Correlation of interdeparture times in M/G/1 and M/G/1/K queues

Correlation of consecutive interdeparture times characterizes the output process in a queueing system. We present a recursive procedure for calculating the joint distribution of an arbitrary number of consecutive interdeparture times in M/G/1 and M/G/1/K queues. We then obtain explicitly the covariances of nonadjacent interdeparture times, and display the correlation coefficients that reveal the long-range dependence.