Generalized Petri Nets Research Articles

A General Petri-Net Controller for Avoiding Collisions and Deadlocks in a Partially-Controllable Mixed Traffic System

A General Petri-Net Controller for Avoiding Collisions and Deadlocks in a Partially-Controllable Mixed Traffic System

Petri Net Toolbox for Multi-Robot Planning under Uncertainty

Currently, there is a lack of developer-friendly software tools to formally address multi-robot coordination problems and obtain robust, efficient, and predictable strategies. This paper introduces a software toolbox that encapsulates, in one single package, modeling, planning, and execution algorithms. It implements a state-of-the-art approach to representing multi-robot systems: generalized Petri nets with rewards (GSPNRs). GSPNRs enable capturing multiple robots, decision states, action execution states and respective outcomes, action duration uncertainty, and team-level objectives. We introduce a novel algorithm that simplifies the model design process as it generates a GSPNR from a topological map. We also introduce a novel execution algorithm that coordinates the multi-robot system according to a given policy. This is achieved without compromising the model compactness introduced by representing robots as indistinguishable tokens. We characterize the computational performance of the toolbox with a series of stress tests. These tests reveal a lightweight implementation that requires low CPU and memory usage. We showcase the toolbox functionalities by solving a multi-robot inspection application, where we extend GSPNRs to enable the representation of heterogeneous systems and system resources such as battery levels and counters.

Liveness Analysis and Deadlock Control for Automated Manufacturing Systems With Multiple Resource Requirements

This paper focuses on the liveness analysis and deadlock control for automated manufacturing systems (AMSs) with multiple resource requirements. Such an AMS is modeled by a class of generalized Petri nets called systems of simple sequential processes with multiple resources (S3PMR). It is shown that a deadlock of the considered AMSs can be characterized by the saturation of a structural object in S3PMR, called perfect resource transition-circuit (PRT-circuit). As a consequence, an S3PMR is live if and only if no PRT-circuit is saturated at any reachable marking. To ensure the system liveness, one has to prevent all PRT-circuits from being saturated at all reachable markings. To develop a structurally simple Petri net deadlock controller, we present the concept of an effective transition cover, which is a special subset of PRT-circuits that may be saturated. Then by designing a control place with a proper control variable for each PRT-circuit in an effective transition cover, we obtain a deadlock controller for the system. The needed control variables are determined by an integer linear program. Since the number of PRT-circuits in an effective transition cover is much less than that of all PRT-circuits that need to control, our controller is of small structural size. For an AMS with saturable PRT-circuits, there exists at least a transition cover. An algorithm is presented for checking the effectiveness of transition covers, and transforming noneffective transition covers into effective ones. Finally, some examples are used to illustrate the proposed method.

Computation of Admissible Marking Sets in Weighted Synchronization-Free Petri Nets by Dynamic Programming

We study the computation of admissible marking sets in generalized Petri nets. We first show that the admissibility checking in the generalized Petri net is NP-hard. Then, we consider a special subclass of generalized Petri nets called weighted-synchronization-free nets in which each transition has at most one input place. For a net in this subclass, we propose a generating function to compute by dynamic programming the set of admissible markings for a given generalized mutual exclusion constraint .

Robust Deadlock Prevention for Automated Manufacturing Systems With Unreliable Resources by Using General Petri Nets

Recently, the problem of robust control for automated manufacturing systems (AMSs) with unreliable resources receives increasing attentions. Almost all the existing related works are only concerned with the failure-prone AMSs in which each part stage utilizes only one unit of resources. While, in real-world AMS, it is often necessary to use multiple units of different resources to complete a part. This paper focuses on the robust control of such complex AMSs with a type of unreliable resources. General Petri nets are used to model all the behavior of such AMSs. By adding a control place to the Petri net models for each considered siphon, we develop robust deadlock controllers for the considered AMS. Such a robust controller ensures that the parts of all types can be processed continuously through any of its processing routes, even if one of the unreliable resources fails. Finally, some examples are used to illustrate the proposed method.

The QoS analysis of web services composition based on Jackson queuing network

With the popularity of distributed computing and mobile internet, services composition has become a hot research in the field of service computing. The QoS of web services composition organised by BPEL is determined by the internal structure, the probability distribution in the variables value of BPEL process and the external factors such as the hardware and software processing capabilities of web servers and the load of web servers. At present, the generalised Petri nets, queuing Petri nets, Markov processes and stochastic process algebra model which are widely used and cannot have a comprehensive analysis in obtaining the actual performance of web services composition in internet environment. In this paper, a set of mapping rules are established to transform the internal and external factors which have impacts on the QoS of web services composition into Jackson queuing network, meanwhile, a set of performance indexes and their formula are given. Based on these performance indexes, we comprehensively analyse the performance of web services composition and locate the bottleneck of web services composition when the internal and external factors are changed so that, the performance of web services composition can be predicted before its deployment.

The Complexity of Diagnosability and Opacity Verification for Petri Nets

Diagnosability and opacity are two well-studied problems in discrete-event systems. We revisit these two problems with respect to expressiveness and complexity issues. We first relate different notions of diagnosability and opacity. We consider in particular fairness issues and extend the definition of Germanos et al. [ACM TECS, 2015] of weakly fair diagnosability for safe Petri nets to general Petri nets and to opacity questions. Second, we provide a global picture of complexity results for the verification of diagnosability and opacity. We show that diagnosability is NL-complete for finite state systems, PSPACE-complete for safe Petri nets (even with fairness), and EXPSPACE-complete for general Petri nets without fairness, while non diagnosability is inter-reducible with reachability when fault events are not weakly fair. Opacity is ESPACE-complete for safe Petri nets (even with fairness) and undecidable for general Petri nets already without fairness.

Deadlock and liveness characterization for a class of generalized Petri nets

Petri nets (PNs) are widely adopted for modeling flexible manufacturing systems (FMSs) since they are an effective tool for analyzing the latter’s dynamic behavior and synthesizing a supervisory controller to make a system deadlock-free. As an important subclass of PNs, the weighted system of simple sequential processes with resources (WS3PR) can be used to model many FMSs well. Based on the initial marking and structural properties of a WS3PR without using marking enumeration and state equations, this paper presents a method to check its liveness. We first define two classes of transitions for a resource subnet of WS3PR, based on which, the relationship between markings and strongly connected resource subnets (SCRSs) is analyzed. Next, functions used to check the liveness of a given WS3PR are developed, which take the full advantage of SCRS trees and WS3PR structure. It is shown that, by the proposed method, the computational complexity for a subclass of WS3PR named k-sharing bounded WS3PR is polynomial. Sufficient conditions to check liveness of a WS3PR are finally established. Two examples are used to illustrate the results.

On near-optimal deadlock control for a class of generalized Petri nets using reachability graph

PurposeDeadlock is a rather undesirable phenomenon and must be well solved in flexible manufacturing systems (FMS). This paper aims to propose a general iterative deadlock control method for a class of generalized Petri nets (GPN), namely, G-systems, which can model an FMS with assembly and disassembly operations of multiple resource acquisition. When given an uncontrolled G-system prone to deadlocks, the work focuses on the synthesis of a near-optimal, non-blocking supervisor based on reachability graph (RG) analysis.Design/methodology/approachThe concept of a global idle place (GIP) for an original uncontrolled G-system is presented. To simplify the RG computation of an uncontrolled G-system, a GIP is added temporarily to the net model during monitor computation steps. Starting with one token and then by gradually increasing the number of tokens in the GIP at each iteration step, the related net system is obtained. The minimal-covered-set of all bad markings of the related net system suffering from deadlock can be identified and then removed by additional monitors through an established place-invariant control method. Consequently, all related systems are live, and the GIP is finally removed when the non-blockingness of the controlled system is achieved. Meanwhile, the redundancy of monitors is also checked.FindingsA typical G-system example is provided to demonstrate the applicability and effectiveness of the proposed method. Experiments show that the proposed method is easy to use and provides very high behavioral permissiveness for G-system. Generally, it can achieve an optimal or a near-optimal solution of the non-blocking supervisor.Originality/valueIn this work, the concept of GIP for G-systems is presented for synthesis non-blocking supervisors based on RG analysis. By using GIP, an effective deadlock control method is proposed. Generally, the proposed method can achieve an optimal or a near-optimal, non-blocking supervisor for an uncontrolled G-system prone to deadlocks.

A class of generalized Petri nets and its state equation

By analyzing the evolution nature of a Petri net, this article reports a generalized state equation for Petri nets, including Petri nets with inhibitor and enabling arcs. By proposing the generaliz...

A suboptimal deadlock control policy for designing non-blocking supervisors in flexible manufacturing systems

This work aims to resolve deadlock problems in flexible manufacturing systems. A novel deadlock control policy in the frame of Petri nets formalism is presented for a class of generalized Petri nets, namely G-systems, which can usually model assembly and disassembly operations of multiple resource acquisition. Based on the concept of elementary siphons, all strict minimal siphons (SMS) in an uncontrolled net system are first divided into elementary siphons and dependent ones. After that, a set of linear inequality constraints expressed by state vectors can be formalized for elementary siphons. After being modified by utilizing the conjunctive/disjunctive resources upstream neighborhood policy, a set of generalized mutual exclusion constraints expressed by marking vectors can be obtained. Then, the additional monitors are only designed for elementary siphons, whose control depth variables can be obtained by solving a linear programming problem. As a result, the controllability of dependent ones can be ensured by properly supervising its elementary siphons. Finally, all strict minimal siphons are max′-controlled and no insufficiently marked siphon is generated, which indicates that the sequential resources are allocated reasonably to guarantee the absence of deadlock states. The proposed method can usually lead to a near-optimal non-blocking supervisor with simple structure. A G-system example prone to deadlocks is used to illustrate the applicability and the effectiveness of the proposed method.

Update to "Extraction of elementary siphons in a class of generalized Petri nets using graph theory" [Engineering Computations (2014) 31(2)331-352

Purpose The purpose of this paper is to correct some mistakes in recently published paper (Hou, Y.F., Li, Z.W., Zhao, M., and Liu, D. (2014) “Extraction of elementary siphons in a class of generalized Petri nets using graph theory”, Engineering Computations, Vol.31, No.2, pp.331-352). Design/methodology/approach In (Hou et al., 2014), based on the concepts of initial resource weighted digraphs and restricted subgraphs, a structurally simple liveness-enforcing supervisor for WS3PR was designed. To demonstrate the effectiveness and applicability of the proposed method, a flexible manufacturing system (FMS) example was presented. However, there are some mistakes in the considered example. The derived monitors were incorrect, which caused the result that the final controlled net system is not live. Findings In order to correct the errors in (Hou et al., 2014), a liveness-enforcing Petri nets supervisor with revised monitors for the considered example was redesigned by applying the method in (Hou et al., 2014). Originality/value This paper corrected the mistakes in (Hou et al., 2014). Consequently, a liveness-enforcing Petri net supervisor is redesigned.

An Efficient Siphon-Based Deadlock Prevention Policy for a Class of Generalized Petri Nets

We propose a new deadlock prevention policy for an important class of resource allocation systems (RASs) that appear in the modeling of flexible manufacturing systems (FMSs). The model of this class in terms of generalized Petri nets is, namely, S4PR. On the basis of recent structural analysis results related to the elementary siphons in generalized Petri nets on one hand and an efficient deadlock avoidance policy proposed for the class of conjunctive/disjunctive (C/D) RASs on the other hand, we show how one can generate monitors to be added to a net system such that all its strict minimal siphons aremax′-controlled and no insufficiently marked siphon is generated. Thereby, a new, simple, and more permissive liveness-enforcing supervisor synthesis method for S4PR is established.

On Invariant-Based Monitors That Enforce Liveness in a Class of Partially Controlled General Petri Nets

We consider a class of Petri Net structures where the existence of a liveness enforcing supervisory policy (LESP) for an initial marking implies there is a LESP for a larger initial marking. That is, the set of initial markings for which there is a LESP for any instance of this class is right-closed. If a transition is prevented from firing at a marking by a LESP, and all LESPs, irrespective of the implementation-paradigm that is chosen, prescribe the same control for the marking, then it is a minimally restrictive LESP. It is possible to synthesize the minimally restrictive LESP for any instance of this class that uses this right-closed set of markings. Alternately, one could consider invariant-based monitors for liveness enforcement in an instance of this class.

Think-globally-act-locally approach with weighted arcs to the synthesis of a liveness-enforcing supervisor for generalized Petri nets modeling FMSs

This paper proposes a general approach, called a think-globally-act-locally method with weighted arcs (TGALW), which can be used to compute a liveness-enforcing supervisor (LES) for the Petri net (PN) model of a flexible manufacturing system (FMS) prone to deadlocks. Compared with siphon-based deadlock prevention policies that are usually rather conservative, the method is especially effective for generalized PN classes such as S4R and S4PR and also leads to optimal or near optimal LESs while maintaining the necessary computations simple. An original PNM is first transformed into a net that is behaviorally equivalent to it. A global sink/source place (GP) is used temporarily in the design steps and is finally removed when the liveness of the system is achieved. At each iteration step, bad markings are identified and then controlled by monitors through an established place-invariant based method. A condition of the optimal controllability of a bad marking is proposed, i.e., if all bad markings are optimally controlled at each iteration step, the TGALW method can find an optimal LES. Redundancy of monitors is checked. Typical examples existing in the literature are used to demonstrate applicability and the effectiveness of the proposed method.

On a Sufficient Information Structure for Supervisory Policies That Enforce Liveness in a Class of General Petri Nets

A Petri net (PN) is said to be live if it is possible to fire any transition, although not immediately, from every reachable marking. A liveness enforcing supervisory policy (LESP) determines which controllable transition is to be prevented from firing at a marking, to ensure the supervised Petri net (PN) is live. In this paper, we restrict our attention to a class of general Petri nets (PN) structures, where the existence of an LESP for an instance initialized at a marking, implies the existence of an LESP when the same instance is initialized with a termwise-larger initial marking. We show that the minimally restrictive LESP for an instance N from this class is characterized by a collection of boolean formulae {Θ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">tc</sub> (N)} <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">tc∈Tc</sub> , where Tc is the set of controllable transitions in the PN. The literals in Θ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">tc</sub> (N) are true if and only if the token-load of specific places meet a threshold. Consequently, appropriately placed threshold-sensors, which detect if the token-load of a place is greater than or equal to a predetermined threshold, provide sufficient information to implement the minimally restrictive LESP. The paper concludes with some directions for future research.

On enumerating minimal siphons in Petri nets using CLP and SAT solvers: theoretical and practical complexity

Petri nets are a simple formalism for modeling concurrent computation. They are also an interesting tool for modeling and analysing biochemical reaction systems, bridging the gap between purely qualitative and quantitative models. Biological networks can indeed be complex, large, and with many unknown kinetic parameters, which makes the development of quantitative models difficult. In this paper, we focus on the Petri net representation of biochemical reactions and on two structural properties of Petri nets, siphons and traps, that bring us information about the persistence of some molecular species, independently of the kinetics. We first study the theoretical time complexity of minimal siphon decision problems in general Petri nets, and present three new complexity results: first, we show that the existence of a siphon of a given cardinality is NP-complete; second, we prove that deciding the Siphon-Trap property is co-NP-complete; third, we prove that deciding the existence of a minimal siphon containing a given set of places, deciding the existence of a siphon of a given cardinality and deciding the Siphon-Trap property can be done in linear time in Petri nets of bounded tree-width. Then, we present a Boolean model of siphons and traps, and two method for enumerating all minimal siphons and traps of a Petri net, by using a SAT solver and a Constraint Logic Program (CLP) respectively. On a benchmark of 345 Petri nets of hundreds of places and transitions, extracted from biological models from the BioModels repository, as well as on a benchmark composed of 80 Petri nets from the Petriweb database of industrial processes, we show that both the SAT and CLP methods are overall faster by one or two orders of magnitude compared to the state-of-the-art algorithm from the Petri net community, and are in fact able to solve all the enumeration problems of our practical benchmarks. We investigate why these programs perform so well in practice, and provide some elements of explanation related to our theoretical complexity results.

Macro liveness graph and liveness of ω-independent unbounded nets

Liveness is a basic property of a system and the liveness issue of unbounded Petri nets remains one of the most difficult problems in this field. This work proposes a novel method to decide the liveness of a class of unbounded generalized Petri nets called ω-independent unbounded nets, breaking the existing limits to one-place-unbounded nets. An algorithm to construct a macro liveness graph (MLG) is developed and a critical condition based on MLG deciding the liveness of ω-independent unbounded nets is proposed. Examples are provided to demonstrate its effectiveness.

Deadlock Control for a Class of Generalized Petri Nets Based on Proper Resource Allocation

AbstractThis article develops a deadlock prevention policy for a class of generalized Petri nets, namely G‐systems, which can model flexible manufacturing systems with machining, assembly, and disassembly operations. In this research, a polynomial complexity control policy for non‐blocking supervisors is established by properly adjusting resource allocation. First, a set of linear inequality constraints is derived with respect to different resource requirements such that the allocation of the system resources to various requesting processes can be appropriately restricted, that is, the resulting system has no deadlock state by imposing monitors on operation places. Moreover, an algorithm is proposed to identify the redundant constraints such that structurally simple liveness‐enforcing net supervisors can be obtained. Compared with existing polices, the proposed method can usually lead to a suboptimal supervisor with high computational efficiency. Finally, a flexible manufacturing system example is utilized to demonstrate the proposed method.

A livelock control policy for a flexible manufacturing system modeling with a subclass of generalized Petri nets

AbstractLivelocks, like deadlocks, can result in the serious problems in running process of flexible manufacturing systems (FMSs) as well. Current deadlock control policies based on the approaches of siphon detection and control, cannot cope with livelocks in a system of sequential systems with shared resources (S4R), a typical subclass of Petri nets that can model FMSs. On the basis of the mixed integer programming method, this study proposes a livelock control policy (LCP) that can not only solve the new smart siphons (NSSs) associated with livelocks or deadlocks in an S4R system directly, but also make the solved NSSs max′-controlled by adding the corresponding control places (CPs). As a result, an original S4R system with livelocks or deadlocks can be turned into the live controlled one in which no NSSs can be found. The related theoretical analysis and several examples are given to demonstrate the proposed LCP. Compared with the existing methods in the literature, the proposed one is more general and...