A second order analysis of the waiting time in the M/G/1 retrial queue

We are concerned with the M/G/1 queue with repeated attempts where a customer who finds the server busy leaves the service area and repeats his request after a random amount of time. We concentrate on the study of the waiting time process. Its analysis in terms of Laplace transforms has been discussed in the literature. However, this solution has important limitations in practice. For instance, we cannot calculate the first moments of the waiting time, W, by direct differentiation. This paper supplements the existing work and provides a direct method of computation for the second moment of W. Then the maximum entropy approach is used to estimate the true waiting time distribution.