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Equilibrium and pricing analysis for an unreliable retrial queue with limited idle period and single vacation

Author

Listed:
  • Shan Gao

    (Fuyang Normal College)

  • Hua Dong

    (Qufu Normal University)

  • Xianchao Wang

    (Fuyang Normal College)

Abstract

This paper treats an M/M/1 retrial queue with an unreliable server, where the server is subject to random breakdowns and repairs when he is serving a customer. Whenever the server becomes idle, he will spare a limited period to wait possible new arrivals or repeated customers if any. If no customer arrives during this period, the server will take a single vacation. Under a given reward-cost structure, arriving customers have to decide to balk or to enter the orbit if they find the server unavailable at their arrival epochs. Firstly, we study some important performance measures. Secondly, we derive the equilibrium joining strategies for the customers, respectively, in noncooperative and cooperative cases. Thirdly, we study the pricing problem that the social planner faces to eliminate the gap between the individual optimal and socially optimal strategies. Finally, we present some numerical examples to illustrate the effect of some system parameters on optimal joining probabilities and Maximum of social welfare.

Suggested Citation

  • Shan Gao & Hua Dong & Xianchao Wang, 2021. "Equilibrium and pricing analysis for an unreliable retrial queue with limited idle period and single vacation," Operational Research, Springer, vol. 21(1), pages 621-643, March.
    • Handle: RePEc:spr:operea:v:21:y:2021:i:1:d:10.1007_s12351-018-0437-7
    DOI: 10.1007/s12351-018-0437-7
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    References listed on IDEAS

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    1. Antonis Economou & Spyridoula Kanta, 2011. "Equilibrium customer strategies and social–profit maximization in the single‐server constant retrial queue," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(2), pages 107-122, March.
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    Cited by:

    1. Fan Xu & Ruiling Tian & Qi Shao, 2024. "Optimal Pricing Strategy in an Unreliable M/M/1 Retrial Queue with Delayed Repair and Breakdown Deterioration," Methodology and Computing in Applied Probability, Springer, vol. 26(2), pages 1-22, June.
    2. V., Saravanan & V., Poongothai & P., Godhandaraman, 2023. "Performance analysis of a multi server retrial queueing system with unreliable server, discouragement and vacation model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 214(C), pages 204-226.
    3. Gabi Hanukov & Uri Yechiali, 2024. "Orbit while in service," Operational Research, Springer, vol. 24(2), pages 1-32, June.

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