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On an exponential server with general cyclic arrivals

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A E n¦ M ¦ 1 queue is defined as a single server queue with exponential service time and general cyclic arrival distributions of cycle length n. The waiting time distribution for such a queue is proved to be a sum of n exponential terms; this is a generalization of G ¦ M ¦ 1 queue results. Based on this a method for obtaining the steady-state waiting time distributions for E n¦ M ¦ 1 queues is introduced. An example is presented to show an application of E n¦ M ¦ 1 queues in deterministic routing.

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The work was supported in part by the U.S. Air Force Office of Scientific Research under grant AFOSR 78-3654 A to the Department of Computer Science

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Agrawala, A.K., Tripathi, S.K. On an exponential server with general cyclic arrivals. Acta Informatica 18, 319–334 (1982). https://doi.org/10.1007/BF00263197

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