Local time membrane systems and time Petri nets

It had been shown that Merlin's Time Petri Nets are a special case of Time Stream Petri Nets. In this paper, we show that there does not exist a time equivalence between both models. We extend first this result to the non equivalence of Timed Automata and Time Petri Nets and second to the non equivalence of Timed Link Petri Net and Timed Transition Petri Net.

The paper is a partial synthesis of the work that a team within the Faculty of Managerial and Technological Engineering has in the field of modeling and simulation of systems with Petri nets. The paper deals with three issues. The first part is Modeling and simulation of manufacturing systems with timed Petri nets. The first part presents the way in which the performances of some manufacturing systems are evaluated using timed Petri nets. The first example is a manufacturing system specific to the textile industry. The system has three production lines. In this case, the modeling with timed Petri nets allows the analysis of the operation of the flow lines and highlights the bottleneck. Another modeled manufacturing system is specific to a series production, more precisely it refers to the manufacture of gas cookers within a company from Oradea. The model with Petri nets also describes the supply sequences of the stocks of parts and subassemblies. The next modeled system is an automated manufacturing system for the packaging of detergents. The complexity of the Detergent Packing System and the high level of automation, require the use of efficient modeling and simulation methods to verify the validity of the solutions adopted. In this chapter is present the model of a robotic welding cell. The second part of the paper, the transition from timed Petri nets to hierarchical colored Petri nets, shows how Petri nets were developed for a robotic cell for metallographic analysis. The third part is dedicated to modeling with colored Petri nets timed with complex colors of the flexible manufacturing cell A007 within the Department of Industrial Engineering.

Performance analysis can be carried out in several ways, especially in case of Markovian models. In order to interpret high level of abstraction, we often use modeling tools like timed Petri nets (TPNs). Although some subclasses of TPNs (e.g. stochastic Petri nets (SPNs) [17, 19]) can be handled analytically, a general timed Petri net is hard to evaluate via numerical analysis. However, the simulation of SPNs or deterministic and stochastic Petri nets (DSPNs) [16] are supported by many known tools (see, e.g. [3, 20]), it is hard to find a simulation tool for timed Petri nets with generally distributed (i.e., particular but arbitrarily chosen) firing times. In this paper, we present TiPeNeSS (Timed Petri Net Simulator Software) which supports the simulation of timed Petri nets containing transitions with generally distributed firing delays. The input of the software (the Petri net and the parameters) is defined in an XML file, what allows us to generate results in batch mode. Besides, we describe a case study in which we optimize the frequency of the regular maintenance in a manufacturing process.

Behaviour Equivalent Max-Plus Automata for a Class of Timed Petri Nets

A correct and rapid inference is required for practical use of expert system for fault section estimation in power systems. This paper proposes a new model-based expert system for fault section estimation using colored and timed Petri nets. The Petri nets simplify the inference procedure greatly because it can represent the causalities among faults of power system components, protective actions of relays and circuit breakers. They can also represent the operating states of these protective devices explicitly, or, more precisely, whether a relay has been actuated correctly or falsely, etc. In addition, time sequence information on actuated relays and tripped circuit breakers can be handled by using the colored and timed Petri nets. Therefore, the operating states of relays and circuit breakers can be inferred more correctly. Petri nets are suited for parallel processing so well that there is a possibility of reducing the inference time considerably. In the proposed system, the inference is executed by setting the initial states in the Petri nets using the information on the actuated relays and the tripped circuit breakers and then operating the Petri nets. There have been several test cases which used a prototype system on the Macintosh computer employing Object Common Lisp, and good results have been obtained.

The recently introduced method, which was called ldquostretching,rdquo is extended to timed Petri nets which may have both controllable and uncontrollable transitions. Using this method, a new Petri net, called ldquostretched Petri net,rdquo which has only unit firing durations, is obtained to represent a timed-transition Petri net. Using this net, the state of the original timed Petri net can be represented easily. This representation also makes it easy to design a supervisory controller for a timed Petri net for any purpose. In this paper, supervisory controller design to avoid deadlock is considered in particular. Using this method, a controller is first designed for the stretched Petri net. Then, using this controller, a controller for the original timed Petri net is obtained. Algorithms to construct the reachability sets of the stretched and original timed Petri nets, as well as algorithms to obtain the controller for the original timed Petri net are presented. These algorithms are implemented using Matlab. Examples are also presented to illustrate the introduced approach.

Timed Petri nets can be used to model and analyse scheduling problems. To support the modelling of scheduling problems, we provide a method to map tasks, resources and constraints onto a timed Petri net. By mapping scheduling problems onto Petri nets, we are able to use standard Petri net theory. In this paper we will show that we can use Petri net based tools and techniques to find conflicting and redundant precedences, upper- and lower-bounds for the makespan, etc. This is illustrated by a Petri net based analysis of the notorious 10×10 problem due to Fisher & Thompson (1963)

Basic graph models of processes, such as Petri nets, have usually omitted the concept of time as a parameter. Time has been added to the Petri net model in two ways. The timed Petri net (TPN) uses a fixed number of discrete time intervals. The stochastic Petri net (SPN) uses an exponentially distributed random variable. In this paper, a discrete time stochastic Petri model is described. These discrete time SPN's fill the gap between TPN and normal SPN. However, the use of discrete time complicates the SPN model in that more than one transition may fire at a time step. Finally, an example of a live and bounded Petri net which has nonempty, disjoint, recurrent subsets of markings is given.

Efficient State Space Search for Time Petri Nets

We propose rewriting logic as a unifying framework for a wide range of nets models. We treat in detail place/transition nets and important extensions of the basic model by individual tokens, test arcs, and time. Based on the idea that Petri nets are monoids suggested by Meseguer and Montanari we define a rewriting semantics that maps place/transition nets into rewriting logic specifications. We furthermore generalize this result to a general form of algebraic net specifications subsuming also colored nets as a special case. The soundness and completeness results we state relate the commutative process semantics of nets proposed by Best and Devillers to the model-theoretic semantics of rewriting logic in the sense of natural isomorphisms between suitable functors. In addition we show how place/transition nets with test arcs and timed nets can be equipped with a rewriting semantics and discuss how other extensions can be treated along similar lines. Beyond the conceptual unification of quite different kinds of nets within a single framework, the rewriting semantics can provide a guide for future extensions of nets and help to cope with the growing diversity of models in this field. On the practical side, a major application of the rewriting semantics is its use as a logical and operational representation of net models for formal verification and for the efficient execution and analysis using a rewriting engine such as Maude, which also allows us to specify different execution and analysis strategies in the same rewriting logic language by means of reflection.

Petri Nets (PNs) are an effective structure for modeling and analyzing asynchronous systems with concurrent and parallel activities. A Petri net models the static properties of a discrete event system concentrating on two basic concepts: events and conditions. Most of the theoretical work on Petri nets is a formal definition of Petri nets structures, which consist of a set of places, representing conditions, a set of transitions, representing events, an input function and an output function. For practical purposes, a graphical representation is more useful. Two types of nodes portray places and transitions. A circle is a place and a bar is a transition. There is no inherent measure of time in a classical Petri net. To approach time-based evaluation of system performances, Timed Petri Nets (TPNs) were introduced. Modeling the notion of time is not straightforward. There are several possibilities for introducing time in PNs, among them timed transitions and timed places. This paper reviews several published examples where Petri Nets were used in different circumstances such as estimating expected utilization of processing resources at steady state in open queueing networks, verifying computerized simulations and batch planning in textile industry.

Petri net (PN) is a classical tool for modeling, simulation, and analysis. With the emergence of distributed manufacturing system (DMS), PN has been evolved into different forms such as colored PN (CPN) and timed PN (TPN). To fulfill the practical requirements, CPN has been extended to a larger and more complex model. Meanwhile, DMS becomes an important issue for industry, and how to model a complex manufacturing network for better throughput needs further investigation. A simple single type of PN only cannot fulfill all contemporary requirements at the same time. This paper proposes a new concept for a new PN-hierarchical timed CPN (HTCPN), which can be a powerful tool for modeling, simulation, and analysis for current large complex distributed manufacturing system. This paper presents a general structure of DMS and uses HTCPN to model the manufacturing system as discrete event with dynamic behavior. The proposed approach shows superiority on modeling large complex manufacturing system as it represents the material flow and transitions clearly and provides overview and detailed description for DMS.

To solve the problem of deadlock prevention for timed Petri nets, an effective deadlock prevention policy based on elementary siphons is proposed in this paper. Without enumerating reachable markings, deadlock prevention is achieved by adding monitors for elementary siphons, increasing control depth variables when necessary, and removing implicit, liveness‐restricted and redundant control places. The final supervisor is live. First, a timed Petri net is stretched into a stretched Petri net (SPN). Unchanging the system performance, each transition in the SPN has a unit delay time. Then the siphon‐control‐based approach is applied. Monitors computed according to the marking constraints are added to the SPN model to ensure all strict minimal siphons in the net invariant‐controlled. A liveness‐enforcing supervisor with simple structure can be obtained by reverting the SPN into a TdPN. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

Timed Petri nets are useful in performance evaluation of concurrent systems. The maximum computation rate is achieved for minimal cycle time of timed Petri net. It is known that minimal cycle time problem for P-invariant Petri nets is NP-complete. In this paper we prove that the minimal cycle time problem, for non-P-invariant Petri nets and for a small subclass of P-invariant Petri nets called free-choice nets having live and safe marking, is NP-complete.

Patients moving though a healthcare facility to receive medical service form patient flow. Optimizing patient flow is crucial to improving the efficiency of healthcare practice, providing a positive experience for patients and healthcare teams. Patient flow is event-driven, and thus Petri nets are a good fit for its modeling and analysis. In this chapter, the fundamental concepts of Petri nets, including transition firing rules, modeling power, structural and behavioral properties are briefly introduced. Petri net modeling practice in healthcare systems and patient flows, in particular, is discussed. Details of patient flow performance analysis based on stochastic timed Petri nets, such as the average patient waiting time, resource constraints modeling, task durations modeling, and patient flow hierarchical modeling that handles complexity are discussed.KeywordsPatient flowPetri netsModelingPerformance analysisResource constraints