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Transient Analysis of a Modified Differentiated Vacation Queueing System for Energy-Saving in WiMAX

Author

Listed:
  • A. Mohammed Shapique

    (IFET College of Engineering)

  • R. Sudhesh

    (UCE: BIT Campus, Anna University)

  • S. Dharmaraja

    (Indian Institute of Technology Delhi)

Abstract

A modified differentiated vacation queueing system with a close-down period and impatient customers is investigated in this research paper. The proposed model can be applied to study the energy management mechanisms of WiMAX and tethered high altitude platform (HAP) systems. In this system, the WiMAX mobile station (MS) switches to a close-down period for a random duration at the end of the busy period. At the end of the close-down period, if the system is non-empty, the MS switches to a functional state. Otherwise, the MS takes an ordinary vacation. The MS switches to a working vacation (WV) if the system is empty at the end of the ordinary vacation period. Jobs arriving during the WV are served at a slower service rate. Jobs may become impatient in any state of the system except during the regular busy period. Explicit expressions for the transient and steady-state probabilities of this system are obtained using continued fraction and confluent hypergeometric functions. Furthermore, performance indices such as mean, variance, average abandonment rate, and system throughput are computed. Finally, a cost-profit analysis and graphical illustrations are provided.

Suggested Citation

  • A. Mohammed Shapique & R. Sudhesh & S. Dharmaraja, 2024. "Transient Analysis of a Modified Differentiated Vacation Queueing System for Energy-Saving in WiMAX," Methodology and Computing in Applied Probability, Springer, vol. 26(3), pages 1-33, September.
    • Handle: RePEc:spr:metcap:v:26:y:2024:i:3:d:10.1007_s11009-024-10094-x
    DOI: 10.1007/s11009-024-10094-x
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    References listed on IDEAS

    as
    1. M. I. G. Suranga Sampath & K. Kalidass & Jicheng Liu, 2020. "Transient Analysis of an M/M/1 Queueing System Subjected to Multiple Differentiated Vacations, Impatient Customers and a Waiting Server with Application to IEEE 802.16E Power Saving Mechanism," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(1), pages 297-320, March.
    2. Sudhesh R. & Mohammed Shapique A. & Dharmaraja S., 2022. "Analysis of a Multiple Dual-Stage Vacation Queueing System with Disaster and Repairable Server," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2485-2508, December.
    3. Ammar, Sherif I., 2015. "Transient analysis of an M/M/1 queue with impatient behavior and multiple vacations," Applied Mathematics and Computation, Elsevier, vol. 260(C), pages 97-105.
    4. Naishuo Tian & Zhe George Zhang, 2006. "Vacation Queueing Models Theory and Applications," International Series in Operations Research and Management Science, Springer, number 978-0-387-33723-4, December.
    5. Ioannis Dimitriou, 2016. "Queueing analysis of the DRX power saving mechanism in fault-tolerant 3GPP LTE wireless networks," Annals of Operations Research, Springer, vol. 239(2), pages 521-552, April.
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