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

After our researches on the effect of a non-sharing resource in a kth order which is the concept of customization manufacturing, in this article we extend the research on the closed-form solution of control-related states to the so-called A-net which has one top non-sharing circle subnet connected to the idle place of left process in a deficient kth order system and is the fundamental model of different productions sharing the same common parts in manufacturing. The formulas just are depended on the parameter k and states’ function of top non-sharing circle subnet for a subclass of nets with k sharing resources. By combining the concept of the partial deadlock avoidance/prevention policy, the moment to launch resource (controller) allocation based on the current state, and the construction of closed-form solution for deficient kth order system, it can realize the concept of dynamic non-sharing processes’ allocation.