Performance Comparison of Queues with Batch Renewal Arrivals in Continuous and Discrete Times

It has been proven that the batch renewal process is the least biased choice of traffic process given the infinite sets of measures of the traffic correlation, (i.e. indices of dispersion, covariances or correlation functions) in the discrete time domain. The same conclusion is expected to hold in the continuous time domain. That motivates the study and comparison of similar queues, fed by batch renewal traffic, in both domains. In this paper, performance distributions are obtained for the GI^G/M^[X]/1/N queue in continuous time and compared with the corresponding results for the GI^G/Geo^[X]/1/N queue in discrete time. The expressions for queue length distribution, blocking probability and waiting time distributions are derived. They can be used to assess the adverse effect on buffer performance that is induced by traffic correlation. The queueing model with batch Poisson arrival, as special case, is also presented. The queue length distribution is interpreted by maximum entropy.