Queueing performance of a tree type ATM network

A queueing network structured as a directed tree, where only transmissions towards its head are allowed, is considered. Input to each queue is assumed to follow a discrete-time Gaussian process. To compute loss probabilities, each queue is considered independently and its input statistics are derived by approximating output statistics of its immediate sources. Performance statistics of a single Gaussian queue can be accurately approximated as a function of three parameters: the mean and variance of the arrival process, and a parameter related to the asymptotic rate of the long term variance. Of these three parameters only the variance changes when the traffic is filtered through an infinite buffer queue. In this paper we derive an approximation of the variance of the output process. Comparisons with simulations show that the approximation is accurate. Having the parameters of the output process, the single queue analysis is extended to a tree type network of queues. A small example of a network of three queues is simulated and the performance results are found to be close to results obtained analytically.