An analysis of a multilayered open queueing network with population constraint and constant service times

In this paper, we consider a queueing network model, 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 is an arbitrary distribution. A major characteristic of this model is that the lower layer flow is halted by the state of higher layer. We present some properties that the interchange of nodes does not make any difference to customer's waiting time in the queueing network under a certian condition. The queueing network can be transformed into a simplified queueing network. A dramatic simplification of the queueing network is shown. It is interesting to see how the simplification development for sliding window flow control can be applied to multi-layered queueing network.