A deadlock prevention policy for a class of Petri nets S<sup>3</sup>PMR based on elementary siphons

Abstract

To solve the problem of deadlocks in Flexible Manufacturing Systems (FMS), this paper presents an effective deadlock-free policy for a special class of Petri nets, S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> PMR. The deadlock avoidance policy (DAP) of Conjunctive/Disjunctive Resources Upstream Neighborhood (C/D RUN) is combinated with the deadlock prevention policy (DPP), and the underlying (sequential) resources are allocated reasonably to guarantee the absence of deadlock states and processes. Siphons in an S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> PMR net model are distinguished by elementary and dependent ones, a set of generalized mutual exclusion constraints (GMEC) expressed by the marking vector can be formalized from the set of elementary siphons. Then monitors based on the GMEC are added only to the elementary siphons of the plant model such that all siphons in the S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> PMR net are all invariant-controlled and no emptiable siphon is generated due to the addition of the monitors. A practical application is utilized to illustrate the validity of the proposed novel method to design deadlock-free supervisores for S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> PMR net model.