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On Controllability of Dependent Siphons for Deadlock Prevention in Generalized Petri Nets

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2 Author(s)
Li, Z. ; Technion - Israel Inst. of Technol., Haifa ; Mi Zhao

A fair amount of research has shown the importance of siphons in the analysis and control of deadlocks in a variety of resource allocation systems by using a Petri net formalism. In this paper, siphons in a generalized Petri net are classified into elementary and dependent ones, as done for ordinary nets in our previous work. Conditions are derived under which a dependent siphon is controlled by properly supervising its elementary siphons, which indicates that the controllability of dependent siphons in an ordinary Petri net is a special case of that in a generalized one. The application of the controllability of dependent siphons is shown by considering the deadlock prevention problem for a class of resource allocation systems, namely, G-system that allows multiple resource acquisitions and flexible routings in a flexible manufacturing system with machining, assembly, and disassembly operations. We develop a monitor-based deadlock prevention policy that first adds monitors for elementary siphons only to a G-system plant model such that the resultant net system satisfies the maximal controlled-siphon property (maximal cs-property). Then, by linear programming, initial tokens in the additional monitors are decided such that liveness is enforced to the supervised system. Also, a simplified live marking relationship for a G-system between the initial tokens of the source places and those of the resource places is derived. Finally, the proposed deadlock prevention methods are illustrated by using an example.

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Systems, Man and Cybernetics, Part A: Systems and Humans, IEEE Transactions on  (Volume:38 ,  Issue: 2 )