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Exact Time-Dependent Queue-Length Solution to a Discrete-Time Geo / D /1 Queue

Author

Listed:
  • Jung Woo Baek

    (Department of Industrial Engineering, Chosun University, Gwangju 61452, Korea)

  • Yun Han Bae

    (Department of Mathematics Education, Sangmyung University, Seoul 03016, Korea)

Abstract

Time-dependent solutions to queuing models are beneficial for evaluating the performance of real-world systems such as communication, transportation, and service systems. However, restricted results have been reported due to mathematical complexity. In this study, we present a time-dependent queue-length formula for a discrete-time G e o / D / 1 queue starting with a positive number of initial customers. We derive the time-dependent formula in closed form.

Suggested Citation

  • Jung Woo Baek & Yun Han Bae, 2019. "Exact Time-Dependent Queue-Length Solution to a Discrete-Time Geo / D /1 Queue," Mathematics, MDPI, vol. 7(8), pages 1-8, August.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:8:p:717-:d:255594
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    References listed on IDEAS

    as
    1. Leonenko, G.M., 2009. "A new formula for the transient solution of the Erlang queueing model," Statistics & Probability Letters, Elsevier, vol. 79(3), pages 400-406, February.
    2. Sharma, O. P. & Gupta, U. C., 1982. "Transient Behaviour of an M/M/1/N queue," Stochastic Processes and their Applications, Elsevier, vol. 13(3), pages 327-331, September.
    Full references (including those not matched with items on IDEAS)

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