An Algorithm for Computing Serial Correlations of Times inGI/G/1 Queues with Rational Arrival Processes
Management Science · 1979 · Volume 25 · Issue 1
Abstract
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.
Keywords
autocorrelation function, general queue, waiting times, computation
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