A simple derivation of queueing delay in a tree network of discrete-time queues with deterministic service time

We consider a network of discrete-time queues in which the service time is deterministic and the same at each queue. Such a network of queues arises in a data communication network model where data is formatted into fixed-length packets. An important performance index in such networks is queueing delay. The model generally used for the analysis of delay in a large network is based on Kleinrock´s(1964) independence assumption, which assumes that the queues at each link behave as independent queues regardless of the interaction of traffic between the different links. This model is reasonably good for systems involving exponential arrivals, a densely connected network and uniform loading among source-destination pairs. Otherwise the model becomes very inaccurate in predicting delay