On the serial correlation for number in system in the stationary GI/M/1 bulk arrival and GI/Em/1 queues
David A. Stanford, Bernard Pagurek · Journal of Applied Probability · 1992
The generating functions for the serial covariances for number in system in the stationary GI/M/1 bulk arrival queue with fixed bulk sizes, and the GI/Em/1 queue, are derived. Expressions for the infinite sum of the serial correlation coefficients are also presented, as well as the first serial correlation coefficient in the case of the bulk arrival queue. Several numerical examples are considered.