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Analytically Simple and Computationally Efficient Results for the GI X / Geo / c Queues

Author

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  • Mohan L. Chaudhry
  • James J. Kim
  • Abhijit D. Banik

Abstract

A simple solution to determine the distributions of queue-lengths at different observation epochs for the model GI X / Geo / c is presented. In the past, various discrete-time queueing models, particularly the multiserver bulk-arrival queues, have been solved using complicated methods that lead to incomplete results. The purpose of this paper is to use the roots method to solve the model GI X / Geo / c that leads to a result that is analytically elegant and computationally efficient. This method works well even for the case when the inter-batch-arrival times follow heavy-tailed distributions. The roots of the underlying characteristic equation form the basis for all distributions of queue-lengths at different time epochs.

Suggested Citation

  • Mohan L. Chaudhry & James J. Kim & Abhijit D. Banik, 2019. "Analytically Simple and Computationally Efficient Results for the GI X / Geo / c Queues," Journal of Probability and Statistics, Hindawi, vol. 2019, pages 1-18, September.
    • Handle: RePEc:hin:jnljps:6480139
    DOI: 10.1155/2019/6480139
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    Cited by:

    1. Divya Velayudhan Nair & Achyutha Krishnamoorthy & Agassi Melikov & Sevinj Aliyeva, 2021. "MMAP/(PH,PH)/1 Queue with Priority Loss through Feedback," Mathematics, MDPI, vol. 9(15), pages 1-26, July.
    2. Freek Verdonck & Herwig Bruneel & Sabine Wittevrongel, 2021. "Delay in a 2-State Discrete-Time Queue with Stochastic State-Period Lengths and State-Dependent Server Availability and Arrivals," Mathematics, MDPI, vol. 9(14), pages 1-17, July.
    3. 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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