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Algorithms for computing waiting time distributions under different queue disciplines for the D‐BMAP/PH/1

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  • Imed Frigui
  • Attahiru Sule Alfa
  • Xiaoyi Xu

Abstract

A queueing system characterized by the discrete batch Markovian arrival process (D‐BMAP) and a probability of phase type distribution for the service time is one that arises frequently in the area of telecommunications. Under this arrival process and service time distribution we derive the waiting time distribution for three queue disciplines: first in first out (FIFO), last in first out (LIFO), and service in random order (SIRO). We also outline efficient algorithmic procedures for computing the waiting time distributions under each discipline. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44: 559–576, 1997

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  • 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.
    • Handle: RePEc:wly:navres:v:44:y:1997:i:6:p:559-576
    DOI: 10.1002/(SICI)1520-6750(199709)44:63.0.CO;2-2
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    References listed on IDEAS

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    1. Mary A. Johnson & Jennifer A. Luhman, 1994. "Behaviour of queueing approximations based on sample moments," Applied Stochastic Models and Data Analysis, John Wiley & Sons, vol. 10(4), pages 233-246.
    2. Alfa, Attahiru Sule & Frigui, Imed, 1996. "Discrete NT-policy single server queue with Markovian arrival process and phase type service," European Journal of Operational Research, Elsevier, vol. 88(3), pages 599-613, February.
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    Cited by:

    1. 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.

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