Augmented Marked Graphs Research Articles

Decentralized Enforcement of Linear State Specifications for Augmented Marked Graphs With a Coordinator

Decentralized Enforcement of Linear State Specifications for Augmented Marked Graphs With a Coordinator

Event Circular Waits and Their Analysis via Petri Nets

Deadlock control of automated manufacturing systems has been widely investigated in recent decades. According to classical Coffman theory, resource circular wait (RW) is viewed as a necessary condition for deadlocks to occur. However, the fact is not as simple as so. Counterexamples are presented to show that RWs do not necessarily appear together with deadlocks. Event circular waits (EWs) are proposed as an alternative to represent a fundamental necessary condition of deadlocks. First, we present the formal definitions of EWs in a type of Petri nets, i.e., weighted augmented marked graphs (WAMGs), and show that EWs are more general and essential than RWs in describing the cause of deadlocks. Second, we show a new classification of siphons, i.e., types I, II, III, and IV, and illustrate the relationship between undermarked siphons and EWs in the WAMGs. Third, we show that EWs are more efficient than RWs for deadlock avoidance since deadlocks can be avoided earlier at a specified marking by using EWs rather than RWs. Several examples are given to clarify the theory throughout this paper.

Liveness-Enforcing Supervision in AMS-Oriented HAMGs: An Approach Based on New Characterization of Siphons Using Petri Nets

In the context of automated manufacturing systems, flexibility and synchronization are two main representative formations. Supervisory control techniques for flexibility have gained increasing attention, but those for synchronization operations have received little notice. Based on their comparison, our work makes threefold contributions. First, we propose a novel characterization of siphons, i.e., type I and type II, based on a special kind of Petri nets, namely, hierarchical augmented marked graphs (HAMGs), which integrate multilevel synchronization into a system. This characterization of siphons is further proved to be a crucial and essential description for both synchronization and flexibility. Second, event circular-wait is proposed to describe the occurrence of deadlocks in HAMGs. Its counterpart is resource circular-wait in flexibility. Ours is a more general and accurate characterization of deadlocks. The liveness of HAMGs can be attributed to the absence of undermarked siphons. Third, a unified liveness-enforcing supervisory control is established based on new characterization of siphons with the aid of generalized mutual exclusion constraints. Supervisor simplification based on inequality analysis is provided for structure simplicity. An experimental study illustrates the correctness of such characterization and the effectiveness of our proposed control method.

Proper Augmented Marked Graphs : Properties, Characterizations and Applications

Augmented marked graphs possess a special structure for modelling distributed systems with shared resources. Not only inheriting the desirable properties of augmented marked graphs such as on liveness and reversibility, proper augmented marked graphs also exhibit other desirable properties, including boundedness and conservativeness. However, proper augmented marked graphs have a rather complicated definition that inevitably undermines the usability in system modelling. In this paper, based on composition of live and bounded marked graphs, new characterizations for proper augmented marked graphs are devised. Through these characterizations, proper augmented marked graphs can be effectively used in modelling and analyzing conflicting processes of a distributed system. Applications to distributed transaction processing with shared resources are discussed. DOI: http://dx.doi.org/10.5755/j01.itc.46.1.13970

COMPOSITION OF AUGMENTED MARKED GRAPHS AND ITS APPLICATION TO COMPONENT-BASED SYSTEM DESIGN

Augmented marked graphs possess some structural characteristics which are especially desirable for modelling systems with common resources. This paper first investigates the composition of augmented marked graphs via common resource places. Special focus is placed on preservation of four properties, namely, liveness, boundedness, reversibility and conservativeness. It is then applied to component-based system design, where the system components are specified as augmented marked graphs and composed via their common resource places. Based on the preservation of properties of this composition, the liveness, boundedness, reversibility and conservativeness of the integrated system can be readily derived. Examples of manufacturing system integration are used for illustration.

Process Completing Sequences for Resource Allocation Systems with Synchronization

This paper considers the problem of establishing live resource allocation in workflows with synchronization stages. Establishing live resource allocation in this class of systems is challenging since deciding whether a given level of resource capacities is sufficient to complete a single process is NP-complete. In this paper, we develop two necessary conditions and one sufficient condition that provide quickly computable tests for the existence of process completing sequences. The necessary conditions are based on the sequence of completions of n subprocesses that merge together at a synchronization. Although the worst case complexity is O(2n), we expect the number of subprocesses combined at any synchronization will be sufficiently small so that total computation time remains manageable. The sufficient condition uses a reduction scheme that computes a sufficient capacity level of each resource type to complete and merge all n subprocesses. The worst case complexity is O(nċm), where m is the number of synchronizations. Finally, the paper develops capacity bounds and polynomial methods for generating feasible resource allocation sequences for merging systems with single unit allocation. This method is based on single step look-ahead for deadly marked siphons and is O(2n). Throughout the paper, we use a class of Petri nets called Generalized Augmented Marked Graphs to represent our resource allocation systems.

Supervisor Design to Enforce Production Ratio and Absence of Deadlock in Automated Manufacturing Systems

This paper proposes a new Petri net class, namely, Ratio-enforced weighted Augmented Marked Graphs (RAMGs), and solves ratio control and liveness-enforcing supervision problems for automated manufacturing systems. RAMGs can ensure the required product ratios as demanded by production planners. Since the deadlock of such a system can be attributed to improper acquisition of finite shared resources, a supervisor is introduced such that they are properly allocated. This paper proves that ratio and supervisory controllers for an RAMG can be separately designed. Their design methods are presented. Examples are given to illustrate them.

Deadlock prevention and performance oriented supervision in flexible manufacturing cells: A hierarchical approach

In this paper, a hierarchical control system is proposed for automated flexible manufacturing cells (FMCs) that operate in a job shop flow setting. The control system is made up of a higher level scheduler that optimizes the production flow within the cell, and a lower level supervisor that implements the decisions of the scheduler on the shop floor. To obtain the supervisor, a production schedule is transformed into an augmented Marked Graph (MG) model that can interact with the cell devices. Because of the flow complexities inherent in job shop systems, they are usually prone to deadlocks. Accordingly, this paper also proposes a necessary condition for deadlock occurrence in the scheduling phase. The proposed approach is validated by implementation in an experimental manufacturing cell.

Low-Cost and High-Performance Supervision in Ratio-Enforced Automated Manufacturing Systems Using Timed Petri Nets

In the context of automated manufacturing, this work proposes a new special class of timed Petri nets, namely, Timed ratio-enforced Augmented Marked Graph (TAMG) and its low-cost and high-performance supervisor synthesis methodology. A supervisor is composed of a set of control places (monitors), each of which is easy to be algebraically specified by a generalized mutual exclusion constraint (GMEC) to prevent certain siphons from being undermarked. In order to make a good tradeoff between the supervisor implementation cost and system performance, a mixed integer programming (MIP) approach is formulated to synthesize the monitors. An example is used to validate the effectiveness and efficiency of the proposed method. The results show that the proposed method remarkably outperforms any existing ones.

Reachability Analysis of Augmented Marked Graphs via Integer Linear Programming

Augmented marked graphs (AMGs) are extensions of marked graphs that allow resource sharing. It has been shown that AMGs are useful for modeling and analyzing certain types of flexible manufacturing systems (FMSs). To our knowledge, the techniques developed for analyzing AMGs are mostly based upon checking certain Petri net structures such as siphons. This article exploits the integer linear programming approach for the analysis of a subclass of AMGs called decomposable AMGs. We show that reachability between two configurations of a decomposable AMG can be equated with solving an instance of integer linear programming. We further extend our technique to model checking a type of branching time temporal logics. Examples arisen in FMSs are used to demonstrate the application of our technique.

Boundedness and conservativeness of augmented marked graphs

Augmented marked graphs are often used in modelling shared resource systems. A major reason is that they possess a structure especially desirable for modelling shared resources. Yet, the properties of augmented marked graphs are not extensively studied. Only some siphon-based and cycle-based characterisations for deadlock freeness, liveness and reversibility are reported in the literature. This paper investigates the boundedness and conservativeness of augmented marked graphs. Based on R-transform, a necessary and sufficient condition for bounded and conservative augmented marked graphs is proposed. This is useful in analysing the capacity overflow for systems modelled as augmented marked graphs.

MODELLING AND ANALYSIS OF MANUFACTURING SYSTEMS USING AUGMENTED MARKED GRAPHS

A manufacturing system is typically an event-driven system in which the processes are asynchronous in nature and used to compete with each other for common resources. As the sharing of resources may induce erroneous situations such as deadlocks, in manufacturing system design, a major design objective is to achieve a live and reversible system. Augmented marked graphs possess specific structural characteristics and dynamic properties which are especially desirable for modelling and analysing manufacturing systems. This paper begins with a review of augmented marked graphs and their properties. Then, we show the modelling of a manufacturing system using an augmented marked graph, and the analysis of the system liveness and reversibility based on the properties of augmented marked graphs.

Cycle inclusion property of augmented marked graphs

Cycle inclusion property of augmented marked graphs

New characterization for live and reversible augmented marked graphs

New characterization for live and reversible augmented marked graphs

Design, analysis and implementation of a real-world manufacturing cell controller based on Petri nets

The primary function of a flexible manufacturing cell controller is to coordinate equipment within a cell to perform a sequence of manufacturing operations required by flexible production. In this paper, we present the modelling, analysis and implementation of a real-world cell controller. A Petri net-based development environment for cell controller design and implementation is described. The intended advantage of the proposed environment is that, users can define and/or change operation flow directly on the modelled Petri net, without programming efforts, otherwise required for general cell controller implementation. The proposed environment is used to design and implement a real-world flexible manufacturing cell controller at National Taiwan University of Science and Technology (NTUST). A scenario-based approach is adopted to model the operation flows in the cell, and from the scenario, we construct its Petri net model. To our knowledge, this is the first work that formalizes the conversion of scenarios to Petri nets. The resultant net is an augmented marked graph (Chu and Xie, 1997, IEEE Trans. Robotics Automat., 13(6), 793 - 804), whose liveness and reversibility are related to empty siphons. For qualitative analysis, after we reduce the net, we are able to generate all minimal siphons and traps, and show that the cell model is live and reversible.

Deadlock analysis of Petri nets using siphons and mathematical programming

This paper exploits the potential of siphons for the analysis of Petri nets, It generalizes the well-known Commoner condition and is based on the notion of potential deadlocks which are siphons that eventually become empty. A linear programming based sufficient condition under which a siphon is not a potential deadlock is obtained. Based on the new sufficient condition, a mathematical programming approach and a mixed-integer programming approach are proposed for checking general Petri nets and structurally bounded Petri nets respectively without explicitly generating siphons. Stronger results are obtained for asymmetric choice nets and augmented marked graphs. In particular, we show that an asymmetric choice net is live iff it is potential-deadlock-free and an augmented marked graph is live and reversible iff it is potential-deadlock-free.

The Construction of Augmented Marked Graphs

An algorithm for constructing augmented marked graphs is presented in this paper to increase the modeling power of marked graphs and to model manufacturing systems in which every product has a single manufacturing process and each operation requires a given set of shared resources.