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Evaluation of the Waiting Time in a Finite Capacity Queue with Bursty Input and a Generalized Push-Out Strategy

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  • Chris Blondia

    (IDLab-Department of Computer Science, University of Antwerp-imec, 2000 Antwerp, Belgium)

Abstract

In this paper, we study a finite capacity queue where the arrival process is a special case of the discrete time Markov modulated Poisson process, the service times are generally distributed, and the server takes repeated vacations when the system is empty. The buffer acceptance strategy is based on a generalized push-out scheme: when the buffer is full, an arriving customer pushes out the N t h customer in the queue, where N takes values between 2 and the capacity of the system, and the arriving customer joins the end of the queue. Such a strategy is important when, as well as short waiting times for served customers, the time a pushed-out customer occupies a buffer space is also an important performance measure. The Laplace transform of the waiting time of a served customer is determined. Numerical examples show the influence of the bustiness of the input process and also the trade-off between the average waiting time of served customers and the occupancy of the buffer space of pushed-out customers.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:24:p:4771-:d:1004452
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    References listed on IDEAS

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    1. 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.
    2. Rostislav V. Razumchik, 2014. "Analysis Of Finite Capacity Queue With Negative Customers And Bunker For Ousted Customers Using Chebyshev And Gegenbauer Polynomials," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 31(04), pages 1-21.
    3. 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.
    4. Shoji Kasahara & Hideaki Takagi & Yutaka Takahashi & Toshiharu Hasegawa, 1996. "M / G / 1 / K system with push-out scheme under vacation policy," International Journal of Stochastic Analysis, Hindawi, vol. 9, pages 1-15, January.
    5. Yutae Lee & Bong Dae Choi & Bara Kim & Dan Keun Sung, 2007. "Delay Analysis of an M / G / 1 / K Priority Queueing System with Push-out Scheme," Mathematical Problems in Engineering, Hindawi, vol. 2007, pages 1-12, December.
    6. Kilhwan Kim & Xindong Peng, 2022. "Finite-Buffer M/G/1 Queues with Time and Space Priorities," Mathematical Problems in Engineering, Hindawi, vol. 2022, pages 1-30, May.
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