A new Petri net modeling technique for the performance analysis of discrete event dynamic systems

摘要

An interesting modeling problem is the need to model one or more of the system modules without exposition to the other system modules. This modeling problem arises due to our interest in these modules or incomplete knowledge, or inherent complexity, of the rest of the system modules. Whenever the performance measures (one or more) of the desired modules are available through previous performance studies, data sheets, or previous experimental works, the required performance measures for the whole system can be predicted from our proposed modeling technique. The incomplete knowledge problem of the dynamic behavior of some system modules has been studied by control theory. In the control area, such systems are known as partially observed discrete event dynamic systems, or POS systems. To the best of our knowledge, the performance evaluation of the POS system has not been addressed by the Petri net theory yet. Therefore, in this paper, we propose a new modeling technique for solving this kind of problem based on using the Petri net theory (i.e. Stochastic Reward Nets (SRNs)) in conjunction with the optimal control theory. In this technique, we develop an SRN Equivalent Model (EM) for the modeled system. The SRN EM-model consists of two main nets and their interface nets. One of the main nets represents the part(s) of interest or the known part(s) of the overall POS system that allows us to model its dynamic behavior and evaluate its performance measures. The other main net represents the remaining part(s) of the overall POS system that feeds the part(s) of interest. The well-known maximum principles have been used to develop an algorithm for determining the unknown transition rates of the proposed model. Numerical simulations are given to show that the proposed approach is more effective than the conventional modeling techniques, especially when dealing with systems having a large number of states.