An Algorithm for Computing Serial Correlations of Times in GI/G/1 Queues with Rational Arrival Processes
- 1 January 1979
- journal article
- Published by Institute for Operations Research and the Management Sciences (INFORMS) in Management Science
- Vol. 25 (1) , 54-63
- https://doi.org/10.1287/mnsc.25.1.54
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 Kr (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
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