Analysis of queueing networks with population constraints and applications to manufacturing

The authors consider closed queuing networks with general service times and subnetworks having population constraints. Each such subnetwork consist of a subset of stations of the original network. The population constraint of a subnetwork prescribes that the total number of customers than can be simultaneously present inside the subnetwork is limited to a fixed value, called the capacity of the subnetwork. A customer wanting to enter a subnetwork while it is full must wait in an external queue. As soon as a customer leaves the subnetwork, the first customer in line is allowed to enter the subnetwork. Such queuing networks with population constraints are of interest for modeling and analysis of manufacturing systems. Two approximate techniques for analyzing such networks, namely the aggregation technique and the method of R. Marie (1979, 1980), are compared