Loss Systems with Mixed Renewal and Poisson Inputs

When two independent streams of customers compete for the same servers, as happens for example when first-routed and overflow traffic streams share a single trunk-group, the state of the system seen by the two different types of arriving customers will in general be different. In a loss system with mixed renewal and Poisson inputs, the blocking experienced by the renewal-type customers can be markedly different from that seen by the Poissonian customers. This paper derives the distribution of the number of busy servers seen by the two streams, and outlines a numerical procedure for computing the distributions. Examples of blocking probabilities for two cases of the renewal stream are given.