A maximum entropy approach for the busy period of the M/G/1 retrial queue

This paper concerns the busy period of a single server queueing model with exponentially distributed repeated attempts. Several authors have analyzed the structure of the busy period in terms of the Laplace transform, but the information about the density function is limited to first and second order moments. We use the maximum entropy principle to find the least biased density function subject to several mean value constraints. We perform results for three different service time distributions: 3-stage Erlang, hyperexponential and exponential. Also a numerical comparative analysis between the exact Laplace transform and the corresponding maximum entropy density is presented.