Parameterized of Control Related States of Gen-Right k-th order system of Petri nets based on proof by model of Gen-Left

摘要

Previously, Chao pioneered the very first closed-form solution of the number of Control Related States for a k-th order system, by which formulas the number of each type of states in a particular and large Petri net can be enumerated in real-time and the possibility of launching a partial deadlock prevention/avoidance policy can be realized according to the indicator of the real-time derived future deadlock ratio. After the closed-form solution research on the Gen-Left system, this paper progresses one step further in constructing the closed-form solution for the Gen-Right system using the concept of “proof by model” of the Gen-Left system, which is a more efficient and theoretical knowledge-based analysis methodology compared to siphon net structure analysis and of which basis is the validated information of its reverse net. Due to the closed-form solution of Gen-Left and Gen-Right, we can complete the decision-making of the non-sharing resource allocation loading balance of the whole variant k-th order system and applying the solution of Gen-Left and Gen-Right a simple deadlock avoidance function algorithm is introduced in this paper.