Reachability-related analysis of double-deficient k-th order systems of Petri nets in terms of a closed-form solution

Yu, Tsung‐Hsien

doi:10.1109/iecon.2017.8216521

Cited by 1 publication

(2 citation statements)

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“…One of to be solved problems is what kind of product of which subsystem to be manufactured will be more efficient in utilisation of processes and sharing resources based on current state. 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 better margin effect of reachability, we can set up a dynamic initial token allocation mechanism according to which system has the lowest DRO value.…”

Section: Applications Of Cfs For Modelling Systems By Pnmentioning

confidence: 99%

“…Second, Yu (2016a) proposed that we can dynamically allocate a dummy non-sharing waiting resource (denoted by deadlock thread holder, DTH) based on which location DTH allocated will increase maximum reachability to avoid deadlock, where the location can be calculated real-time by CFS. 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.…”

Section: Introductionmentioning

confidence: 99%

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

2021

International Journal of Control

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Topological reverse mirroring' (TRM) is a new knowledge-based methodology for more efficiently analysing reachability to derive the closed-form formulas (CFF) of the number of Control-Related states for PNs. According to variant k-th order systems, TRM is constructed by proving that both Gen-Right(k, gen) and Gen_Left(k, k−gen) are the topological reverse nets of Gen-Left(k, gen) such that there is a reversible oneto-one mapping (Mirroring) between these two systems. Thus Gen-Right(k, gen) and Gen-Left(k, k−gen) have same CFF which can be immediately derived by replacing the parameter 'gen' by 'k−gen' in validated CFF for Gen-Left(k, gen). The shown applications of TRM include the reachability analysing for systems with non-sharing sub-net; Deficient tokens; multi-non-sharing/multi-tokens resources; and multi-processes. This paper reports the core methodology to accelerate furthering emerging system-control applications for more complicated PNs based on the real-time information derived by their CFF.

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Section: Applications Of Cfs For Modelling Systems By Pnmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Reachability-related analysis of double-deficient k-th order systems of Petri nets in terms of a closed-form solution

Cited by 1 publication

References 24 publications

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

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

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