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The Geo / G a , Y /1/ N Queue Revisited

Author

Listed:
  • Mohan Chaudhry

    (Department of Mathematics and Computer Science, Royal Military College of Canada, P.O. Box 17000, Kingston, ON K7K 7B4, Canada)

  • Veena Goswami

    (School of Computer Applications, Kalinga Institute of Industrial Technology, Bhubaneswar 751 024, India)

Abstract

We not only present an alternative and simpler approach to find steady-state distributions of the number of jobs for the finite-space queueing model G e o / G a , Y / 1 / N using roots of the inherent characteristic equation, but also correct errors in some published papers. The server has a random service capacity Y , and it processes the jobs only when the number of jobs in the system is at least ‘ a ’, a threshold value. The main advantage of this alternative process is that it gives a unified approach in dealing with both finite- and infinite-buffer systems. The queue-length distribution is obtained both at departure and random epochs. We derive the relation between the discrete-time Geo/ G a , Y /1/N queue and its continuous-time analogue. Finally, we deal with performance measures and numerical results.

Suggested Citation

  • Mohan Chaudhry & Veena Goswami, 2022. "The Geo / G a , Y /1/ N Queue Revisited," Mathematics, MDPI, vol. 10(17), pages 1-17, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:17:p:3142-:d:904026
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    References listed on IDEAS

    as
    1. Mohan L. Chaudhry & Carl M. Harris & William G. Marchal, 1990. "Robustness of Rootfinding in Single-Server Queueing Models," INFORMS Journal on Computing, INFORMS, vol. 2(3), pages 273-286, August.
    2. D. Denteneer & A.J.E.M. Janssen & J.S.H. van Leeuwaarden, 2005. "Moment inequalities for the discrete-time bulk service queue," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 61(1), pages 85-108, March.
    3. Yi, Xeung W. & Kim, Nam K. & Yoon, Bong K. & Chae, Kyung C., 2007. "Analysis of the queue-length distribution for the discrete-time batch-service Geo/Ga,Y/1/K queue," European Journal of Operational Research, Elsevier, vol. 181(2), pages 787-792, September.
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