Discrete-time batch renewal processes with applications to the performance modelling of ATM switch architectures

The indices of dispersion have been proposed for appropriate characterisation of bursty, correlated ATM traffic. However, the analysis of such systems is complex and is often found to be intractable. In this paper it is suggested that, in describing arrival processes for finite buffer queues with deterministic service, batch renewal processes may accurately approximate processes having unbounded indices of dispersion. Analysis of finite buffer queues with deterministic service and batch renewal arrival processes is described and closed form expressions for queue length and loss probabilities are derived. Numerical examples are included in order to examine the effect of correlation of the arrival process on the performance metrics of a multibuffered ATM switch architecture. It is expected that these results will play the role of effective building blocks for the analysis of general ATM networks carrying bursty, correlated traffic