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Probability analysis of the repairable queueing systemM/G(E k /H)/1

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Abstract

The repairable queueing system (RQS) in which the server has an exponential lifetime distribution has been studied in several articles [1–4]. Here, we deal with the new RQSM/G(E k /H)/1 in which the lifetime distribution of the server is Erlangian. By forming a vector Markov process, i.e. by using the method of supplementary variables, we obtained some system characters, the reliability indices of the server, and the time distribution of a customer spent on the server. For this RQS, the generalized service time distribution of each customer will depend on the remainder life of the server. Based on this, a new kind of queues, for which the service time distributions are chosen by the customers in some stochastic manner, appears in queueing theory.

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References

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Authors and Affiliations

  1. Department of Mathematics, Shanghai University of Science and Technology, 201800, Shanghai, P.R. China

    Ding-Hua Shi

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  1. Ding-Hua Shi
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Project supported by the National Natural Science Foundation of China.

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Shi, DH. Probability analysis of the repairable queueing systemM/G(E k /H)/1. Ann Oper Res 24, 185–203 (1990). https://doi.org/10.1007/BF02216823

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  • DOI: https://doi.org/10.1007/BF02216823

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