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M / G /1/ N Queue with Vacation Time and Exhaustive Service Discipline

Author

Listed:
  • Tony T. Lee

    (AT&T Bell Laboratories, Holmdel, New Jersey)

Abstract

This paper studies an M / G /1 queueing system with a finite waiting room and with server vacation times consisting of periods of time that the server is away from the queue doing additional work. This model has been used in conjunction with a related model to analyze the performance of a processor with a cyclic scheduling algorithm and where, due to finite queueing capacities, losses are a primary concern. Service at the queue is exhaustive, in that a busy period at the queue ends only when the queue is empty. At each termination of a busy period, the server takes an independent vacation. The queue length process is studied using the embedded Markov chain. Using a combination of the supplementary variable and sample biasing techniques, we derive the general queue length distribution of the time continuous process, as well as the blocking probability of the system, due to the finite waiting room in the queue. We also obtain the busy period and waiting time distributions.

Suggested Citation

  • Tony T. Lee, 1984. "M / G /1/ N Queue with Vacation Time and Exhaustive Service Discipline," Operations Research, INFORMS, vol. 32(4), pages 774-784, August.
    • Handle: RePEc:inm:oropre:v:32:y:1984:i:4:p:774-784
    DOI: 10.1287/opre.32.4.774
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    Citations

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    Cited by:

    1. Chris Blondia, 2021. "A queueing model for a wireless sensor node using energy harvesting," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 77(2), pages 335-349, June.
    2. Chris Blondia, 2022. "Evaluation of the Waiting Time in a Finite Capacity Queue with Bursty Input and a Generalized Push-Out Strategy," Mathematics, MDPI, vol. 10(24), pages 1-12, December.
    3. Luis Zabala & Josu Doncel & Armando Ferro, 2023. "Modeling a Linux Packet-Capturing System with a Queueing System with Vacations," Mathematics, MDPI, vol. 11(7), pages 1-27, March.
    4. Mu-Song Chen & Hao-Wei Yen, 2016. "A two-stage approach in solving the state probabilities of the multi-queue //1 model," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(5), pages 1230-1244, April.
    5. Grasman, Scott E. & Olsen, Tava Lennon & Birge, John R., 2005. "Finite buffer polling models with routing," European Journal of Operational Research, Elsevier, vol. 165(3), pages 794-809, September.
    6. Seok Ho Chang & Dae Won Choi, 2006. "Modeling and Performance Analysis of a Finite-Buffer Queue with Batch Arrivals, Batch Services, and Setup Times: The M X /G Y /1/K + B Queue with Setup Times," INFORMS Journal on Computing, INFORMS, vol. 18(2), pages 218-228, May.
    7. V. Deepa & M. Haridass, 2023. "Simulation Analysis of a Base Station Using Finite Buffer M/G/1 Queueing System with Variant Sleeps," Methodology and Computing in Applied Probability, Springer, vol. 25(4), pages 1-18, December.
    8. Doo Il Choi & Dae-Eun Lim, 2020. "Analysis of the State-Dependent Queueing Model and Its Application to Battery Swapping and Charging Stations," Sustainability, MDPI, vol. 12(6), pages 1-15, March.

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