Approximate techniques for general closed queueing networks with subnetworks having population constraints

Abstract

We consider closed queueing networks with general service times and subnetworks having population constraints. Each such subnetwork consists of a subset of stations of the original network. The population constraint of a subnetwork prescribes that the total number of customers that can be simultaneously present inside the subnetwork is limited to a fixed value called the capacity of the subnetwork. A customer who wants to enter the subnetwork while it is full has to wait in an external queue. As soon as a customer leaves the subnetwork, the first-in-line customer is allowed to enter the subnetwork. We apply and compare two approximate techniques for analyzing such networks, namely the aggregation technique and Marie's method. We emphasize the similarities and differences between these two techniques. Finally, we compare their accuracy.