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Queues with State-Dependent Stochastic Service Rates

Author

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  • Carl M. Harris

    (Western Electric Company, Inc., Princeton, New Jersey)

Abstract

The standard M / G /1 queuing system is generalized so that the service time parameter becomes a stochastic process, { M n , n = 1, 2, …}, indexed on the length of the queue at the moment service is begun. The service time, T i , of a customer entering into service when a total of i customers are in the system is to be conditioned upon the random variable M i . Some general theory is developed for the model and three specific cases are explored. For each of the examples, both the conditional service-time distributions, { B Tn ∣ M n ( t ∣μ n ), n = 1, 2, …}, and the prior distributions of { M n }, { F M n (μ n ), n = 1, 2, …}, are specified, and results are obtained that characterize queue behavior using the imbedded Markov chain approach. The first case is an illustration of a random, non-state-dependent parameter, while the other two describe different ways a service parameter may be state-dependent. In addition, an industrial example based on the third case is cited.

Suggested Citation

  • Carl M. Harris, 1967. "Queues with State-Dependent Stochastic Service Rates," Operations Research, INFORMS, vol. 15(1), pages 117-130, February.
    • Handle: RePEc:inm:oropre:v:15:y:1967:i:1:p:117-130
    DOI: 10.1287/opre.15.1.117
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    Cited by:

    1. Erhan Cinlar, 1973. "Markov Renewal Theory: A Survey," Discussion Papers 53, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    2. Hossein Abouee-Mehrizi & Opher Baron, 2016. "State-dependent M/G/1 queueing systems," Queueing Systems: Theory and Applications, Springer, vol. 82(1), pages 121-148, February.
    3. Mohammad Delasay & Armann Ingolfsson & Bora Kolfal, 2016. "Modeling Load and Overwork Effects in Queueing Systems with Adaptive Service Rates," Operations Research, INFORMS, vol. 64(4), pages 867-885, August.
    4. Wang, Pu Patrick, 1996. "Queueing models with delayed state-dependent service times," European Journal of Operational Research, Elsevier, vol. 88(3), pages 614-621, February.
    5. Delasay, Mohammad & Ingolfsson, Armann & Kolfal, Bora & Schultz, Kenneth, 2019. "Load effect on service times," European Journal of Operational Research, Elsevier, vol. 279(3), pages 673-686.
    6. Yona Elbaum & Alexander Novoselsky & Evgeny Kagan, 2022. "A Queueing Model for Traffic Flow Control in the Road Intersection," Mathematics, MDPI, vol. 10(21), pages 1-15, October.

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