Petri nets supervisory control for deadlock prevention and avoidance

Deadlock avoidance policies guarantee deadlock-free resource allocation to concurrent competing processes in flexible manufacturing systems. Most deadlock avoidance work in manufacturing deals with systems where each part requires a fired sequence of operations. In contrast, this paper deals with those systems that support sequencing flexibility, that is, the operations required by the part are partially ordered. In this setting, the order in which operations are performed is not predetermined, but becomes a real-time decision. Specifically, the paper characterizes the deadlock detection and avoidance problems for these systems, presents a sub-optimal deadlock avoidance approach, and addresses two relevant special structures on the partial orders for which optimal deadlock avoidance is of polynomial complexity.

Results in the literature have provided efficient control synthesis techniques for the problem of deadlock avoidance in Petri nets. These results are shown to fit within an established framework for the enforcement of linear constraints on the marking behavior of a net. Framing the problem in this way allows uncontrollable and of unobservable transitions to be included in the plant model when deadlock avoidance is performed.

Solving the deadlocks avoidance problem in Resource Allocation Systems (RAS) in Discrete-Event Systems (DES) is a rife problem, especially in Flexible Manufacturing Systems (FMS), alias Automated Manufacturing Systems (AMS). Petri Nets (PN) are an effectual tool often used at this procedure. In principle, there are two basic approaches how to deal with deadlocks in RAS based on PN. They are listed and illustrated here. First of the approaches is realized by means of the supervisor based on P-invariants of PN, while the second one is realized by means of the supervisor based on PN siphons. While the first approach needs to know the reachability graph/tree (RG/RT) expressing the causality of the development of the PN model of RAS, in order to find (after its thorough analysis) the deadlocks, the second approach needs the thorough analysis of the PN model structure by means of finding siphons and traps. Next, both approaches will be applied on the same PN model of RAS and the effectiveness of the achievement of their results will be compared and evaluated. Several simple illustrative examples will be introduced. For the in-depth analysis of the problem of deadlock avoiding, next Part 2 of this paper is prepared, where the newest research will be introduced and illustrated on more complicated examples. If necessary (because of the limited length of particular papers), also the third part – Part 3, will be prepared.

Automated manufacturing systems, including flexible manufacturing systems (FMSs), belong to the class of discrete event dynamic systems. In such a system, potentially conflicting events may occur due to concurrency. The problem of collision and deadlock avoidance can be investigated using Petri nets which are powerful techniques suitable for modeling concurrent processes. A Petri net based approach is employed in this paper to model, detect and avoid collisions and deadlocks in FMSs. Unlike the existing Petri net based techniques, the proposed approach uses the concept of critical states to avoid the system from entering a state leading toward a deadlock state. A multirobot assembly example is used to illustrate the proposed scheme.

The purpose of this paper is to clear up misconceptions about deadlock and present a cohesive treatment suitable for use in class. First some historical examples are given. This is followed by a formal definition and some examples. Second, the concept of a progress is introduced and explained and examples of progress trajectories are presented. Within the diagram the complexities of process progression are illustrated. This provides a convenient visualization for the three resource management policies that combine to permit deadlock. Also using the joint progress diagram, the four approaches to dealing with deadlock can be differentiated in a convenient pictorial fashion. Once that is complete, each of the four approaches can be studied in detail. Third the four approaches (prevent, avoid, detect/recover, and ignore) are described and differentiated. The characteristics and usage patterns of resources are described. Then, one policy is chosen for elimination. Once the policy is chosen, there are three different ways to eliminate that policy. These the relative performance of these three choices are compared. The fourth, fifth and sixth topics are deadlock prevention, deadlock avoidance, and deadlock detection. The key concept in avoidance is that even though resources may be available, they should not be allocated if it is imprudent to do so. A simple avoidance algorithm is presented and practical problems with deadlock avoidance are discussed. In detection recovery, the detection algorithm is shown to be similar to the avoidance algorithm and the recovery algorithms are shown to be complex. The paper concludes by offering suggestions on the important points to cover when teaching deadlock.

The use of shared resources is a major problem occurring in discrete event (DE) systems, including manufacturing systems, computer systems, communication systems, highway/vehicle systems, and others. The issues involve problems of assignment of resources when the same resources are simultaneously requested by more than one job. Failure to suitably assign, or dispatch, resources in such situations can have serious deleterious effects on system performance, resulting in extreme cases in system deadlock [7]. Computer operating systems engineers and industrial engineers have used the concepts of circular wait (CW) and circular blocking in analysis of such phenomena [41, 24]. Various concepts in Petri nets (PN) are extremely useful for dealing with deadlock and a great deal of research has been done from the PN point of view (see references, especially [11, 14, 19]). The PN approaches are often based on the notion of the siphon, which indeed is called a “deadlock” in some works [26]. Unfortunately, it is known that many problems in scheduling, dispatching, and deadlock analysis are NP-hard [12], so that significant increases in computing power do not significantly improve computational ability. Neither PN nor CW approaches have addressed this issue.

The development of theoretical-based methods for the assessment of multi-agent systems properties is of critical importance. This work is a preliminary investigation on methodologies for modeling, analysis and design of multi-agent systems. Multi-agent systems are regarded as discrete-event dynamic systems and Petri nets are used as a modeling tool to assess the structural properties of the multi-agent system. Our methodology consists of defining a simple multi-agent system based on the abstract architecture for intelligent agents. The abstract architecture is modeled as a discrete-event system using Petri nets and structural analysis of the net provides an assessment of the communication and coordination properties of the multi-agent system. Deadlock avoidance in the multi-agent system is considered as an initial key property, and it is evaluated using liveness and boundedness properties of the Petri net model.

Avoiding or preventing deadlocks in simulation tools for train scheduling remains a critical issue, especially when combined with the objective of minimization (e.g., the travel times of the trains). The deadlock avoidance and detection problem is revisited, and a new deadlock avoidance algorithm, called DEADAALG, is proposed based on a resource reservation mechanism. The DEADAALG algorithm is proved to be exact; that is, it either detects an unavoidable deadlock resulting from the input data or provides train scheduling free of deadlocks with the scheduling algorithm SIMTRAS. Moreover, it is shown that SIMTRAS is a polynomial time algorithm with an O(|S|&Middot;|T|2 log |T|) time complexity, where T is the set of trains and S is the set of sections in the railway topo logy. Numerical experiments are conducted on Canada's Vancouver–Calgary single-track corridor of Canadian Pacific Railway Limited. Then it is shown that SIMTRAS is efficient and provides schedules of a quality that is comparable with that of an exact optimization algorithm in tens of seconds for up to 30 trains/day over a planning period of 60 days.

The use of structure theory of Petri nets to develop efficient deadlock prevention and deadlock avoidance methods for flexible manufacturing systems (FMSs) modelled by S4R nets is demonstrated. Major synchronisation patterns, such as generalised parallel and sequential mutual exclusion, frequently observed in FMS contexts can be represented by this class. The liveness property of a given S4R net (deadlock-freeness in the context of FMSs) is characterised in terms of structural Petri net elements called siphons. An efficient method for controlling minimal siphons of a given S4R net is developed where local control places are added to the net. A sufficient condition for liveness of the augmented net is provided. This constitutes a deadlock prevention approach. When the net liveness condition is not satisfied, an on-line controller, using a dynamic resource allocation policy, is developed for the augmented net. The performance of the proposed approaches is illustrated using several examples.

Deadlocks are of paramount importance in resource allocation systems, which are usually treated from the perspective of discrete event systems. This paper develops a deadlock prevention strategy for a system modeled with Petri nets, by endowing appropriate time constraints with certain transitions to schedule the firing priority of enabled transitions in a Petri net such that transition sequences leading to deadlocks are prohibited, i.e., expanding an untimed Petri net model into a time Petri net to prevent deadlocks. To increase the system permissiveness of a time Petri net with time constraints endowed, a control place is designed, which does not expand the reachable space of the original Petri net. The predominant role of the control place is to convert continuously enabled transitions at certain markings into newly enabled transitions, which can prolong the firing time of transitions. Furthermore, we propose a method that merely enumerates deadlock prevention condition inequalities to derive a series of time constraints by probing the connection between deadlock prevention conditions and transitions. The developed method only needs to designate time constraints for partial transitions. Examples are provided to demonstrate the effectiveness of the presented methodology.

A deadlock avoidance supervisory controller for Discrete Event (DE) Systems is implemented. The DE controller uses a novel rule-based matrix dispatching formulation (US patent received). This matrix formulation makes it easy to write down the DE controller from standard manufacturing tools such as the bill of materials or the assembly tree. It is shown that the DE controller's matrix form equations plus the Petri Net (PN) marking transition equation provide a complete dynamical description of DE systems. We provide circular wait analysis (CW) for deadlock-free dispatching rules for Multipart Re-entrant Flow line (MRF) regular systems, and provide a regularity test for these systems in PN and matrix notations. We analyse the so-called critical siphons, and certain critical subsystems to develop a DE controller that guaranties deadlock-free dispatching by limiting the work-in-progress in the critical subsystems associated with each CW. This least-restrictive dispatching policy avoids deadlock. The deadlockfree dispatching rules are implemented by the DE controller on a three-robot, two-machine re-entrant flow line, the Intelligent Material Handling cell at the Automation and Robotics Research Institute of UTA. Technical information given includes the development of the deadlock-free controller in LabVIEW.

Deadlock/livelock problems can cause catastrophic results in flexible manufacturing systems (FMS) by forcing them to stop production processes at an unpredictable stage of production. Therefore, they must be handled properly in order to obtain flawless production in FMS. Petri net (PN) based deadlock/livelock studies for FMS have been widely carried out to obtain live PN models. When a PN model is live, this ensures that the modelled FMS is deadlock-free. Firstly, an uncontrolled (plant) PN model is constructed for the FMS suffering from deadlocks/livelocks. Then reachability graph (RG) analysis of this PN model is carried out to provide all possible reachable states of the modelled system. An RG of a PN model of an FMS suffering from deadlock/livelock problems can be split into the live zone (LZ) and the deadlock zone (DZ). The former is the set of system states considered to be legal (good), while the latter is the set of system states regarded to be illegal (bad). The LZ represents the optimal (maximally permissive) system behavior that must be provided by an optimal control policy. Generally, in PN based liveness studies, a liveness enforcing supervisor (LES) consisting of a set of control places (CP) is computed. Then the controlled (closed-loop) PN model is obtained by merging the plant PN model and the LES. If the number of reachable live states of the controlled PN model is the same as the ones that exist in the LZ, then the controlled model is optimal. Otherwise, it is suboptimal. The greater the number of live reachable states of the RG, the more products to be produced within the FMS. Therefore, the number of reachable live states of the controlled PN model is considered as a quality measure. It defines the behavioral permissiveness of the controlled model. In the literature, to verify the behavioral permissiveness of the PN models, the PN tool called INA (Integrated Net Analyzer) has been widely used. Recently, by means of INA, a method was proposed to compute the number of states within the LZ and the DZ of a given PN model suffering from deadlocks/livelocks. Unfortunately, INA cannot compute RGs of large PNs having a few millions of states. Therefore, in this paper by means of TINA (TIme petri Net Analyzer), an alternative faster and much more efficient method is proposed for the computation of the number of states within the LZ and the DZ for PN models with large RGs. In addition, in order to enable the development of new PN based deadlock prevention methods, further computations are also proposed. These include the computation of the set of states in the DZ, LZ and first met bad markings (FBMs) for a given PN model suffering from deadlocks/livelocks. The applicability and the effectiveness of the proposed methods are demonstrated by considering several well-known examples of FMS from the relevant literature.INDEX TERMS Flexible manufacturing systems (FMS), deadlock, deadlock prevention, Petri Nets (PN), liveness enforcing supervisor (LES), PN computation tools.

Deadlock is as condition that arises when multiple processes are waiting for resources held by other processes. A process cannot release the resources it holds until it can acquire the resources it is waiting for, but it cannot acquire these resources until another process releases them. There are few strategies to deal with the deadlock i.e. detection and recovery, deadlock prevention and deadlock avoidance etc. Deadlock can be avoided if certain information about processes is available in advance of resource allocation. For every resource request, the system sees if granting the request would mean that the system would enter an unsafe state, meaning a state that could result in deadlock. The system then only grants request that would lead to safe states. In this paper a method has been proposed to avoid the deadlock in multiprocessor system. A multiprocessor system with two processors has been used here. Two resources i.e. flash drive and printer have been used here. This paper explains how these processes request and release these resources and overcome unsafe state to enter the safe state. Finally, the deadlock avoidance algorithm for multiprocessors system is presented

This paper reviews the currently available multiprocessor resource allocation policies and analyzes their applicability to the Real-Time Specification for Java and Safety-Critical Java. It also proposes some new RTSJ mechanisms that would facilitate the programming of a variety of synchronized object access protocols. The approach taken to managing potential deadlocks in current multiprocessor resource allocation protocols is rather simplistic. Nested resource accesses are either prohibited or the protocols resort to a group lock. The paper considers an alternative mechanism based on deadlock prevention rather than deadlock avoidance.

Deadlock avoidance in sequential resource allocation systems is a well-defined problem in discrete event system literature, as it underlies the operation of many contemporary technological systems. In the past, the problem has been studied by means of a number of formal frameworks, including the finite-state automata (FSA) and Petri nets (PNs). In this paper, it is shown that a significant class of deadlock avoidance policies (DAPs), known as algebraic polynomial kernel (PK)-DAPs, originally developed in the FSA paradigm, can be analyzed using recent results from PN structural analysis. Furthermore, the approach to DAP analysis and design taken in this paper has led to the effective generalization of the currently available algebraic PK-DAPs, and to their enrichment with new and more flexible policy implementations.