The Sum of Serial Correlations of Waiting and System Times in GI/G/1 Queues

We develop an expression for the sum of the serial correlation coefficients for time in system or waiting time for successive customers in a GI/G/1 queue. In our approach the interarrival time distribution is represented in terms of a class K_r distribution with a rational Laplace-Stieltjes transform. Thus Erlang, hyperexponential, and weighted sum-of-Erlang arrivals are treated exactly and approximate results can be found for other distributions. We present computed results for some Erlang/Erlang systems.