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

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  • B. Pagurek

    (Carleton University, Ottawa, Ontario)

  • C. M. Woodside

    (Carleton University, Ottawa, Ontario)

Abstract

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.

Suggested Citation

  • B. Pagurek & C. M. Woodside, 1979. "The Sum of Serial Correlations of Waiting and System Times in GI / G /1 Queues," Operations Research, INFORMS, vol. 27(4), pages 755-766, August.
    • Handle: RePEc:inm:oropre:v:27:y:1979:i:4:p:755-766
    DOI: 10.1287/opre.27.4.755
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