Strict Minimal Siphon-Based Colored Petri Net Supervisor Synthesis for Automated Manufacturing Systems With Unreliable Resources

Various deadlock control policies for automated manufacturing systems with reliable and shared resources have been developed, based on Petri nets. In practical applications, a resource may be unreliable. Thus, the deadlock control policies proposed in previous studies are not applicable to such applications. This paper proposes a two-step robust deadlock control strategy for systems with unreliable and shared resources. In the first step, a live (deadlock-free) controlled system that does not consider the failure of resources is derived by using strict minimal siphon control. The second step deals with deadlock control issues caused by the failures of the resources. Considering all resource failures, a common recovery subnet based on colored Petri nets is proposed for all resource failures in the Petri net model. The recovery subnet is added to the derived system at the first step to make the system reliable. The proposed method has been tested using an automated manufacturing system deployed at King Saud University.publishedVersio

Comparison and Evaluation of Deadlock Prevention Methods for Different Size Automated Manufacturing Systems

In automated manufacturing systems (AMSs), deadlocks problems can arise due to limited shared resources. Petri nets are an effective tool to prevent deadlocks in AMSs. In this paper, a simulation based on existing deadlock prevention policies and different Petri net models are considered to explore whether a permissive liveness-enforcing Petri net supervisor can provide better time performance. The work of simulation is implemented as follows. (1) Assign the time to the controlled Petri net models, which leads to timed Petri nets. (2) Build the Petri net model using MATLAB software. (3) Run and simulate the model, and simulation results are analyzed to determine which existing policies are suitable for different systems. Siphons and iterative methods are used for deadlocks prevention. Finally, the computational results show that the selected deadlock policies may not imply high resource utilization and plant productivity, which have been shown theoretically in previous publications. However, for all selected AMSs, the iterative methods always lead to structurally and computationally complex liveness-enforcing net supervisors compared to the siphons methods. Moreover, they can provide better behavioral permissiveness than siphons methods for small systems. For large systems, a strict minimal siphon method leads to better behavioral permissiveness than the other methods

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 � subprocesses that merge together at a synchronization. Although the worst case complexity is O(2�), 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 � subprocesses. The worst case complexity is O(�⋅�), where � 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(2�). Throughout the paper, we use a class of Petri nets called Generalized Augmented Marked Graphs to represent our resource allocation systems

On the decidability of problems in liveness of controlled Discrete Event Systems modeled by Petri Nets

A Discrete Event System (DES) is a discrete-state system, where the state changes at discrete-time instants due to the occurrence of events. Informally, a liveness property stipulates that a 'good thing' happens during the evolution of a system. Some examples of liveness properties include starvation freedom -- where the 'good thing' is the process making progress; termination -- in which the good thing is for an evolution to not run forever; and guaranteed service -- such as in resource allocation systems, when every request for resource is satisfied eventually. In this thesis, we consider supervisory policies for DESs that, when they exist, enforce a liveness property by appropriately disabling a subset of preventable events at certain states in the evolution of DES. One of the main contributions of this thesis is the development of a system-theoretic framework for the analysis of Liveness Enforcing Supervisory Policies (LESPs) for DESs. We model uncertainties in the forward- and feedback-path, and present necessary and sufficient conditions for the existence of Liveness Enforcing Supervisory Policies (LESPs) for a general model of DESs in this framework. The existence of an LESP reduces to the membership of the initial state to an appropriately defined set. The membership problem is undecidable. For characterizing decidable instances of this membership problem, we consider a modeling paradigm of DESs known as Petri Nets, which have applications in modeling concurrent systems, software design, manufacturing systems, etc. Petri Net (PN) models are inherently monotonic in the sense that if a transition (which loosely represents an event of the DES) can fire from a marking (a non-negative integer-valued vector that represents the state of the DES being modeled), then it can also fire from any larger marking. The monotonicity creates a possibility of representing an infinite-state system using what can be called a "finite basis" that can lead to decidability. However, we prove that several problems of our interest are still undecidable for arbitrary PN models. That is, informally, a general PN model is still too powerful for the analysis that we are interested in. Much of the thesis is devoted to the characterization of decidable instances of the existence of LESPs for arbitrary PN models within the system-theoretic framework introduced in the thesis. The philosophical implication of the results in this thesis is the existence of what can be called a "finite basis" of an infinite state system under supervision, on which the membership tests can be performed in finite time; hence resulting in the decidability of problems and finite-time termination of algorithms. The thesis discusses various scenarios where such a finite basis exists and how to find them

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 subprocesses that merge together at a synchronization. Although the worst case complexity is O(2), 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 subprocesses. The worst case complexity is O(⋅), where 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(2). Throughout the paper, we use a class of Petri nets called Generalized Augmented Marked Graphs to represent our resource allocation systems

Scheduling and discrete event control of flexible manufacturing systems based on Petri nets

A flexible manufacturing system (FMS) is a computerized production system that can simultaneously manufacture multiple types of products using various resources such as robots and multi-purpose machines. The central problems associated with design of flexible manufacturing systems are related to process planning, scheduling, coordination control, and monitoring. Many methods exist for scheduling and control of flexible manufacturing systems, although very few methods have addressed the complexity of whole FMS operations. This thesis presents a Petri net based method for deadlock-free scheduling and discrete event control of flexible manufacturing systems. A significant advantage of Petri net based methods is their powerful modeling capability. Petri nets can explicitly and concisely model the concurrent and asynchronous activities, multi-layer resource sharing, routing flexibility, limited buffers and precedence constraints in FMSs. Petri nets can also provide an explicit way for considering deadlock situations in FMSs, and thus facilitate significantly the design of a deadlock-free scheduling and control system. The contributions of this work are multifold. First, it develops a methodology for discrete event controller synthesis for flexible manufacturing systems in a timed Petri net framework. The resulting Petri nets have the desired qualitative properties of liveness, boundedness (safeness), and reversibility, which imply freedom from deadlock, no capacity overflow, and cyclic behavior, respectively. This precludes the costly mathematical analysis for these properties and reduces on-line computation overhead to avoid deadlocks. The performance and sensitivity of resulting Petri nets, thus corresponding control systems, are evaluated. Second, it introduces a hybrid heuristic search algorithm based on Petri nets for deadlock-free scheduling of flexible manufacturing systems. The issues such as deadlock, routing flexibility, multiple lot size, limited buffer size and material handling (loading/unloading) are explored. Third, it proposes a way to employ fuzzy dispatching rules in a Petri net framework for multi-criterion scheduling. Finally, it shows the effectiveness of the developed methods through several manufacturing system examples compared with benchmark dispatching rules, integer programming and Lagrangian relaxation approaches

Approximation methods for stochastic petri nets

Stochastic Marked Graphs are a concurrent decision free formalism provided with a powerful synchronization mechanism generalizing conventional Fork Join Queueing Networks. In some particular cases the analysis of the throughput can be done analytically. Otherwise the analysis suffers from the classical state explosion problem. Embedded in the divide and conquer paradigm, approximation techniques are introduced for the analysis of stochastic marked graphs and Macroplace/Macrotransition-nets (MPMT-nets), a new subclass introduced herein. MPMT-nets are a subclass of Petri nets that allow limited choice, concurrency and sharing of resources. The modeling power of MPMT is much larger than that of marked graphs, e.g., MPMT-nets can model manufacturing flow lines with unreliable machines and dataflow graphs where choice and synchronization occur. The basic idea leads to the notion of a cut to split the original net system into two subnets. The cuts lead to two aggregated net systems where one of the subnets is reduced to a single transition. A further reduction leads to a basic skeleton. The generalization of the idea leads to multiple cuts, where single cuts can be applied recursively leading to a hierarchical decomposition. Based on the decomposition, a response time approximation technique for the performance analysis is introduced. Also, delay equivalence, which has previously been introduced in the context of marked graphs by Woodside et al., Marie's method and flow equivalent aggregation are applied to the aggregated net systems. The experimental results show that response time approximation converges quickly and shows reasonable accuracy in most cases. The convergence of Marie's method and flow equivalent aggregation are applied to the aggregated net systems. The experimental results show that response time approximation converges quickly and shows reasonable accuracy in most cases. The convergence of Marie's is slower, but the accuracy is generally better. Delay equivalence often fails to converge, while flow equivalent aggregation can lead to potentially bad results if a strong dependence of the mean completion time on the interarrival process exists

Discrete Event Systems: Models and Applications; Proceedings of an IIASA Conference, Sopron, Hungary, August 3-7, 1987

Work in discrete event systems has just begun. There is a great deal of activity now, and much enthusiasm. There is considerable diversity reflecting differences in the intellectual formation of workers in the field and in the applications that guide their effort. This diversity is manifested in a proliferation of DEM formalisms. Some of the formalisms are essentially different. Some of the "new" formalisms are reinventions of existing formalisms presented in new terms. These "duplications" reveal both the new domains of intended application as well as the difficulty in keeping up with work that is published in journals on computer science, communications, signal processing, automatic control, and mathematical systems theory - to name the main disciplines with active research programs in discrete event systems. The first eight papers deal with models at the logical level, the next four are at the temporal level and the last six are at the stochastic level. Of these eighteen papers, three focus on manufacturing, four on communication networks, one on digital signal processing, the remaining ten papers address methodological issues ranging from simulation to computational complexity of some synthesis problems. The authors have made good efforts to make their contributions self-contained and to provide a representative bibliography. The volume should therefore be both accessible and useful to those who are just getting interested in discrete event systems