An Analysis of a Multilayered Open Queueing Network with Population Constraint and 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 characteristics of this model is that the lower layer flow is halted by the state of higher layer. We present some properties that the inter-change of nodes does not make any difference to customer's waiting time in the queueing network under a certain 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 developed for sliding window flow control, can be applied to multi-layered queueing network