Sequence of Control in (SPMR)-P-3
Huang et al. propose a more permissive siphon-based algorithm for deadlock prevention of a subclass of Petri nets, (SPMR)-P-3. It iteratively (based on a mixed integer programming (MIP) technique) adds two kinds of control places called ordinary control (OC) places and weighted control (WC) places to the original model to prevent siphons from becoming unmarked. Numerical experiments indicate that the proposed policy appears to be more permissive than closely related approaches in the literature. The presence of WC renders the net a generalized Petri net, which is harder to analyze, and it is unclear how the above traditional MIP must be modified. We show that all monitors with WC places in all cases presented are redundant and can be removed while maintaining the maximal number of good states. We also (1) show that OC places and WC places are associated with resource and mixture siphons, respectively; (2) identify the condition and examples for a WC places to be redundant; (3) explore different types of problematic siphons; and (4) identify the correct sequence of adding monitors to avoid redundant monitors.
siphons deadlock prevention petri nets