Deadlock Avoidance Problem Research Articles

A Place-Timed Petri Net-Based Method to Avoid Deadlock and Conflict in Railway Networks

The real-time traffic control of railway networks imposes safety constraints and authorizes movements of trains. This work deals with it by focusing on conflict and deadlock avoidance problems. A place-timed Petri net model is developed for a railway network. Based on it, a conflict avoidance method is presented to ensure that safety principles in railway networks are respected. Also, a polynomial deadlock avoidance policy based on the Banker’s algorithm is proposed. It authorizes the movement of trains between block sections and stations. The proposed conflict avoidance method and deadlock avoidance policy together ensure a railway network to be conflict-free and deadlock-free. Experimental results show that they are effective and efficient.

Milk-run routing and scheduling subject to different pick-up/delivery profiles and congestion-avoidance constraints

Abstract Two kinds of intertwined decisions: the routing decisions, which determine the set of sequences of stations visited by each tugger train’s route, and the scheduling decisions, which plan congestion-free movements of tugger train fleets, are considered. The problem under study can be seen as extension of the pick-up and delivery problem with time windows in which different profiles of separately executed delivery and pick-up operations are assumed. The NP-hard character of the problem considered follows from its roots derived from the vehicle routing and the deadlock-avoidance problems. In this regard, a constraint programming paradigm allowing the further integration of multi-period, multi-trip and multi-commodity flows with various customers’ demands as well as distribution network topology constraints is applied. Consequently, a recursive formulation of a well-known constraint satisfaction problem is proposed. The computer experiments provided illustrate the possibility of using the approach presented in systems of real-life scale.

Transition Cover-Based Robust Petri Net Controllers for Automated Manufacturing Systems With a Type of Unreliable Resources

So far, the majority of deadlock control policies for automated manufacturing systems (AMSs) are based on the assumption that no resource fails; while for AMSs with unreliable resources, the main concerns are deadlock avoidance problems. This paper focuses on the robust deadlock prevention problem for AMSs with a type of unreliable resources, and assumes that at most one of unreliable resources fails at a time. Petri net is introduced to model the considered AMS. Deadlock can be characterized in terms of maximal perfect resource transition-circuits (MPRT-circuits). To develop robust Petri net deadlock controllers with small structures for the system, a new concept of strong transition covers is presented, which is a special kind of transition covers. By designing a control place with a proper control variable to each MPRT-circuit in the strong transition cover, a 1-robust Petri net controller is obtained, whereas the control variables can be determined by an integer linear programming. Such a 1-robust controller ensures that the system can process all types of parts infinitely even if one of unreliable resources fails. Since the number of MPRT-circuits in a strong transition cover is much less than that of all MPRT-circuits, our Petri net controller is of small structural size. Each AMS with a type of unreliable resources has at least a transition cover. An algorithm is presented for checking the strongness of transition covers, and transforming weak transition covers into strong ones. Finally, some examples are given to illustrate the effectiveness of the proposed method.

Robust Deadlock Avoidance for Sequential Resource Allocation Systems With Resource Outages

While the supervisory control (SC) problem of (maximally permissive) deadlock avoidance for sequential resource allocation systems (RASs) has been extensively studied in the literature, the corresponding results that are able to address potential resource outages are quite limited, both, in terms of their volume and their control capability. This paper leverages the recently developed SC theory for switched discrete event systems (s-DES) in order to provide a novel systematic treatment of this more complicated version of the RAS deadlock avoidance problem. Following the modeling paradigm of s-DES, both the operation of the considered RAS and the corresponding maximally permissive SC policy are decomposed over a number of operational modes that are defined by the running sets of the failing resources. In particular, the target supervisor must be decomposed to a set of “localized predicates,” where each predicate is associated with one of the operational modes. A significant part, and a primary contribution, of this paper concerns the development of these localized predicates that will enable the formal characterization and the effective computation of the sought supervisor. With these predicates available, a distributed representation for the sought supervisor that is appropriate for real-time implementation is eventually obtained through an adaptation of the relevant distributed algorithm that is provided by the current s-DES SC theory. Note to Practitioners —This paper extends the existing theory of deadlock avoidance for buffer-space allocation in flexibly automated production systems so that it accounts for disruptive effects due to potential temporary outages of some of the system servers. The set of the failing servers at any time instant defines the corresponding operational mode for the underlying resource allocation system. The primary problem that is addressed by this paper is the synthesis of a resource allocation policy that will ensure the ability of all process instances that do not require the failing resources in a particular mode, to execute repetitively and complete successfully while the system remains in that mode. In line with some past literature on this problem, we call the corresponding supervisory control problem as “robust deadlock avoidance,” and we leverage results from the recently emerged theory for modeling and control of switched discrete event systems in order to characterize and compute a maximally permissive solution for it.

Polynomial-complexity supervisory control for flexible assembly systems based on Petri nets

ABSTRACTFlexible assembly systems (FASs) are a class of resource allocation systems with assembly processes as their inevitable components. Deadlock resolution and liveness enforcement play important roles in the supervisory control of FASs. Design of deadlock avoidance policies (DAPs) for FASs has received significant attention recently. The computational feasibility of real-time DAPs is of great importance for the policies’ online implementation in practical applications. However, there are difficulties brought by the existence of assembly processes. So far, nearly all known DAPs with polynomial-time complexity apply only to systems without assembly operations. This study focuses on the deadlock-avoidance control problem of a broader class of FASs as compared to those discussed in the existing work. Specifically, for an FAS addressed in this paper, each resource can be shared by any two operations, and it also allows multiple resource acquisition at each processing step. This work develops a novel DAP for such FASs, which is based on their Petri-net models and actually an improved Banker’s algorithm that consists of three executable algorithms. Moreover, the computational time complexity of the DAP is polynomial in the size of the system model. The application of the proposed method to some examples illustrates its effectiveness and efficiency.

A Multistep Look-Ahead Deadlock Avoidance Policy for Automated Manufacturing Systems

For an automated manufacturing system (AMS), it is a computationally intractable problem to find a maximally permissive deadlock avoidance policy (DAP) in a general case, since the decision on the safety of a reachable state is NP-hard. This paper focuses on the deadlock avoidance problem for systems of simple sequential processes with resources (S3PR) by using Petri nets structural analysis theory. Inspired by the one-step look-ahead DAP that is an established result, which is of polynomial complexity, for an S3PR without one-unit-capacity resources shared by two or more resource-transition circuits (in the Petri net model) that do not include each other, this research explores a multiple-step look-ahead deadlock avoidance policy for a system modeled with an S3PR that contains a shared one-unit-capacity resource in resource-transition circuits. It is shown that the development of an optimal DAP for the considered class of Petri nets is also of polynomial complexity. It is indicated that the steps needed to look ahead in a DAP depend on the structure of the net model. A number of examples are used to illustrate the proposed method.

Controllable Deadlocks in Parallel Resource-Constrained Workflows

We study the verification of the soundness property for workflow nets extended with resources. A workflow is sound if it terminates properly (no deadlocks and livelocks are possible). A class of resource-constrained workflow nets (RCWF-nets) is considered, where resources can be used by a process instance, but cannot be created or spent. Two sound RCWF-nets using the same set of resources can be put in parallel. This parallel composition may in some cases produce additional deadlocks. A problem of deadlock avoidance in parallel workflows is studied, some methods of deadlock search and control are presented.

Deadlock Avoidance and Detection in Railway Simulation Systems

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.

Maximizing Active Storage Resources with Deadlock Avoidance in Workflow-Based Computations

Workflow-based workloads usually consist of multiple instances of the same workflow, which are jobs with control or data dependencies to carry out a well-defined scientific computation task, with each instance acting on its own input data. To maximize the performance, a high degree of concurrency is always achieved by running multiple instances simultaneously. However, since the amount of storage is limited on most systems, deadlock due to oversubscribed storage requests is a potential problem. To address this problem, we integrate two novel concepts with the traditional problem of deadlock avoidance by proposing two algorithms that can maximize active (not just allocated) resource utilization and minimize makespan. Our approach is based on the well-known banker's algorithm, but our algorithms make the important distinction between active and inactive resources, which is not a part of previous approaches. The central idea is to leverage the data-flow information to dynamically approximate localized maximum claim (i.e., the resource requirements of the remaining jobs of the instance) to improve either interinstance or intrainstance concurrency and still avoid deadlock. Through simulation-based studies, we show how our proposed algorithms are better than the classic banker's algorithm and the more recent Lang's algorithm in terms of makespan and active storage resource utilization.

De-De Dodging Algorithm for Scheduling Multiple Workflows in Hybrid Cloud

Workflow-based applications usually consist of multiple instances depending on a single workflow, which are jobs with control or data dependencies to provide a well-defined scientific computation task, with each instances acting on its own input data. Due to the raise in convention of many applications currently, there is necessitating for high processing and storage capacity along with the consideration of cost and instance use and also without any deadlocks between those instances. To improve the performance of the entire system a high degree of concurrency is obtained by running multiple instances at the same time. On the other hand, since the amount of storage is limited on most systems, deadlock due to numerous storage requests would-be a problem. In this paper we have proposed a new dependency and deadlock avoidance (De-De algorithm) algorithm along with the consideration of both instance and value. The TCHC algorithm that comes to the decision of desiring which resource should be chartered from public providers is now combined with the newly proposed De-De algorithm considering that each instance of both single and multiple workflows should work without any deadlocks. To address this problem, we have combined two new concepts with the traditional problem of deadlock avoidance by proposing a single algorithm that can maximize active (not just allocated) resource utilization and minimize makespan. Our approach is based on the well-known banker’s algorithm, but our algorithms make the important distinction between active and passive resources, which is not a part of previous approaches. Through simulation-based studies, we show how our proposed algorithms are better than the classic banker’s algorithm.

Designing Compact and Maximally Permissive Deadlock Avoidance Policies for Complex Resource Allocation Systems Through Classification Theory: The Linear Case

Most of the past research on the problem of deadlock avoidance for complex resource allocation systems (RAS) has acknowledged the fact that the computation of the maximally permissive deadlock avoidance policy (DAP) possesses super-polynomial complexity for most RAS classes, and therefore, it has resorted to solutions that trade off maximal permissiveness for computational tractability. In this paper, we distinguish between the off-line and the on-line computation that is required for the effective implementation of the maximally permissive DAP, and we seek to develop representations of this policy that will require minimal on-line computation. The particular representation that we adopt is that of a compact classifier that will effect the underlying dichotomy of the reachable state space into safe and unsafe subspaces. Furthermore, in this first study of the aforementioned problem, we restrict our attention to a particular RAS class that is motivated by an ongoing project of ours called Gadara, and accepts separation of the safe and unsafe subspaces of its instantiations through a set of linear inequalities. Through a series of reductions of the derived classification problem, we are also able to attain extensive reductions in the computational complexity of the off-line task of the construction of the sought classifier. We formally establish completeness and optimality properties for the proposed design procedures. We also offer heuristics that, if necessary, can alleviate the computational effort that is necessary for the construction of the sought classifier. Finally, we demonstrate the efficacy of the developed approaches through a series of computational experiments. To the best of our knowledge, these experiments also establish the ability of the proposed methodology to effectively compute tractable implementations of the maximally permissive DAP for problem instances significantly beyond the capacity of any other approach currently available in the literature.

Process vs resource‐oriented Petri net modeling of automated manufacturing systems

AbstractSince the 1980s, Petri nets (PN) have been widely used to model automated manufacturing systems (AMS) for analysis, performance evaluation, simulation, and control. They are mostly based on process‐oriented modeling methods and thus termed as process‐oriented PN (POPN) in this paper. The recent study of deadlock avoidance problems in AMS led to another type of PN called resource‐oriented PN (ROPN). This paper, for the first time, compares these two modeling methods and resultant models in terms of modeling power, model complexity for analysis and control, and some critical properties. POPN models the part production processes straightforwardly, while ROPN is more compact and effective for deadlock resolution. The relations between these two models are investigated. Several examples are used to illustrate them. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

Deadlock free Control Synthesis for Partially Controllable Marked Graphs

This paper deals with the problem of deadlock avoidance in control synthesis for a discrete event systems modeled by marked graphs. The specifications are modeled by General Mutual Exclusion Constraints. We show that, even that the system to be controlled is live, the restriction introduced by the controller may generate deadlocks. Therefore, the research work we present in this paper focuses on enhancing an existing control synthesis technique in order to provide a deadlock free maximal permissive control law.

Optimal deadlock avoidance for complex resource allocation systems through classification theory

Most of the past research on the problem of deadlock avoidance for sequential complex resource allocation systems (RAS) has acknowledged the fact that the maximally permissive deadlock avoidance policy (DAP) possesses super-polynomial complexity for most RAS classes, and it has resorted to solutions that trade off maximal permissiveness for computational tractability. In this work, we seek the effective implementation of the maximally permissive DAP for a broad spectrum of RAS, by distinguishing between the off-line and the on-line computation that is required for the specification of this policy, and developing a representation of the derived result that will require minimal on-line computation. The particular representation that we adopt is that of a compact classifier that will effect the underlying dichotomy of the reachable state space into safe and unsafe subspaces. Through a series of reductions of the posed classification problem, we are also able to attain extensive reductions in the computational complexity of the off-line task of the construction of the sought classifier. A series of computational experiments demonstrate the efficacy of the proposed approach and establish its ability to provide tractable implementations of the maximally permissive DAP for problem instances significantly beyond the capacity of any other approach currently available in the literature.

Optimal Petri-Net-Based Polynomial-Complexity Deadlock-Avoidance Policies for Automated Manufacturing Systems

Even for a simple automated manufacturing system (AMS), such as a general single-unit resource allocation system, the computation of an optimal or maximally permissive deadlock-avoidance policy (DAP) is NP-hard. Based on its Petri-net model, this paper addresses the deadlock-avoidance problem in AMSs, which can be modeled by systems of simple sequential processes with resources. First, deadlock is characterized as a perfect resource-transition circuit that is saturated at a reachable state. Second, for AMSs that do not have one-unit resources shared by two or more perfect resource-transition circuits that do not contain each other, it is proved that there are only two kinds of reachable states: safe states and deadlock. An algorithm for determining the safety of a new state resulting from a safe one is then presented, which has polynomial complexity. Hence, the optimal DAP with polynomial complexity can be obtained by a one-step look-ahead method, and the deadlock-avoidance problem is polynomially solved with Petri nets for the first time. Finally, by reducing a Petri-net model and applying the design of optimal DAP to the reduced one, a suboptimal DAP for a general AMS is synthesized, and its computation is of polynomial complexity.

Modeling and Control of Fluid Transportation Operations in Production Plants With Petri Nets

In industrial plants various material flows take place, connecting processing and storing units to accomplish specific product routings. For example, chemical and batch plants are characterized by fluid exchange between tanks, reactors, filters, distillation columns, etc. Such fluid transportation operations may involve the use of many elementary transporting resources (e.g., pipes and valves), which can be extremely complicated to manage, especially in the case of concurrent material transfer and possibly conflicting commands. A systematic modeling and control approach for such operations is proposed based on Petri nets, which employs aggregate transportation resources denoted lines, for which suitable definitions of dependency and compatibility are provided. The actual management of valves is demanded to a specific control module, which computes valve commands with simple logical rules on the basis of the marking of resource places in the supervisor Petri net. The hierarchical and modular control architecture separates the resource allocation and deadlock avoidance problems from the physical device management, thus limiting system complexity. The general ideas discussed in this brief have been exemplified with a simple batch process example drawn from the literature.

Deadlock modeling and control of semiconductor track systems using resource-oriented Petri nets

This paper addresses the deadlock avoidance problem in track systems in semiconductor fabrication. For the system without buffer space in it, the existing deadlock avoidance policies tend to be too conservative. Routing flexibility provides a chance to develop better ones, but makes their computation more complex. This paper models a track system using coloured resource-oriented Petri net (CROPN). Based on the model, a sufficient condition for deadlock-free operation and the corresponding control law are presented. This proposed policy is shown computationally efficient and less conservative than existing methods. An example is presented to demonstrate its application.

Optimal deadlock avoidance Petri net supervisors for automated manufacturing systems

Deadlock avoidance problems are investigated for automated manufacturing systems with flexible routings. Based on the Petri net models of the systems, this paper proposes, for the first time, the concept of perfect maximal resource-transition circuits and their saturated states. The concept facilitates the development of system liveness characterization and deadlock avoidance Petri net supervisors. Deadlock is characterized as some perfect maximal resource-transition circuits reaching their saturated states. For a large class of manufacturing systems, which do not contain center resources, the optimal deadlock avoidance Petri net supervisors are presented. For a general manufacturing system, a method is proposed for reducing the system Petri net model so that the reduced model does not contain center resources and, hence, has optimal deadlock avoidance Petri net supervisor. The controlled reduced Petri net model can then be used as the liveness supervisor of the system.

A Deadlock Avoidance Approach for Nonsequential Resource Allocation Systems

The paper concentrates on the deadlock-avoidance problem for a class of resource allocation systems modeling manufacturing systems. In these systems, a set of production orders have to be executed in a concurrent way. To be executed, each step of each production order needs a set of reusable system resources. The competition for the use of these resources can lead to deadlock problems. Many solutions, from different perspectives, can be found in the literature for deadlock-related problems when the production orders have a sequential nature [sequential resource allocation systems (S-RAS)]. However, in the case in which the involved processes have a nonsequential nature [nonsequential resource allocation systems (NS-RAS)], the problem becomes more complex. In this paper, we propose a deadlock avoidance algorithm for this last class of systems. We also show the usefulness of the proposed solution by means of its application to a real system.

Deadlock avoidance in sequential resource allocation systems with multiple resource acquisitions and flexible routings

Considers the deadlock avoidance problem for the class of conjunctive/disjunctive (sequential) resource allocation systems (C/D-RAS), which allows for multiple resource acquisitions and flexible routings. First, a siphon-based characterization for the liveness of Petri nets (PNs) modeling C/D-RAS is developed, and subsequently, this characterization facilitates the development of a polynomial-complexity deadlock avoidance policy (DAP) that is appropriate for the considered RAS class. The resulting policy is characterized as C/D-RUN. The last part of the paper exploits the aforementioned siphon-based characterization of C/D-RAS liveness, in order to develop a sufficiency condition for C/D-RAS liveness that takes the convenient form of a mixed integer programming (MIP) formulation. The availability of this MIP formulation subsequently allows the automatic correctness verification of any tentative C/D-RAS DAP for which the controlled system behavior remains in the class of PNs modeling C/D-RAS, and the effective flexibility enhancement of the aforementioned C/D-RUN DAP implementations. Finally, we notice that, in addition to extending and complementing the current theory on deadlock-free sequential resource allocation to the most powerful class of C/D-RAS, the presented results also (i) nontrivially generalize important concepts and techniques of ordinary PN structural analysis to the broader class of nonordinary PNs, while (ii) from a practical standpoint, they can find direct application in the (work-) flow management of modern production, service and/or transportation environments.