Computation of control related states of bottom kth-order system (with a non-sharing resource place) of Petri nets

Abstract

Earlier, Chao pioneered the very first closed-form solution of the number of reachable and other states for marked graphs and kth-order systems, which is the simplest class of systems of simple sequential processes with resources. This paper progresses one step further by enumerating reachable, forbidden, live and deadlock states for bottom kth-order systems, which have one non-sharing resource place in the bottom position of the right-side process, with a formula depending on parameter k for a subclass of nets with k sharing resources.

Topological reverse mirroring: a new efficient knowledge-based methodology of reachability analysis for Petri nets

“…Final but not the last, Yu (2017) showed that lower modified deficient reachability ratio (DRO)(the number of reachable states under deficient intial tokens/ the number of reachable states) has a better margin effect of reachability, we can set up a dynamic initial token allocation mechanism for a multi-independent insufficient k-th order systems according to which system has the lowest DRO value. Chao et al have constructed CFS for k-th order/k-net system with a non-sharing resource r * in different locations (Chao & Yu, 2013, 2015a, 2016Chao, Yu, & Chen, 2014;Chao, Yu, & Lin, 2014;Chao, Yu, & Liou, 2014;Chao, Yu, & Wu, 2014; by siphon analysis method, respectively. However, the problem is that we have got as many independent analysis efforts as different net structures there are.…”

Construct the closed-form solution of A-net of Petri nets by case study

“…This is the first step that allows the exponential computation time for particular and very large PNs to be reduced into intra-seconds. We have also progressed one step further to analyze the effect of non-sharing resources of kth order and k-net systems based on the token number of idle place in each process being equal to the number of resource places in the associated process [33][34][35][36][37] and proposed the ''proof by model'' methodology to accelerate the construction of the closed-form formula for PNs. 36,37 One of contributions of the closed-form solution of PN is that the solution can enhance the capability of dynamically modeling large real-time systems.…”