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Waiting-time analysis of D-$${ BMAP}{/}G{/}1$$BMAP/G/1 queueing system

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  • S. K. Samanta

    (National Institute of Technology)

Abstract

This paper presents a simple procedure to evaluate the actual waiting-time distributions for the first- and an arbitrary-customer of an arrival batch in the D-BMAP/G / 1 queueing system. The analysis is based on the remaining service time as the supplementary variable and the roots of the associated characteristic equation of the vector-generating function of the actual waiting-time distribution. Numerical aspects have been tested for a variety of service-time distribution and a sample of numerical outputs is presented.

Suggested Citation

  • S. K. Samanta, 2020. "Waiting-time analysis of D-$${ BMAP}{/}G{/}1$$BMAP/G/1 queueing system," Annals of Operations Research, Springer, vol. 284(1), pages 401-413, January.
    • Handle: RePEc:spr:annopr:v:284:y:2020:i:1:d:10.1007_s10479-015-1974-6
    DOI: 10.1007/s10479-015-1974-6
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    References listed on IDEAS

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    1. Imed Frigui & Attahiru Sule Alfa & Xiaoyi Xu, 1997. "Algorithms for computing waiting time distributions under different queue disciplines for the D‐BMAP/PH/1," Naval Research Logistics (NRL), John Wiley & Sons, vol. 44(6), pages 559-576, September.
    2. M. L. Chaudhry & Gagandeep Singh & U. C. Gupta, 2013. "A Simple and Complete Computational Analysis of MAP/R/1 Queue Using Roots," Methodology and Computing in Applied Probability, Springer, vol. 15(3), pages 563-582, September.
    3. 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.
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