The Covariance Structure of the Departure Process from M/G/1 Queues with Finite Waiting Lines

SUMMARY This paper contains a study of the departure process from M/G/1 queues with a waiting space of size N> 0. The property of the departure process which receives the most attention is the covariance of pairs of departure intervals, although a more thorough investigation of the probabilistic structure is undertaken for the case N= 1. A main result of the paper is that in the M/G/1 queue with N = 1, departure intervals separated by one or more intervals are independent. When G is the deterministic server, the departure stream is a renewal process. The paper concludes with an expression for the covariance of any pair of intervals in the departure process for any value of N, and numerical values for correlations in the case of a deterministic server with N= 2.