Deadlock Prevention Policy Research Articles

Extended elementary siphon-based deadlock prevention policy for a class of generalised Petri nets

This paper develops a novel deadlock prevention policy for a class of generalised Petri nets, namely S4PR that can well model flexible manufacturing systems (FMS). The analysis of generalised Petri nets leads us to characterise deadlock situations in terms of insufficiently marked siphons. The theory of elementary siphons guides our efforts towards the development of structurally simple liveness-enforcing supervisors. Therefore, insufficiently marked siphons can be classified into elementary ones and dependent ones. The controllability of a dependent siphon can be ensured by properly supervising its elementary ones. In order to find a compact and proper set of elementary siphons for S4PR, the concept of augmented siphons is proposed. Then, the concept of max′-controlled siphons is employed, which can relax the siphon controllability condition. By explicitly controlling elementary siphons via adding monitors, a liveness-enforcing controlled system can be found. In addition, the liveness-enforcing supervisor with more permissive behaviour is obtained through the rearrangement of the output arcs of the monitors. Finally, an FMS case study is utilised to demonstrate the proposed method.

A New Deadlock Prevention Policy for a Class of Petri Nets Based on Source Transition Control

A New Deadlock Prevention Policy for a Class of Petri Nets Based on Source Transition Control

Computationally Improved Optimal Control Methodology for Linear Programming Problems of Flexible Manufacturing Systems

Deadlock prevention policies are used to solve the deadlock problems of FMSs. It is well known that the theory of regions is the efficient method for obtaining optimal (i.e., maximally permissive) controllers. All legal and live maximal behaviors of Petri net models can be preserved by using marking/transition-separation instances (MTSIs) or event-state-separation-problem (ESSP) methods. However, they encountered great difficulties in solving all sets of inequalities that is an extremely time consuming problem. Moreover, the number of linear programming problems (LPPs) of legal markings is also exponential with net size when a plant net grows exponentially. This paper proposes a novel methodology to reduce the number of MTSIs/ESSPs and LPPs. In this paper, we used the well-known reduction approach Murata (1989) to simply the construct of system such that the problem of LPPs can then be reduced. Additionally, critical ones of crucial marking/transition-separation instances (COCMTSI) are developed and used in our deadlock prevention policy that allows designers to employ few MTSIs to deal with deadlocks. Experimental results indicate that the computational cost can be reduced. To our knowledge, this deadlock prevention policy is the most efficient policy to obtain maximal permissive behavior of Petri net models than past approaches.

Sequence Control of Essential Siphons for Deadlock Prevention in Petri Nets

Deadlock prevention is crucial to the modeling of flexible manufacturing systems. In the Petri net framework, deadlock prevention is often addressed by siphon-based control (SC) policies. Recent research results show that SC methods can avoid full siphon enumeration by using mixed integer programming (MIP) to greatly increase the computational efficiency so that it can be applied in large systems in computable time. Besides, maximally permissive control solutions can be obtained by means of iterative siphon control (ISC) approaches and MIP. Then the remaining problems are redundancy and MIP iterations. Redundant controllers make the closed-loop system more complicated and each MIP iteration increases the total computational time. This article proposes a revised ISC deadlock prevention policy which can achieve better results than the other reported methods in terms of redundancy and MIP iterations while maintaining the maximal permissiveness. Several benchmark examples are provided to illustrate the proposed approach and to be compared with the other reported methods.

Transition-Based Deadlock Detection and Recovery Policy for FMSs Using Graph Technique

A transition-controlled deadlock detection and recovery prevention policy is presented for a subclass of Petri nets used to model flexible manufacturing systems. The subclass is called systems of simple sequential processes with resources (S 3 PR). The proposed policy is different from the standard deadlock prevention policies. Instead of adding control places, this policy adds a controlled transition to solve a group of deadlocked markings that have the same graph-based property. Finally, the results of our study indicate that the proposed policy appears to be more permissive than those existing ones that add control places.

Supervisor Reconfiguration for Deadlock Prevention by Resources Reallocation

Analysis and control of deadlocks play an important role in the design and operation of automated flexible manufacturing systems (FMSs). In FMS, deadlocks are highly undesirable situations, which always cause unnecessary cost. The design problem of an optimal supervisor is in general NP-hard. A computationally efficient method often ends up with a suboptimal one. This paper develops a deadlock prevention policy based on resources reallocation and supervisor reconfiguration. First, given a plant model, we reallocate the marking of each resource place to be one, obtaining a net model whose reachable states are much less than that of the original one. In this case, we find a controlled system for it by using the theory of regions. Next, the markings of the resource places in the controlled system are restored to their original ones. Without changing the structure of the obtained controlled system, we compute the markings of the monitors gradually, which can be realized by two algorithms proposed in this paper. Finally, we decide a marking for each monitor such that it makes the controlled system live with nearly optimal permissive behavior. Two FMS examples are used to illustrate the application of the proposed method and show its superior efficiency.

A Literature Review of Deadlock Prevention Policy Based on Petri Nets for Automated Manufacturing Systems

Deadlock is an undesired situation in a highly automated system due to the fact that no system can allow its occurrence which may produce some unnecessary economic losses or serious consequences. There are three mathematical tools to handle deadlocks in resource allocation systems: graph theory, finite state machine, and Petri net. Due to its inherent characteristics, Petri nets are widely applied to manufacturing systems. Generally, these existing deadlock methods are classified into three strategies: deadlock detection and recovery, deadlock avoidance, and deadlock prevention. In this paper, a review of deadlock prevention policies and merits and drawbacks of these policies are presented. Then it gives the possible trend of the research in the future.

Iterative Deadlock Control by Using Petri Nets

Deadlocks should be eliminated in resource allocation systems such as flexible manufacturing systems. An iterative deadlock control policy is usually considered to be a natural solution with reasonable computational cost for a large-scale system where direct methods would be prohibitively expensive (and in some cases impossible) even with the best available computing power. This paper reviews the existing iterative deadlock prevention policies for discrete event systems that are modeled with Petri nets. A number of technical problems in the existing iterative deadlock control approaches are formulated and discussed. Their solutions are illustrated through case studies. We conclude that the suitability, effectiveness, and efficiency of an iterative deadlock control approach are sensitive to specific examples, and no general algorithm is found in the literature, which works well for all cases.

A Hybrid Model of Complex Automated Warehouse Systems—Part II: Analysis and Experimental Results

An automated warehouse system has two main components: an automated storage and retrieval subsystem consisting of a number of aisles, each one served by a crane, and a picking area which is formed by bays where stock units coming from the aisles are partially emptied by human operators. These two components are connected via an interface area consisting of carousels, conveyors and buffers. This area is usually modeled as a discrete event system, while the overall system performance depends also on continuous time phenomena. In Part I, a hybrid modeling approach based on a new Petri net formalism and a freeware simulation tool have been presented. The concepts of Hybrid Petri Nets and Colored Petri Nets are merged to obtain modular and compact models for automated warehouse systems. Part II now focuses on the application of this formalism to automated warehouse systems analysis and performance evaluation. Liveness analysis is performed by means of a hybrid automaton obtained from the net model. A deadlock prevention policy is synthesized working on an aggregated model. Finally, a real case study is considered to show the effectiveness of the approach.

Controllability Conditions of Resultant Siphons in a Class of Petri Nets

Strict minimal siphons (SMSs) play a key role in the development of deadlock prevention policies by using Petri nets for flexible manufacturing systems (FMSs). In this paper, given two SMSs and their resultant siphon, the concept of key resource subsets is proposed which is shown to be the critical factor in deciding the controllability conditions of the latter. A necessary and sufficient condition is then proposed under which the resultant siphon can be always marked if its two SMSs are M-controlled, i.e., invariant controlled via the method proposed by Moody and Antsaklis. As for a resultant siphon that is composed by more than two composable SMSs, a sufficient condition is proposed under which it can be always marked if its SMSs are M-controlled. They are established by analyzing the structural characteristics and markings of the resource subnets in a class of Petri nets called L-S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> PR. When they are applied to some classes of S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> PR nets, i.e., those whose controlled ones are maximally permissive and live once their original SMSs are M-controlled, the number of monitors may be reduced. An FMS example is used to illustrate the application of the results.

Enhancement of an efficient control policy for FMSs using the theory of regions and selective siphon method

Deadlocks are an important problem in resource allocation systems such as flexible manufacturing systems. The theory of regions and the siphon-based method are usually used in the most deadlock prevention policies. The theory of regions that can obtain a maximally permissive controller is usually considered to be a natural solution with seasonable computational cost for flexible manufacturing systems. The selective siphon method allows one to use fewer control places than the conventional one. This paper employs both methods above. The former can identify the set of curial marking/transition–separation instance; the latter can reduce the computational cost. We can infer that the novel policy is the most efficient policy than the traditional methods, and also, the maximal permissive behavior of Petri net models can still be obtained.

Deadlocked Prevention Method for Flexible Manufacturing Systems Using the Theory of Regions and Reduction Technology

The theory of regions has been recognized as the powerful method of deadlock prevention policy for obtaining maximally permissive controllers. All legal and live maximal behavior of Petri net models can be preserved by using marking/transition-separation instances or event-state-separation-problem methods. However, they encountered great difficulties in solving all sets of inequalities that is an extremely time consuming problem. Additionally, the number of linear programming problems of legal markings is also exponential with net size when a plant net grows exponentially. This work proposes a novel methodology to reduce the above contributions. In this paper, the reachability condition equations in the theory of region can be reduced under the reduction approach. The problem of the issue can then be reduced. Moreover, a crucial marking/transition-separation instances is developed in our deadlock prevention policy that allows designers to employ few marking/transition-separation instances to deal with deadlocks. The advantage of the proposed policy is that a maximally permissive controller can be obtained with drastically reduced computation.

Behaviorally Optimal and Structurally Simple Liveness-Enforcing Supervisors of Flexible Manufacturing Systems

This paper presents two iterative deadlock prevention policies for flexible manufacturing systems (FMSs). Both can find a maximally permissive liveness-enforcing supervisor with a small number of control places. A vector covering approach is used to obtain a minimal covering set of legal markings and a minimal covered set of first-met bad markings (FBMs), which are much smaller than the sets of legal markings and FBMs, respectively. At each iteration, by solving an integer linear programming problem (ILPP), a place invariant (PI) associated with a control place is designed to forbid as many FBMs as possible, and no markings in the minimal covering set of legal markings are forbidden. The objective function of the ILPP maximizes the number of FBMs that are forbidden by the PI. Then, the forbidden FBMs by the PI are removed from the minimal covered set of FBMs. This process is carried out until all FBMs are forbidden. Two ILPP design techniques are developed for the control policies. Though the proposed methods cannot in general guarantee the minimality of the supervisory structure, they reduce the overall computational time greatly, which is shown by numerical studies. Finally, a number of FMS examples from the literature are presented to illustrate the proposed methods.

An extraction algorithm for a set of elementary siphons based on mixed-integer programming

Elementary siphons are useful in the development of a deadlock prevention policy for a discrete event system modeled with Petri nets. This paper proposes an algorithm to iteratively extract a set of elementary siphons in a class of Petri nets, called system of simple sequential processes with resources (S3PR). At each iteration, by a mixed-integer programming (MIP) method, the proposed algorithm finds a maximal unmarked siphon, classifies the places in it, extracts an elementary siphon from the classified places, and adds a new constraint in order to extract the next elementary siphon. This algorithm iteratively executes until no new unmarked siphons can be found. It finally obtains a unique set of elementary siphons and avoids a complete siphon enumeration. A theoretical analysis and examples are given to demonstrate its efficiency and practical potentials.

A Polynomial Algorithm for Computing Elementary Siphons in a Class of Petri Nets

A set of elementary siphons plays a key role in the development of deadlock prevention policies for automated manufacturing systems. This paper addresses the computation problem for elementary siphons in a subclass of Petri nets which are basic systems of simple sequential processes with resources (BS3PR) and can model many automated manufacturing systems. An algorithm for enumerating elementary siphons is established by the one-to-one relationship between maximal perfect resource-transition circuits (MPCs) and strict minimal siphons. A set of MPCs is first computed, followed by a set of elementary siphons in a BS3PR. The presented algorithm is proved to have polynomial-time complexity. An example is used to illustrate the algorithm.

A deadlock prevention policy for a class of Petri net models of flexible manufacturing systems

This paper focuses on the problem of deadlocks in automated flexible manufacturing systems (FMS). Based on Petri nets, a deadlock prevention policy is proposed for a special class of Petri nets, S3PR. We embed the deadlock avoidance policy (DAP) of conjunctive/disjunctive resources upstream neighbourhood (C/D RUN) into the deadlock prevention policy (DPP), and allocate the underlying (sequential) resources reasonably to guarantee the absence of deadlock states and processes. First, siphons in a net model are distinguished by elementary and dependent ones. From the set of elementary siphons, a set of linear inequality constraints expressed by the state vector can be formalised. After being modified by the proposed policy, a set of generalised mutual exclusion constraints (GMEC) expressed by the marking vector can be found. Then monitors based on the GMEC are added to the plant model such that the elementary siphons in the S3PR net are all invariant-controlled and no emptiable siphon is generated due to the addition of the monitors. This novel deadlock prevention policy can usually lead to a more permissive supervisor by adding a smaller number of monitors and arcs than the existing methods for the design of liveness-enforcing Petri net supervisors. Two manufacturing examples are utilised to illustrate the proposed method and compared with the existing ones.

An iterative method for synthesizing non-blocking supervisors for a class of generalized Petri nets using mathematical programming

This paper presents a novel and computational deadlock prevention policy for a class of generalized Petri nets, namely G-systems, which allows multiple resource acquisitions and flexible routings with machining, assembly and disassembly operations. In this research, a mixed integer programming (MIP)-based deadlock detection technique is used to find an insufficiently marked minimal siphon from a maximal deadly marked siphon for generalized Petri nets. In addition, two-stage control method is employed for deadlock prevention in Petri net model. Such proposed method is an iterative approach consisting of two stages. The first one is called siphons control, which adds a control place to the original net for each insufficiently marked minimal siphon. The objective is to prevent minimal siphons from being insufficiently marked. The second one, called control-induced siphons control, is to add a control place to the augmented net with its output arcs connecting to source transitions, which assures that there is no new insufficiently marked siphon generated due to the addition of the monitors. Compared with the existing approaches, the proposed deadlock prevention policy can usually lead to a non-blocking supervisor with more permissive behavior and high computational efficiency for a sizeable plant model due to avoiding complete siphon enumeration. Finally, a practical flexible manufacturing system (FMS) example is utilized to illustrate the proposed method.

Siphon extraction for deadlock control in flexible manufacturing systems by using Petri nets

Siphons can be used to characterise deadlock states and solve deadlock problems in Petri nets that model flexible manufacturing systems. This article presents a novel deadlock prevention policy for Petri nets using siphon extraction. At each iteration, a siphon extraction algorithm finds a maximal deadly marked siphon, classifies the places in it, and decides a necessary siphon from the classified places. Accordingly, the deadlock prevention policy adds a proper control place (CP) to make each necessary siphon marked or max-controlled until the controlled system is live. By adopting the classification of places, deciding necessary siphons, and adding the proper CPs, the proposed deadlock prevention policy avoids a complete siphon enumeration, adds a small number of CPs, and leads to a liveness-enforcing supervisor with a simple structure compared with closely related approaches in the literature. Finally, a case study shows its appealing behavioural permissiveness.

Petri Net Channelized-Based Deadlock Prevention Policy for Flexible Manufacturing Systems

Petri nets are employed to model flexible manufacturing systems (FMSs). However, the system deadlocked are possible happened. The conventional deadlock prevention policies are always to forbid the system entering the deadlock by using the control places. To obtain a live system, some dead markings must be sacrificed in the traditional policies. Therefore, the original reachability states of the original model can not be conserved. However, this paper is able to maintain all the reachability states of the original net and guaranty the control system live. Under our control policy, all number of reachability states of the original net will be preserved. Finally, two examples are performed that can reach the maximal permissiveness for FMSs using Petri net models (PNMs).

An improved maximally permissive deadlock prevention policy based on the theory of regions and reduction approach

The theory of regions has been recognised as the powerful method of deadlock prevention policy for obtaining maximally permissive controllers. It is well known that all legal and live maximal behaviour of Petri net models can be preserved by using marking/transition-separation instances (MTSIs) or event-state-separation-problem (ESSP) methods. However, they encountered great difficulties in solving all sets of inequalities that is an extremely time-consuming problem. Moreover, the number of linear programming problems (LPPs) of legal markings is also exponential with net size when a plant net grows exponentially. This work proposes a novel methodology to reduce the number of MTSIs, ESSPs and LPPs. To do so, the reachability condition equations in the theory of region can be reduced under the reduction approach. The problem of LPPs can then be reduced. Additionally, crucial marking/transition-separation instances is developed in our deadlock prevention policy that allows designers to employ few MTSIs to deal with deadlocks. The advantage of the proposed policy is that a maximally permissive controller can be obtained with drastically reduced computation. Finally, experimental results infer that our proposed policy seems to be the most efficient policy among existing methods.