Chengying Wang

A Method to Compute Strict Minimal Siphons in a Class of Petri Nets Based on Loop Resource Subsets

Strict minimal siphons (SMS) play an important role in the development of deadlock control policies for flexible manufacturing systems (FMS). For a class of Petri nets called Systems of Simple Sequential Processes with Resources (S3PR), the resource circuit-based method is an effective way to compute SMS. In this paper, a more effective one to compute SMS is proposed. First, the concepts of loop resource subsets and their characteristic resource subnets are proposed. Next, sufficient and necessary conditions for loop resource subsets to generate SMS are established. Finally, an algorithm is given to find all the SMS based on loop resource subsets. Since the number of loop resource subsets is much less than that of resource circuits and their combinations, the computational efficiency of the SMS enumeration task is significantly improved by the proposed method. An FMS example is used to illustrate the application of the proposed method, and computational time comparisons are provided on several S3PRs to show its superior efficiency.

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-S3PR. When they are applied to some classes of S3PR 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.

Design of Optimal Monitor-Based Supervisors for a Class of Petri Nets With Uncontrollable Transitions

For a class of Petri nets whose uncontrollable influence subnets are forward synchronization and backward conflict-free nets, this paper proposes an algorithm to transform a given generalized mutual exclusion constraint (GMEC) into an optimal admissible one. Based on the proposed constraint transformation, a method is given to synthesize an optimal monitor-based supervisors. The proposed method utilizes an optimal monitor-based supervisor to enforce a GMEC containing infinite elements, which has not been seen in any prior research. Moreover, it has higher computational efficiency at the expense of application scope than some existing methods. An example is used to illustrate the application of the proposed method.

A New Modified Reachability Tree Approach and Its Applications to Unbounded Petri Nets

This paper proposes a new modified reachability tree (NMRT) approach for a class of unbounded generalized Petri nets called ω-independent nets. The NMRT of an ω-independent net consists of all and only reachable markings from its initial marking. Moreover, the applications of the NMRT to deadlock analysis for ω-independent nets are developed. The proposed method has a larger application scope than all the existing methods. Several examples are provided to show its superiority over them.

Comments on "Siphon-Based Deadlock Prevention Policy for Flexible Manufacturing Systems

A siphon-based algorithm for deadlock prevention of Petri nets called Algorithm H2 is proposed in the above paper. However, the illustrative examples for Algorithm H2 are incorrect because of the redundant weighted control (WC) places which control some marked siphons. This correspondence modifies the illustrative examples by removing the redundant control places and getting a maximally permissive control for the original net. As no WC place is presented in the modified examples, the examples cannot well illustrate Algorithm H2.

Design of Liveness-Enforcing Supervisors for S3PR Based on Complementary Places

In this article, an algorithm is proposed to design liveness-enforcing supervisors for systems of simple sequential processes with resources (S3PR) based on complementary places. Firstly, a mixed integer programming (MIP) based deadlock detection method is used to find unmarked strict minimal siphons from an infinite-capacity net. Next, the finite-capacity net, in which liveness can be enforced, is obtained by adding capacity function to the infinite-capacity net. Finally, complementary-place transformation is used to transform the finite-capacity net into an infinite-capacity net. This article focuses on adding a complementary place to each operation place that is related to unmarked siphons, deals with the deadlock problem from a new view point, and hence advances the deadlock control theory. Compared with the existing methods, the new policy is easier to implement for real industrial systems. More importantly, design of a complementary-place supervisor is very easy. Finally, in some cases, the new policy can obtain a structurally simpler supervisor with more permissive behavior than the existing methods do. A flexible manufacturing systems (FMS) example is used to compare the proposed policy with some other methods.

An algorithm to find the minimal initial markings of resource places ensuring liveness of finite-capacity S3PR

Deadlock prevention can be achieved by configuring proper initial markings to obtain a live Petri net model. For a class of Petri nets called finite-capacity Systems of Simple Sequential Processes with Resources (S3PR), an algorithm is proposed to find the minimal initial markings of resource places ensuring its liveness. First, conditions on initial markings of resource places are computed under which the strict minimal siphons (SMS) can never be emptied. Then, the minimal initial markings of resource places are computed to ensure liveness of the net. By the proposed algorithm, a live net can be obtained without changing the structure of the original model. The main practical implication of our work is that it can lower the facility cost. A simple example is used to illustrate the application of the algorithm.

A transformation algorithm for optimal admissible generalized mutual exclusion constraints on Petri nets with uncontrollable transitions

For a class of Petri nets whose uncontrollable influence subnets are forward synchronization and backward conflict free (FSBCF) nets, this work studies their structure and properties and proposes an algorithm to transform a given generalized mutual exclusion constraint (GMEC) into an optimal admissible one. Compared with the path-based constraint transformation approaches, the proposed method has much higher computational efficiency. An example is used to illustrate the application of the proposed method.

Computation of all minimal siphons in Petri nets

Efficient extraction of minimal siphons is fundamentally important in deadlock control. So far, methods that are based on problem reduction and decomposition are recognized as effective ways. In this paper, an improved method is proposed to identify all minimal siphons. New conditions are proposed under which a problem needs not be decomposed. It significantly simplifies the process of problem decomposition in the existing methods, thereby reducing the memory and improving the computational efficiency. An example is used to illustrate the application of the proposed method.

Extracting all minimal siphons from maximal unmarked siphons in manufacturing-oriented Petri nets

Deadlock control is an important research issue in automated manufacturing systems that have a high degree of resource sharing and concurrency. Since minimal siphons are closely tied with deadlocks in Petri net models, their efficient extraction is fundamentally important. The existing methods can rapidly extract one minimal siphon given a maximal unmarked siphon that is obtained by using a mixed integer programming approach. This paper for the first time presents an extraction algorithm that can efficiently extract all minimal ones. The idea is based on the generation and use of a subnet tree structure given the places in a maximal unmarked siphon. Several Petri net models of automated manufacturing systems are used to illustrate the proposed concepts and methods.