Combined Siphon and Marking Generation for Deadlock Prevention in Petri Nets

Abstract

In Petri-net (PN) modeling of flexible manufacturing systems, deadlock prevention is often addressed by means of siphon-control methods. Constraints that avoid the emptying of siphons can be easily implemented using additional places suitably connected to the PN transitions. Efficient siphon-based techniques achieve highly permissive solutions using as few control places as possible. One such technique employs a set-covering approach to optimally match emptiable siphons to critical markings. In this paper, a modified version of the method is proposed that achieves the same results in terms of permissivity and size of the control subnet but avoids full siphon enumeration. This greatly reduces the overall computational time and memory requirements and allows the applicability of the method to large-size models

A Computationally Improved Optimal Solution for Deadlocked Problems of Flexible Manufacturing Systems Using Theory of Regions

“…Two FMS examples are used to evaluate our deadlock prevention policy [12][13][14][15][16][17][18][19][20][21][22][23] . Example I: An FMS is shown in Figure 10 12 .…”

“…However, as indicated by Li et al 18 , it requires the repeated calculation of reachability graphs. Piroddi et al propose a combined selective siphons and critical markings in a reachability graph algorithm to obtain optimal controllers via iterations 19 . They successfully identify the critical uncontrolled siphons and control them to make a deadlock-prone PN live.…”

Development of Critical-Siphon Theory to Fastest Deadlock Controller for Flexible Manufacturing Systems and Computer-Integrated Manufacturing

“…Similarly, monitors are added for S22. The final controlled monitor is shown in [10], where a theorem is developed to show how a monitor becomes redundant after adding a monitor for the refinement region p8, p9 for S22.…”

“…Recently, maximally permissive control policies [7][8][9][10][11] with little redundancy have emerged. They however suffer from either complete state enumeration-based on region theory [7][8][9][10][11] or the concept of selective-siphons [10,11]. Both are NP-hard and take exponential amount of time.…”

An elementary siphon-based deadlock control algorithm with maximally reachable number to cope with deadlock problems in ordinary Petri nets

“…[7][8][9][10][11][12][13] In the past two decades, the research of resolving deadlocks has become the hot issues and many scholars and researchers have achieved a lot of remarkable results in theory and practical applications. 6,[14][15][16][17][18][19][20][21][22][23][24][25][26] Because of their own characteristics to easily and concisely describe the concurrent execution of processes and the reasonable distribution of shared resources in an FMS, 12,27 Petri nets have been widely used to model, analyze, and simulate the static and dynamic behaviors of an FMS, especially in deadlock problems. Using Petri nets, three policies, called deadlock detection and recovery (DDR), 1,28 deadlock avoidance (DA), 1,4 and deadlock prevention (DP) 6,10,[23][24][25][28][29][30][31][32] , respectively, are developed to cope with deadlock problems in FMSs.…”