Deadlock Avoidance in Sequential Resource Allocation Systems with Multiple Resource Acquisitions and Flexible Routings

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This paper considers the deadlock avoidance problem for the class of conjunctive/disjunctive (sequential) resource allocation systems (C/D-RAS), which allows for multiple resource acquisitions and flexible routings. First, a new siphon-based characterization for the liveness of Petri nets (PNs) modeling C/D-RAS is developed, and subsequently, this characterization facilitates the development of a polynomial-complexity deadlock avoidance policy (DAP) that is appropriate for the considered RAS class. The resulting policy is characterized as C/D-RUN, since the starting point for the policy development was motivated by the RUN DAP, originally developed for sequential RAS with unit resource allocations and no routing flexibility. The last part of the paper exploits the aforementioned siphon-based characterization of C/D-RAS liveness, in order to develop a sufficiency condition for C/D-RAS liveness that takes the convenient form of a mixed integer programming (MIP) formulation. The availability of this MIP formulation subsequently allows the "automatic" correctness verification of any tentative C/D-RAS DAP for which the controlled system behavior remains in the class of PNs modeling C/D-RAS, and the effective flexibility enhancement of the aforementioned C/D-RUN DAP implementations. Finally, we notice that, in addition to extending and complementing the current theory on deadlock-free sequential resource allocation to the most powerful class of C/D-RAS, the presented results also (i) nontrivially generalize important concepts and techniques of ordinary PN structural analysis to the broader class of nonordinary PNs, while (ii) from a practical standpoint, they can find direct application in the (work-) flow management of modern production, service and/or transportation environments.
Publisher
IEEE-Inst Electrical Electronics Engineers Inc
Issue Date
2001
Language
English
Article Type
Article
Keywords

MANUFACTURING SYSTEMS; PETRI NETS; FEEDBACK-CONTROL; POLICIES

Citation

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, v.46, no.10, pp.1572 - 1583

ISSN
0018-9286
URI
http://hdl.handle.net/10203/79922
Appears in Collection
RIMS Journal Papers
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