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Efficiency of a markovian queue with non homogeneous vacations and strategic customers under partial vacation interruption

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  • Sylia Abdoun

    (RIIMA Laboratory, University of Science and Technology Houari Boumediene USTHB)

  • Samira Taleb

    (RIIMA Laboratory, University of Science and Technology Houari Boumediene USTHB)

Abstract

We analyse the efficiency of an M/M/1 queue with non homogeneous vacations and partial vacation interruption. This type of queues are successfully used to model Base Station Sleep modes in 5 G technology. We consider two models where customers differ in their beliefs regarding the dynamic of the system. In the first model customers have only information on the server state, while, in the second model customers possess no information on the server status neither the number of customer on the system. In both models, we used the matrix geometric method to obtain the stationary distribution and derive the system performance measures. Additionally, we delved into customers’ behavior by determining individual and social joining probabilities. Our analysis extended to evaluating the system efficiency through the examination of efficiency measures such as throughput and the price of anarchy.

Suggested Citation

  • Sylia Abdoun & Samira Taleb, 2025. "Efficiency of a markovian queue with non homogeneous vacations and strategic customers under partial vacation interruption," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 88(2), pages 1-18, June.
    • Handle: RePEc:spr:telsys:v:88:y:2025:i:2:d:10.1007_s11235-025-01272-4
    DOI: 10.1007/s11235-025-01272-4
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    References listed on IDEAS

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    1. Priyanka Kalita & Dharmaraja Selvamuthu, 2023. "Stochastic modelling of sleeping strategy in 5G base station for energy efficiency," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 83(2), pages 115-133, June.
    2. Ayane Nakamura & Tuan Phung-Duc, 2023. "Equilibrium Analysis for Batch Service Queueing Systems with Strategic Choice of Batch Size," Mathematics, MDPI, vol. 11(18), pages 1-22, September.
    3. Liron Ravner & Yutaka Sakuma, 2021. "Strategic arrivals to a queue with service rate uncertainty," Queueing Systems: Theory and Applications, Springer, vol. 97(3), pages 303-341, April.
    4. Preetjot Kaur & Roopali Garg & Vinay Kukreja, 2023. "Energy-efficiency schemes for base stations in 5G heterogeneous networks: a systematic literature review," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 84(1), pages 115-151, September.
    5. 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.
    6. Mark Fackrell & Peter Taylor & Jiesen Wang, 2021. "Strategic customer behavior in an M/M/1 feedback queue," Queueing Systems: Theory and Applications, Springer, vol. 97(3), pages 223-259, April.
    7. S. Srivatsa Srinivas & Rahul R. Marathe, 2020. "Equilibrium in a finite capacity M/M/1 queue with unknown service rates consisting of strategic and non-strategic customers," Queueing Systems: Theory and Applications, Springer, vol. 96(3), pages 329-356, December.
    8. 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, June.
    9. Shone, Rob & Knight, Vincent A. & Williams, Janet E., 2013. "Comparisons between observable and unobservable M/M/1 queues with respect to optimal customer behavior," European Journal of Operational Research, Elsevier, vol. 227(1), pages 133-141.
    10. Shweta Upadhyaya, 2016. "Queueing systems with vacation: an overview," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 9(2), pages 167-213.
    11. V. Deepa & M. Haridass & Dharmaraja Selvamuthu & Priyanka Kalita, 2023. "Analysis of energy efficiency of small cell base station in 4G/5G networks," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 82(3), pages 381-401, March.
    12. Naor, P, 1969. "The Regulation of Queue Size by Levying Tolls," Econometrica, Econometric Society, vol. 37(1), pages 15-24, January.
    13. Liuqing He & Ruiling Tian & Yunna Han & Xinyu Wu, 2024. "Optimal joining strategies in a repairable retrial queue with reserved time and N-policy," Operational Research, Springer, vol. 24(1), pages 1-22, March.
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