An Algorithm for Computing Serial Correlations of Times in GI/G/1 Queues with Rational Arrival Processes

An algorithm is given for computing the serial correlations of the waiting time, and of the time in system, for successive customers in a GI/G/1 queue. The method depends on representing the inter-arrival time distribution in terms of a process in class K_r (i.e., distributions with a rational Laplace transform). Thus Erlang, hyperexponential and weighted sum-of-Erlang arrivals are treated exactly, and approximate results can be found for other distributions. Computed correlation functions for some Erlang/Erlang systems are presented as examples.