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Transient analysis of two heterogeneous servers queueing system with differentiated vacations subject to system disaster, server repair

Author

Listed:
  • Venugopal Karthick

    (College of Engineering and Technology)

  • Vaidhiyanathan Suvitha

    (College of Engineering and Technology)

  • Ramupillai Sudhesh

    (UCE: BIT Campus, Anna University)

Abstract

This research paper examines the dynamic behavior of a heterogeneous two-server queuing model that incorporates differentiated vacation periods. Additionally, the model accounts for the possibility of a disaster occurring during busy periods and vacations, with immediate initiation of the repair process. The motivation for this study stems from the two types of power-saving mechanisms found in IEEE 802.16E. The paper presents explicit expressions, obtained using generating functions, for the time-dependent probabilities of system size, expressed in terms of modified Bessel functions. To further validate the theoretical findings, numerical illustrations have been included.

Suggested Citation

  • Venugopal Karthick & Vaidhiyanathan Suvitha & Ramupillai Sudhesh, 2024. "Transient analysis of two heterogeneous servers queueing system with differentiated vacations subject to system disaster, server repair," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 86(2), pages 751-776, November.
    • Handle: RePEc:spr:sankhb:v:86:y:2024:i:2:d:10.1007_s13571-024-00339-7
    DOI: 10.1007/s13571-024-00339-7
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    References listed on IDEAS

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    1. Yonatan Levy & Uri Yechiali, 1975. "Utilization of Idle Time in an M/G/1 Queueing System," Management Science, INFORMS, vol. 22(2), pages 202-211, October.
    2. B. Krishna Kumar & S.R. Anantha Lakshmi & S. Anbarasu & S. Pavai Madheswari, 2014. "Transient and steady-state analysis of queueing systems with catastrophes and impatient customers," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 6(5), pages 523-549.
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