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A New and Pragmatic Approach to the GIX/Geo/c/N Queues Using Roots

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  • J. J. Kim

    (Royal Military College of Canada)

  • M. L. Chaudhry

    (Royal Military College of Canada)

  • V. Goswami

    (Kalinga Institute of Industrial Technology)

  • A. D. Banik

    (Indian Institute of Technology Bhubaneswar)

Abstract

A simple and complete solution to determine the distributions of queue lengths at different observation epochs for the model GIX/Geo/c/N is presented. In the past, various discrete-time queueing models, particularly the multi-server bulk-arrival queues with finite-buffer have been solved using complicated methods that lead to results in a non-explicit form. The purpose of this paper is to present a simple derivation for the model GIX/Geo/c/N that leads to a complete solution in an explicit form. The same method can also be used to solve the GIX/Geo/c/N queues with heavy-tailed inter-batch-arrival time distributions. The roots of the underlying characteristic equation form the basis for all distributions of queue lengths at different time epochs. All queue-length distributions are in the form of sums of geometric terms.

Suggested Citation

  • J. J. Kim & M. L. Chaudhry & V. Goswami & A. D. Banik, 2021. "A New and Pragmatic Approach to the GIX/Geo/c/N Queues Using Roots," Methodology and Computing in Applied Probability, Springer, vol. 23(1), pages 273-289, March.
    • Handle: RePEc:spr:metcap:v:23:y:2021:i:1:d:10.1007_s11009-020-09836-4
    DOI: 10.1007/s11009-020-09836-4
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    References listed on IDEAS

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    1. M. L. Chaudhry & U. C. Gupta & V. Goswami, 2001. "Modeling and Analysis of Discrete-Time Multiserver Queues with Batch Arrivals: GI X /Geom/m," INFORMS Journal on Computing, INFORMS, vol. 13(3), pages 172-180, August.
    2. Arunava Maity & U. C. Gupta, 2015. "A Comparative Numerical Study of the Spectral Theory Approach of Nishimura and the Roots Method Based on the Analysis of BDMMAP/G/1 Queue," International Journal of Stochastic Analysis, Hindawi, vol. 2015, pages 1-9, February.
    3. Mohan L. Chaudhry & James J. Kim, 2016. "Analytically elegant and computationally efficient results in terms of roots for the $$GI^{X}/M/c$$ G I X / M / c queueing system," Queueing Systems: Theory and Applications, Springer, vol. 82(1), pages 237-257, February.
    4. Carl M. Harris & Percy H. Brill & Martin J. Fischer, 2000. "Internet-Type Queues with Power-Tailed Interarrival Times and Computational Methods for Their Analysis," INFORMS Journal on Computing, INFORMS, vol. 12(4), pages 261-271, November.
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    Cited by:

    1. Michiel De Muynck & Herwig Bruneel & Sabine Wittevrongel, 2023. "Analysis of a Queue with General Service Demands and Multiple Servers with Variable Service Capacities," Mathematics, MDPI, vol. 11(4), pages 1-21, February.

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