Timed Petri Nets Research Articles

Schedule Optimization of Time Petri Nets Based on Ant Colony Systems

This paper presents a time Petri net model with the optimizing mechanism based on ant colony systems that addresses the problem of schedule optimization. The choice rules and pheromone update rules of artificial ants are embedded into the evolution rules of a time Petri net, so the modeling and scheduling analysis of real systems can be integrated into the same model. Compared with the approaches based on the heuristic search and genetic algorithms, our method efficiently unifies the modeling and analysis of schedule problems based on a time Petri net.

Optimisation of block erection scheduling based on a Petri net and discrete PSO

The shipyard block erection system (SBES) is a typical discrete-event dynamic system. To model multiprocessing paths and a concurrent assembly procedure, a timed Petri net (TPN) is proposed. The definition of a Petri net is extended to accord with the real-world SBES organisation. The basic TPN modules are presented to model the corresponding variable structures in the SBES, and then the scheduling model of the whole SBES is easily constructed. A modified discrete particle swarm optimisation (PSO) based on the reachability analysis of Petri nets is developed for scheduling of the SBES. In the proposed algorithm, particles are coded by welding transitions and selecting places of the TPN model, and then the collaboration and competition of particle individuals is simulated by crossover and mutation operators in a genetic algorithm. Numerical simulation suggests that the proposed TPN–PSO scheduler can provide an improvement over the conventional scheduling method. Finally, a case study of the optimisation of a back block erection process is provided to illustrate the effectiveness of the method.

State equations of stochastic timed petri nets with informational relations

The use of timed Petri nets for simulation modeling is analyzed. An equation for transforming states of timed Petri nets and fundamental matrix equations of a stochastic timed Petri net with conflicting and multichannel transitions and informational relations are obtained.

Supply chain modelling and managing, using timed coloured Petri nets: a case study

This paper aims at developing a new methodology for designing and managing a supply chain (SC) and, at the same time, for evaluating the performance of every stakeholder involved in a production chain. The methodology proposed has been applied to a footwear supply chain and is based on coloured Petri nets (CPNs). The supply chain analysed in this paper is a complex production system consisting of a network of manufacturers and service suppliers related to logistics systems that provide transportation and storage. The model developed uses coloured, timed Petri nets to represent a supply chain and it is such that resources are the Petri Net (PN) places, the tokens are jobs, orders and/or products, while the colours represent job attributes. These colours are used to encode different data types and values that are attached to tokens. A “coloured token” represents a specific production order or a certain amount of a particular material supplied. Thus, it can be processed in different ways and it can be easily localised within the CPN model. The use of coloured Petri nets allows companies to create a compact representation of states, actions and events of the modelled system. The particular structure of this network allows the designers the easy realisation of a simulator using an “object-oriented”, dedicated programming, which is a useful tool for developing what-if analyses.

Timing in Multimodal Turn-Taking Interactions: Control and Analysis Using Timed Petri Nets

research-article Free Access Share on Timing in multimodal turn-taking interactions: control and analysis using timed Petri nets Authors: Crystal Chao Georgia Institute of Technology Georgia Institute of TechnologyView Profile , Andrea L. Thomaz Georgia Institute of Technology Georgia Institute of TechnologyView Profile Authors Info & Claims Journal of Human-Robot InteractionVolume 1Issue 1July 2012 pp 4–25https://doi.org/10.5898/JHRI.1.1.ChaoOnline:28 July 2012Publication History 12citation458DownloadsMetricsTotal Citations12Total Downloads458Last 12 Months115Last 6 weeks10 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my Alerts New Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF

Time properties dedicated transformation from UML-MARTE activity to time transition system

Critical Real-Time Systems (RTS) have strong requirements concerning system's reliability. UML and its profile MARTE are standardized modeling languages widely accepted by industrial designers to cope with the development of complex RTS. Relying on Model-Driven Engineering (MDE), time properties verification of UML-MARTE specifications at early phases of the system lifecycle becomes possible. A key issue is to eliminate the gap between UML semi-formal semantics and fully formal executable semantics using model transformation. The model transformation must guarantee the consistency between high-level user models and lowerlevel verification models. Meanwhile, it should guarantee that the subsequent verification is not too expensive and can be applied to real size industrial models. This paper presents an approach to translate UML-MARTE Activity Diagrams into Time Transition System (TTS) with the aim of efficiently verifying time properties in RTS. TTS is a generalization of Time Petri Nets (TPN) with the priority and data handling at the transition level, supported by TINA model checker. This contribution focuses on how to define the TTS formal semantics to avoid the core problem of state space explosion in model checking. This work has been integrated in a time properties verification framework for UML-MARTE RTS specifications. The proposed method is evaluated using a representative case study. Experimental results are given to demonstrate the method's performance.

Internet Host Reliability Modeling with Time Petri Nets

Understanding the reliability of components is important for modeling the reliability of a distributed system. Careful modeling allows the construction of highly fault-tolerant distributed data applications and less expensive. Petri nets have been extensively used in the modeling and analysis of concurrent and distributed systems. Particular importance of Petri nets are in the development of concurrent and distributed systems. One of the standard concepts of time-dependent Petri nets is the one, where each transition gets a continuous time interval, specifying the range of the transition‟s reaction time. This extension of classical Petri nets is called Time Petri nets. In the internet the host is to obtain the data required to implement the functions of the Internet. In this paper, a method to model the internet host reliability with Time Petri nets is proposed.

Using Constraint Programming for solving the Reachability Problem in Timed Petri Nets: Evaluation of Basic Labeling Strategies

In this paper, we propose to use a constraint programming approach to address the reachability problem in Timed Petri Nets (TPNs). TPNs can be used to model a wide class of systems, from manufacturing issues to formal verification of embedded systems. Many of the considered problems can be modeled as reachability problems in TPNs. To reduce the space state explosion brought by the exploration of the TPN behavior, we propose to follow the incremental methodology proposed by Bourdeaud'huy and Hanafi (2006), who translate the reachability graph of Timed PNs into a mathematical model. We improve this model by adding valid inequalities and search for solutions using Constraint Programming (CP). More particularly, we compare different labeling strategies and assess their respective efficiency.

An Efficient Mixed Integer Programming Model Based on Timed Petri Nets for Diverse Complex Cluster Tool Scheduling Problems

Cluster tools are automated production cells which are largely used for semiconductor manufacturing. They consist of several processing modules (PMs) and a transportation robot. Since cluster tools have limited buffers and diverse scheduling requirements such as complex wafer flow patterns, parallel PMs, wafer residency time constraints, and dual-arm robot, and so on, their scheduling problems are difficult. Due to the diversity of scheduling problems, dealing with those problems one by one may be impractical. Computational complexity is another difficulty. In this paper, we propose an efficient scheduling method to deal with diverse complex cluster tool scheduling problems by using timed Petri nets (TPN). We propose TPN models of cluster tools with various scheduling requirements. Then, based on the TPN models and their state equations, we develop a new mixed integer programming (MIP) model that can efficiently determine the optimal cyclic schedules. We show that many kinds of scheduling requirements such as parallel, reentrant and multiple material flows, a dual-armed robot, and time constrained PMs can be dealt with by the MIP model. Through experiments, we also show that the MIP model can efficiently solve most practical cluster tool scheduling problems.

A Flight Plan Rescheduling in Air Traffic Management Problem: A Time Discret Event System Approach

Abstract Motivated by the importance of congestion in air traffic problem and its bad effects on airlines companies and passenger's security, we propose a decision support framework for flight rescheduling in air traffic management based on ground delay, rerouting 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 Time Petri Nets. This tool, called Time Ordered Binary Decision Diagrams (TOBDDs) 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.

Analysis and Synthesis of the Flexible Manufacturing System Potential Behaviors

The Flexible Manufacturing Systems (FMS) behaviors can be successfully modeled by Delay Time Petri Nets (DTPNs). The DTPN contains delayed arcs, timed, untimed, controlled and uncontrolled transitions. To manage the FMS complexity the reduction method can be used. A new method of study using a defined DTPN language is proposed. Due to the fact that the reachability graph of the DTPN corresponding to a FMS is too large, a Genetic Algorithm (GA) is used off-line for the synthesis of the DTPN that fulfills the specification and avoids deadlocks. An on-line controller can be used to schedule the controlled transitions.

A concurrency-preserving translation from time Petri nets to networks of timed automata

Several formalisms to model distributed real-time systems coexist in the literature. This naturally induces a need to compare their expressiveness and to translate models from one formalism to another when possible. The first formal comparisons of the expressiveness of these models focused on the preservation of the sequential behavior of the models, using notions like timed language equivalence or timed bisimilarity. They do not consider preservation of concurrency. In this paper we define timed traces as a partial order representation of executions of our models for real-time distributed systems. Timed traces provide an alternative to timed words, and take the distribution of actions into account. We propose a translation between two popular formalisms that describe timed concurrent systems: 1-bounded time Petri nets (TPN) and networks of timed automata (NTA). Our translation preserves the distribution of actions, that is we require that if the TPN represents the product of several components (called processes), then each process should have its counterpart as one timed automaton in the resulting NTA.

Modeling and analyzing the impact of authorization on workflow executions

It has been a subject of a significant amount of research to automate the execution of workflows (or business processes) on computer resources. However, many workflow scenarios still require human involvement, which introduces additional security and authorization concerns. This paper presents a novel mechanism for modeling the execution of workflows with human involvement under Role-based Authorization Control. Our modeling approach applies Colored Timed Petri-Nets to allow various authorization constraints to be modeled, including role, temporal, cardinality, BoD (Binding of Duty), SoD (Separation of Duty), role hierarchy constraints etc. We also model the execution of tasks with different levels of human involvement and as such allow the interactions between workflow authorization and workflow execution to be captured. The modeling mechanism is developed in such a way that the construction of the authorization model for a workflow can be automated. This feature is very helpful for modeling large collections of authorization policies and/or complex workflows. A Petri-net toolkit, the CPN Tools, is utilized in the development of the modeling mechanism and to simulate the constructed models. This paper also presents the methods to analyze and calculate the authorization overhead as well as the performance data in terms of various metrics through the model simulations. Based on the simulation results, this paper further proposes the approaches to improving performance given the deployed authorization policies. This work can be used for investigating the impact of authorization, for capacity planning, for the design of workload management strategies, and also to estimate execution performance, when human resources and authorization policies are employed in tandem.

A Constraint Programming Approach for Generating Firing Sequences in Timed Petri Nets With Token Identification

Timed Petri Nets are a good modeling framework to express the behavior of discrete event systems, such as transport or manufacturing systems. They allow to represent easily the distribution of tasks within a complex system, with the capacity to handle time constraints on the duration of these tasks.However, when synchronization is needed between several layers of the system, such models suffer from a lack of mechanisms to identify the components that are handled. Thus, it is difficult to obtain firing sequences avoiding confusion of tokens when activation or coordination patterns are used.Such issues are well addressed with High Level Petri Nets, like Colored PNs where data structures are attached to tokens, allowing to represent a complex behaviour while keeping a compact PN model. However, such models introduce a modeling material that makes it difficult to use direct incremental solving approaches like mathematical or constraint programming, i.e. approaches that do not need to unfold the net and build its whole reachability graph.In this paper, we propose to extend the expressivity of Timed Petri Nets by associating integer identifiers with tokens. Such approach can avoid the confusion of parts in a plant, or trains in a railway network, and allow to model much more possible coordination situations. A constraint programming model is built to follow this new firing semantics, and benchmarks are given to assess its efficiency.

An Efficient Translation Method from Timed Petri Nets to Timed Automata

There are various existing methods translating timed Petri nets to timed automata. However, there is a trade-off between the amount of description and the size of state space. The amount of description and the size of state space affect the feasibility of modeling and analysis like model checking. In this paper, we propose a new translation method from timed Petri nets to timed automata. Our method translates from a timed Petri net to an automaton with the following features: (i) The number of location is 1; (ii) Each edge represents the firing of transition; (iii) Each state implemented as clocks and variables represents a state of the timed Petri net one-to-one correspondingly. Through these features, the amount of description is linear order and the size of state space is the same order as that of the Petri net. We applied our method to three Petri net models of signaling pathways and compared our method with existing methods from the view points of the amount of description and the size of state space. And the comparison results show that our method keeps a good balance between the amount of description and the size of state space. These results also show that our method is effective when checking properties of timed Petri nets.

Improving the Construction of the DBM Over Approximation of the State Space of Real-time Preemptive Systems

We present in this paper an algorithm allowing an efficient computation of the tightest DBM over-approximation of the state space of preemptive systems modeled by using Time Petri Nets with inhibitor arcs. First of all, we propose an algorithm that reduces the effort of computing the tightest DBM over-approximated graph. For this effect, each class of this graph is expressed as a pair (M, D), where M is a marking and D is the system of all DBM inequalities even the redundant ones. We thereby make it possible to compute the system D straightforwardly in its normal form, without requiring to compute the intermediary polyhedra. Hence, we succeed to remove the errors reported in the implementation of other DBM approximations. Then we show that by relaxing a bit in the precision of the DBM approximation, we can achieve to construct more compact graphs while reducing still more the cost of their computation. We provide for this abstraction a suitable equivalence relation that contract yet more the graphs. The experimental results comparing the defined constructions with other approaches are reported.

Efficient computation of quantitative properties of real-time preemptive systems

We propose in this paper an algorithm making it possible an efficient time analysis of the state space of preemptive real-time systems modelled using time Petri nets with inhibitor arcs. For this effect, we discuss how to determine linear and quantitative properties of the remote model from its reachability graph. Then, we propose an algorithm to compute an approximation of the minimal and the maximal time distances of any firing sequence. Contrarily to other techniques, our algorithm enjoys a linear complexity time cost and can be performed on the fly when building the reachability graph without requiring to extend the original model with observers.

FIFO Time Petri Nets for conflicts handling

This paper considers time Petri nets (TPN for short) and its classical semantics (Merlin's semantics). It discusses an alternative semantics, called FIFO-semantics. FIFO-semantics is based on ages of tokens and manages tokens w.r.t. FIFO (First In First Out) discipline (FIFO-TPN). This paper first shows that FIFO-TPN are very appropriate to deal with some conflicting situations (which cannot always be modelled by the classical semantics) and shows its conciseness for conflicts modeling. Then, it compares the theoretical expressiveness of FIFO-TPN vs classical-TPN and shows that, despite FIFO-TPN add expressiveness in the general case, for bounded models, they have the same expressive power w.r.t. weak timed bisimulation.

A Study on Supply Chain Information Integration of Commodity Circulation Based on Grid

The application of grid technology in supply chain information integration is necessary to adapt to the change of competitive environment. The purpose of applying grid technology in Supply Chain integration is to link up all the existing resources and thus to improve the operation efficiency of the supply chain. Take supply chain information integration of commodity circulation as an example. This paper comparatively analyzes the operation efficiency of supply chain integration system under traditional mode and under grid environment with time Petri nets. The results show the superiority of the supply chain integration system under grid environment.

Symmetry Reductions in Timed Continuous Petri Nets Under Infinite Server Semantics

Symmetries in continuous Petri nets result in symmetric system behaviors. This fact is used by the method suggested in this contribution. We present a structured procedure to construct a Petri net of smaller size which has the same dynamical behavior as the original net. It consists of an automated construction of the reduced net including the adaption of arc weights and firing rates and works under mild assumptions on unequal conflicts.