Modelling and Control of Resource Allocation Systems within Discrete Event Systems by Means of Petri Nets -- Part 1: Invariants, Siphons and Traps in Deadlock Avoidance (original) (raw)
Related papers
Control of Deadlocked Discrete-Event Systems Using Petri Nets
Acta Polytechnica Hungarica, 2022
In Discrete-Event Systems (DES), deadlocks frequently occur. Flexible Manufacturing Systems (FMS) have the character of DES. Namely, FMS consist of many cooperating devices (like robots, machine tools, transport belts, etc.). Frequently, deadlocks occur because of insufficient resources. Petri Nets (PN) are often used to model FMS and to synthesize control for them. To deal with deadlocks, first of all, it is necessary to find and/or avoid them. There are several principal approaches for doing this-either by computing and analyzing the PN reachability tree (RT) or by finding PN model siphons. Then, in the former concept, the supervisor is synthesized by means of P-invariants of the PN model used, while in the latter concept the supervisor, based on siphons, is synthesized. In addition to these approaches, additional techniques can sometimes, be applied-e.g. a suitable utilization of added PN transitions.
Deadlock Control of Automated Manufacturing Systems Based on Petri Nets—A Literature Review
IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews), 2000
Deadlocks are a rather undesirable situation in a highly automated flexible manufacturing system. Their occurrences often deteriorate the utilization of resources and may lead to catastrophic results in safety-critical systems. Graph theory, automata, and Petri nets are three important mathematical tools to handle deadlock problems in resource allocation systems. Particularly, Petri nets are considered as a popular formalism due to its inherent characteristics. They have received much attention over the past two decades to deal with deadlock problems in automated manufacturing systems, leading to a variety of deadlock control policies. This research surveys the state-of-the-art deadlock control strategies for automated manufacturing systems by reviewing the principles and techniques involved in preventing, avoiding, and detecting deadlocks. The primary focus of this research is deadlock prevention due to a large and continuing stream of efforts on it. A control strategy is evaluated in terms of computational complexity, behavioral permissiveness, and structural complexity of its liveness-enforcing or deadlock-free supervisor. This comprehensive study provides readers a conglomeration of the updated results in this area and facilitates engineers in finding a suitable approach for their industrial application cases. Future research directions are finally discussed.
Acta Polytechnica Hungarica, 2023
Correct allocation of resources in Automated Manufacturing Systems (AMS) is very important, especially in order to avoid deadlocks and their consequences. Petri Nets (PN) are frequently used for modeling AMS. S 3 PR (Systems of Simple Sequential Processes with Resources) model of Resource Allocation Systems (RAS) based on PN are defined, analyzed and controlled here. S 3 PR are modeled by Ordinary PN (OPN). After defining and creation of such models the deadlock prevention will be performed by two deadlock prevention methods, namely (i) the method based on elementary siphons, and (ii) the method based on preventing strict minimal siphons from being emptied in another way (by means of circuits, holders of resources and complementary siphons). For illustration, two practical examples will be introduced. Both approaches are very useful not only for reliable deadlockfree control of existing AMS, but also at design of new AMS of such kind.
A Petri Net Structure–Based Deadlock Prevention Solution for Sequential Resource Allocation Systems
… and Automation, 2005 …, 2005
A new method for the deadlock prevention problem in concurrent systems where a set of processes share a set of common resources in a conservative way is proposed. It can be applied to flexible manufacturing systems, modeled with Petri nets. In this paper, we present a set of important results related to the deadlock prevention problem in Ë È Ê nets. First, a liveness characterization is introduced, establishing how deadlocks can be studied in terms of circular waits. Second, we show how a circular wait situation corresponds to a particular marking related to a siphon of the Petri net model. Finally, this last characterization is used to obtain an iterative method that successively forbids deadlock related states, synthesizing the control necessary to ensure a final live behavior. The method can be implemented by means of the solutions of a set of integer linear programming problems.
A Method for Deadlock Prevention in Discrete Event Systems Using Petri Nets
1999
Deadlock is the condition of a system that has reached a state in which all of its potential actions are blocked. This paper introduces a deadlock prevention method for discrete events systemsmodeledbyPetrinets. Petrinetshaveabipartitegraphstructureandtheyareparticu- larly well suited to model concurrencies found in manufacturing, communication and computer systems, among others. Given an arbitrary Petri net structure, the deadlock prevention algo- rithm in this paper nds linear inequalities in terms of the marking (state vector). When the Petri net is supervised according to the constraints provided by the algorithm, the supervised netisprovedto bedeadlock-freeforallinitialmarkingsthatsatisfythe supervisionconstraints. Results pertaining to permissivity properties and termination are also proved. The algorithm is applicable to any Petri net with controllable and observable transitions.
Deadlock Prevention for Flexible Manufacturing Systems via Controllable Siphon Basis of Petri Nets
IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2015
Siphons are a kind of special structural objects in a Petri net, and plays a key role in synthesizing a live Petri net controller for flexible manufacturing systems. In order to obtain a small size Petri net controller, this paper introduces the concept of a controllable siphon basis. It then proves that a live Petri net controller can be established by adding a control place and related arcs to each strict minimal siphon (SMS) in a controllable siphon basis. The initial markings of control places are determined by an integer linear program. The number of control places in the obtained controllers is the same as the number of SMSs in the controllable siphon basis, while the latter is no more than that of the activity places in a Petri net model. An algorithm for constructing a controllable siphon basis is proposed, and a new deadlock prevention policy based on it is established. A few examples are provided to demonstrate the proposed concepts and policy and used to compare them with the state-of-the-art methods. Index Terms-Discrete event systems, flexible manufacturing systems, integer linear program (ILP), Petri nets. I. INTRODUCTION A FLEXIBLE manufacturing system (FMS) handles multiple concurrent flows of job processes that can make different products at the same time, and often exploits shared
The International Journal of Advanced Manufacturing Technology, 2004
In a flexible manufacturing system (FMS) with multiple products, deadlocks can arise due to limited shared resources, such as machines, robots, buffers, fixtures etc. The development of efficient deadlock prevention policies, which can optimise the use of system resources, while preventing deadlocks from occurring, has long been an important issue to be addressed. In [1], an optimal deadlock prevention policy was proposed, based on the use of reachability graph (RG) analysis of the Petri net model (PNM) of a given FMS and the synthesis of a set of new net elements, namely places with initial marking and related arcs, to be added to the PNM, using the theory of regions. The policy proposed in [1] is optimal in the sense that it allows the maximal use of resources in the system according to the production requirements. For very big PNMs, the reachability graph of the PNMs becomes very large and the necessary computations to obtain an optimal deadlock prevention policy become more difficult. In this paper, we propose the use of the Petri net reduction approach to simplify very big PNMs so as to make necessary calculations easily in order to obtain an optimal deadlock prevention policy for FMSs. An example is provided for illustration.
Deadlock analysis and control based on Petri nets: A siphon approach review
Advances in Mechanical Engineering, 2017
Deadlocks should be eliminated in highly automated manufacturing systems since their occurrence implies the stoppage of the whole or partial system operation. Over the past decades, Petri nets are increasingly becoming one of the most popular and full-fledged mathematical tools to deal with deadlock problems due to their inherent characteristics. In a Petri net formalism, liveness is an important property of system safeness, which implies the absence of global and local deadlock situations in an automated manufacturing system. The liveness assessment can be performed by verifying the satisfiability of certain predicates on siphons, a well-known structural object in Petri nets. Therefore, siphons have received much attention to analyze and control systems modeled with Petri nets. Particularly, elementary siphon theory plays a key role in the development of structurally simple liveness-enforcing Petri net supervisors, leading to a variety of deadlock control approaches. This survey studies on the state-of-the-art elementary siphon theory of Petri nets including refined concepts of elementary siphons and their extended version, computation methods of siphons and elementary ones, controllability conditions, and their application to deadlock control. As a reference, this work attempts to provide a comprehensive and updated research survey on siphons, elementary siphons, and their applications to the deadlock resolution in Petri nets.
IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans, 2004
A variety of important Petri net-based methods to prevent deadlocks arising in flexible manufacturing systems (FMS) are to add some control places and related arcs to strict minimal siphons (SMS) such that no siphon can be emptied. Since the number of minimal siphons grows in general exponentially with respect to a Petri net size, their disadvantages lie in that they often add too many additional places to the net, thereby making the resulting net model much more complex than the original one. This paper explores ways to minimize the new additions of places while achieving the same control purpose. It proposes for the first time the concept of elementary siphons that are a special class of siphons. The set of elementary siphons in a Petri net is generally a proper subset of the set of all SMS. Its smaller cardinality becomes evident in large Petri net models. This paper proves that by adding a control place for each elementary siphon to make sure that it is marked, deadlock can be successfully prevented. Compared with the existing methods, the new method requires a much smaller number of control places and, therefore, is suitable for large-scale Petri nets. An FMS example is used to illustrate the proposed concepts and policy, and show the significant advantage over the previous methods.
Deadlock control policy for a class of Petri nets without complete siphon enumeration
Siphons are special structures of a Petri net. Their number grows exponentially with the net size. Hence, the traditional siphon-based deadlock control policies have two problems, that is, generating very structurally complex supervisory controllers and requiring intractable computation efforts. This paper intends to use the newly proposed concept, elementary siphons, and a mixed integer programming (MIP) method to design structurally simple supervisory controllers and reduce the computational burden. This method is applicable to a class of Petri nets, System of Simple Sequential Processes with Resources that can well model a wide class of discrete manufacturing systems. Siphons are divided into elementary and dependent ones. The proposed policy consists of three stages: siphon control, control-induced siphon control, and the elimination of control-redundant monitors. First, a monitor (control place) is added for each elementary siphon such that it is invariant-controlled. Because of the addition of monitors to the plant model, control-induced siphons are possibly generated in the augmented net. Next, monitors are added to make control-induced siphons in the augmented net always marked sufficiently without generating new problematic siphons. A MIP technique is used to guarantee that no siphon is insufficiently marked. Finally, we systematically remove control-redundant monitors. Compared with previous work in the literature, the deadlock prevention policy developed in this paper can lead to a structurally simple liveness-enforcing Petri net supervisor with more permissive behaviour by adding only a small number of monitors and arcs. Moreover, complete siphon enumeration is avoided. A manufacturing system example is utilised to illustrate the proposed methods.