On the number of customers served in the M/G/1 retrial queue: first moments and maximum entropy approach

In this paper we present general results on the number of customers. 1, served during the busy period in an M/G/1 retrial system. Its analysis in terms of Laplace transforms has been previously discussed in the literature. However. this solution presents important limitations in practice; in particular. the moments of I cannot be obtained by direct differentiation. We propose a direct method of computation for the second moment of I and also for the probability of k,k less than or equal to 4. customers being served in a busy period. Then, the maximum entropy principle approach is used to estimate the true distribution of I according to the available information.