Mean delay analysis of a statistical multiplexer with batch arrival processes—a generalization to Viterbiʹs formula

The delay analysis of a statistical multiplexer with heterogeneous input sources is presented in this paper. The traffic generated by an individual source is described in terms of a discrete-time Batch Markovian arrival process with geometrically distributed idle periods. An exact closed form expression for the mean packet delay in the system is obtained by exploiting the stochastic structure of the packet arrival processes. The derived expression is a generalization of the formula developed originally by Viterbi.