Algebraic synthesis of efficient deadlock avoidance policies for sequential resource allocation systems

Abstract

Deadlock avoidance in sequential resource allocation systems is a well-de ned problem in Discrete Event System literature, as it underlies the operation of many contemporary technological systems. In the past, the problem has been studied by means of a number of formal frameworks, including the nite state automata (FSA) and Petri nets (PN). In this paper, it is shown that a signi cant class of deadlock avoidance policies (DAP), known as algebraic PK-DAP's, originally developed in the FSA paradigm, can be analyzed using recent results from PN structural analysis. Furthermore, the approach to DAP analysis and design taken in this paper has led to the e ective generalization of the currently available algebraic PK-DAP's, and to their enrichment with new and more exible policy implementations.

Algebraic Deadlock Avoidance Policies for Sequential Resource Allocation Systems

“…Furthermore, a practical and frequently used implementation of the aforementioned plan substitutes the exact characterization of the reachability space R(N , M 0 ) by its superset that is provided by the state equation. 12 The resulting formulation provides a sufficient condition for the non-existence of resource-induced deadly marked siphons S in the entire space R(N , M 0 ) of a given process-resource net N , which in the light of Theorem 2, constitutes also a sufficient condition for the liveness and reversibility of process-resource nets with acyclic, quasi-live, and strongly reversible process subnets. The following corollary summarizes the above discussion: Concluding this discussion, we notice that for the case of P T -ordinary process-resource nets with acyclic, quasi-live, and strongly reversible subnets, a similar but simpler liveness and reversibility sufficiency test can be obtained by focusing on the presence of empty siphons in the original net reachability space, R(N , M 0 ); we refer the reader to [5,12] for a detailed discussion of this formulation.…”

“…The resulting controlled net, N c , has been shown to be live and reversible in [12]. Here we re-establish the liveness of net N c , and the correctness of the DAP expressed by Equation 70, by applying the siphon control criterion of Corollary 4.…”

“…Two algebraic PK-DAPs for the process-resource net of Figure 12, originally developed in [12], are respectively expressed by the constraint sets: …”

Theory of Regions for Control Synthesis without Computing Reachability Graph

“…Besides, in [18], a new method is developed for deadlocks prevention to decrease the number of reachability conditions of TR in order to facilitate the supervisor calculation. Their experimental results seems to be the most effective approach in deadlock prevention policy compared with existing works of [15,19,20]. Unfortunately, the computation of RG and its analysis to determine the basic cycles and the legal/forbidden markings for this method are still heavy.…”

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

“…Their analysis methods used for deadlock prevention in FMS include structural analysis and reachability graphs. Deadlock prevention and avoidance schemes have been developed for controlling FMS [3][4][5][6][7][8] by using the former. In particular, deadlock prevention problems are solved using the concept of siphons [3][4][5][6] .…”