Some notes on the reduction of network dimensionality in nested open queueing networks

In this paper, we study an open and nested tandem queueing network, where the population constraint within each subnetwork is controlled by a semaphore queue. The total number of customers that may be present in the subnetwork can not exceed a given value. Each node has a constant service time and the arrival process to the queueing network follows an arbitrary distribution. A major characteristic of this queueing network is that the low layer flow is halted by the state of the high layer. We develop a simple and equivalent queueing network that has the same performance characteristics as the original queueing network. Using this model, the waiting time on the queueing network can be easily derived. It is interesting to see how the simplification process can be applied to multi-layered queueing network.