Decomposing timed Petri net models of open queueing networks

This paper develops a Petri net-based decomposition approach to model and perform steady-state analysis of open queueing networks with multi-class customers. For each customer class the paper assumes deterministic routeing and different service time distribution. The current decomposition may also consider equipment failures, defective units that have to be re-worked and on-line preparations (to switch from one mix of customers to another) as additional customer classes. In contrast to most of the published works on timed Petri nets, their present use is marked by input flows, originating from external sources. A simple method, directly derived from the timed Petri nets theories, is used for calculating the expected utilization of each server and eventually the maximal productivity of the system for the given deterministic routeing. An important application of the model is in validating discrete-event non-terminating simulation models.