and the reduced RG is constructed such that only reachable paths are retained for computation of the energy-optimal path. Each scheduling subproblem is linearized, and each optimal substructure is computed to store in a routing table. It is proven that the sampling-induced error is bounded, and this upper bound can be reduced by increasing the sampling frequency. Experiment results on an industrial stamping system show the effectiveness of our proposed scheduling method in terms of computational complexity and deviation from optimality.

Using Time Reachability Tree Logic to Specifying and Verifying Temporal Behavior of Workflow-Net

Workflow management has been a hot issue in both academic and industrial research. Deadline assignment is of great significance in workflow management. In order to avoid deadline violation, this paper presents an approach to the schedulability analysis of workflow system modeled in p-time Petri nets by separating timing properties from other behavior properties. The analysis of behavioral properties is conducted based on the reachability graph of the underlying p-Time Petri net, whereas timing constraints are checked in term of absolute and relative firing domains. Our technique is based on a concept called clock-stamped state class (CS-class) and temporal logic. With the reachability graph generated based on CS-class, we can directly compute the end-to-end time delay in workflow execution. We have identified a class of well-structured p-time Petri nets such that their reachability can be easy analyzed and temporal behavior can be easy analyzed by time reachability tree logical.

Monitoring of Packaging Machine Using Synchronized Fuzzy Petri Nets

The aim of this paper is the study and the design of a monitoring module based on P-time Petri nets (P-TPN) for manufacturing job-shops with time constraints. In such systems, operation times are included between a minimum and a maximum value. The monitoring consists in a set of two collaborative PNs. The first is used for modeling of normal behavior of the system by temporal spectrum of the marking. The second model, Synchronized Fuzzy Petri Nets (SinFPN), corresponds to monitoring activities. This paper proposes failures modeling and process monitoring for a flexible manufacturing system with time constrains, using a P-TPNs and SincFPN. A monitoring approach based on fuzzy model able to integrate alarm signals and the moment of appearance of the external events in the supervised system is presented. The aim of this original approach is to show how the detection of the occurrence/persistence of the monitored external events could make the supervision more efficient by performing an early diagnosis. It is illustrated step by step on an example of a packaging machine.

Active robustness of a milk manufacturing workshop with time constraints

This paper deals with the active robustness of a milk manufacturing workshop including time interval constraints. Such systems have robustness properties towards time disturbances. The robustness property can be a static property, but using a dynamic control strategy may increase the robustness value. Controlled P-time Petri nets are used as a modelling tool. Some definitions and a series of lemmas are cited in order to build a theory dealing with robustness problems. In order to avoid the death of marks at the synchronisation transitions of the P-time Petri net model, a robust control strategy facing time disturbances is presented. The proposed approach tries to reject the disturbance as soon as it is observed. Furthermore, this approach is used by an algorithm computing an active robustness margin at a given node. It is illustrated step by step on an example of a milk manufacturing workshop. A comparison with the bound provided for the passive robustness is made.

Towards a new schedulability technique of real-time systems modeled by P-time Petri nets

In this paper, a novel schedulability analysis technique of real-time systems is presented. The developed approach is based on the consideration of the reachability graph of the (untimed) underlying Petri net of the studied model. The schedulability analysis is then conducted in two steps. Once a feasible firing sequence (called occurrence sequence) is highlighted, this sequence is then described under an algebraic form of type Ax ≤ b. The particular features of matrix A lead to a bimonotone linear inequality system. A bimonotone linear inequality is a linear inequality with at most two nonzero coefficients that are of opposite signs (if both different from zero). Thus, deciding whether a firing sequence is schedulable or not takes the form of the solution of a single-source shortest path problem which can be polynomially solved via the Bellman–Ford algorithm.

Scheduling and control of real-time systems based on a token player approach

Petri nets are a powerful formalism for the specification and verification of concurrent systems, such as sequential systems and manufacturing systems. To deal with real-time systems whose time issues become essential, different extensions of Petri nets with time have been proposed in the literature. In this paper, a new scheduling and control technique for real-time systems modeled by ordinary P-time Petri nets is proposed. Its goal is to provide a scheduling for a particular firing sequence, without any violation of timing constraints ensuring that no deadline is missed. It is based on the firing instant notion and it consists in determining an inequality system generated for a possible evolution (in terms of a feasible firing sequence for the untimed underlying Petri net) of the model. This system can be used to check reachability problems as well as evaluating the performances of the model considered and determining the associated control for a definite functioning mode and it introduces partial order on the execution of particular events.

Scheduling FMS with alternative routings using Petri nets and near admissible heuristic search

This paper proposes and evaluates a near admissible heuristic search strategy and its application to a kind of flexible manufacturing system (FMS) scheduling in a Petri net framework. Petri nets can concisely model the strict precedence constraint, multiple kinds of resources, and concurrent activities. To cope with the complexities for scheduling of FMS with alternative routings, this paper proposes an admissible heuristic function based on the execution of P-timed Petri nets and presents an improved dynamic weighting A* strategy using the proposed heuristic function. The search scheme does not need to predict the depth of solution in advance and the quality of the search result is also controllable. Some numerical experiments are carried out to demonstrate usefulness of the algorithm.

Constraint graph-based approach for the analysis and the control of time critical systems

The increasing complexity of manufacturing systems gives rise to the development of new formal methods allowing to handle their particularities. Petri nets are a powerful formalism for the specification and verification of concurrent systems including sequential systems and manufacturing systems. To deal with systems whose time issues become fundamental, different time Petri nets extensions have been developed in the literature, each one being dependent on the application considered. For the time critical systems, their correctness depends not only on the logic correctness but also on the time constraints. Timing issues are essential. In this paper, a new method of analysis and control for P-time Petri nets is proposed. It is based on the firing instant notion and exploits a constraint graph approach.

Vers une nouvelle méthode de synthèse de commande pour les réseaux de Petri p-temporels

Petri nets are a powerful formalism for the specification and verification of concurrent systems such as sequential and manufacturing systems. To take into account efficiently the time parameter different extensions have been developed in the literature, each one being dependent on the application considered. In this paper, a new control technique for p-time Petri nets is proposed. It is based on the firing instant notion and it consists in determining a system of inequalities generated for a possible evolution (in terms of a feasible firing sequence for the untimed underlying Petri net) of the model considered. This system can be used to check reachability problems as well as evaluating the performances of the model considered and determining the associated control for a definite functioning mode. Furthermore, the proposed approach is not restricted to subclasses or safe Petri nets.