In: International Journal of Intelligent Control and Systems, Vol. 3, No. 3, pages 343-358. September 1999.
Abstract: This paper presents an algorithm of polynomial complexity to derive the throughput of a discrete event system via stochastic Petri net (SPN) models. The concept of flow nets, a subclass of SPN, is introduced to model a class of discrete event systems. The mathematical model for the throughput of flow nets is given. For a structurally non-competitive and acyclic flow net, the solution algorithm proceeds in four steps. First, divide the places and transitions into groups according to some rules. Next, list the flow equilibrium equation for each place, which shows the relation among the average flows of its input and output transitions. Then, deduce the relation of the average flow of any non-source transition to that of all source transitions. Finally, determine the throughput of the model. By so doing, we significantly reduce the size of the linear programming problems. For a structurally competitive and cyclic flow net, a procedure is proposed to convert it to a structurally non-competitive and acyclic one in the sense of equivalent throughput. Besides, the paper also shows how to transform an SPN with shared resource to a flow net. An assembly system is used to illustrate the application of the technique for the analysis of throughput.
Keywords: Stochastic Petri nets, throughputs, discrete event systems.