Computation of Elementary Siphons in Petri Nets For Deadlock Control

Abstract

When designing liveness-enforcing Petri net supervisors, unlike other techniques, Li et al. added control places and arcs to a plant net model for its elementary siphons only, greatly reducing the structural complexity of the controlled system. Their method, however, suffers from the expensive computation of siphons. We propose a new T-characteristic vector z to compute strict minimal siphons (SMS) for S 3 PR (systems of simple sequential processes with resources) in an algebraic fashion. For a special subclass of S 3 PR, called S 4 PR (simple S 3 PR), we discover that elementary siphons can be constructed from elementary circuits where all places are resources. Thus, the set of elementary siphons can be computed without the knowledge of all SMS. We also propose to construct characteristic T-vectors h by building a graph to find dependent siphons without their computations.

Comments on “enhancement of an efficient liveness-enforcing supervisor for flexible manufacture systems”

“…based on the theory in [15] in the partial controlled model in Fig. 3) cannot be emptied based on the theory in [17].…”

“…Consequently, deadlocks occur due to processes holding resources mutually waiting for others to release their resources. Deadlock prevention [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] adds monitors to problematic siphons to prevent them from becoming insufficiently marked.…”

Modified definition of characteristic P-vector for elementary siphons in a class of Petri nets

“…One would get away with such troubles for a simple basic subclass of S 3 PR (called BS 3 PR in [13]), where the set of elementary and dependent siphons correspond to that synthesised from elementary and compound (i.e. multiple interconnected) resource circuits (containing only resource places), respectively.…”

“…In [16], a polynomial time algorithm was proposed to find elementary siphons in a graphical fashion, where we also showed that an SMS can be synthesised from a strongly resource subnet in an S 3 PR. The author further proved in [13] that each elementary siphon can be synthesised from an elementary resource circuit, whereas a dependent siphon can be synthesised from a compound resource circuit…”

A Siphon-based Deadlock Prevention Policy for a Class of Petri Nets - S3PMR

“…Monitors or control places and related arcs are often used to achieve such purposes Ezpeleta et al [1995], , Li and Zhou [2004], Huang et al [2001], Chao [2006], , and Uzam [2004]. The work of Ezpeleta et al [1995] is usually considered to be the first using structure theory of Petri nets to design monitor-based liveness-enforcing Petri net supervisors for FMS.…”