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Model Validation and Strategy Analysis in Retrial Queues with Delayed Vacations and Feedback Based on Monte Carlo Simulation

Author

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  • Yanling Huang

    (School of Science, Yanshan University, Qinhuangdao 066004, China)

  • Ruiling Tian

    (School of Science, Yanshan University, Qinhuangdao 066004, China)

  • Junting Su

    (School of Science, Yanshan University, Qinhuangdao 066004, China)

Abstract

Inspired by call centers, this paper models them as a constant retrial queue, with feedback and delayed vacations to balance high efficiency and low cost for service agents. After completing the service, the server randomly waits for an idle period. If customers arrive during this period, the service is provided immediately, otherwise, the server will take a vacation. We first derive steady-state probabilities and key performance measures. Then, the system cost is modeled. Particle Swarm Optimization (PSO), Ant Colony Algorithm (ACA) and Sparrow Search Algorithm (SSA) are applied to obtain the minimum system cost, respectively. To verify the correctness of the theoretical results of the system model, we simulate the model using Monte Carlo simulation to obtain the probabilities of different server states and the expected number of customers in the system, and then compare them with the theoretical values. At the same time, the sensitivity of the performance measures obtained by Monte Carlo simulation to the system parameters is also analyzed. Finally, customer behavior is analyzed, and equilibrium and socially optimal arrival rates are derived. In addition, the efficiency of the system is evaluated by examining efficiency indicators such as throughput and price of anarchy.

Suggested Citation

  • Yanling Huang & Ruiling Tian & Junting Su, 2025. "Model Validation and Strategy Analysis in Retrial Queues with Delayed Vacations and Feedback Based on Monte Carlo Simulation," Mathematics, MDPI, vol. 13(11), pages 1-21, June.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:11:p:1856-:d:1670412
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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.
    2. Economou, Antonis & Logothetis, Dimitrios & Manou, Athanasia, 2022. "The value of reneging for strategic customers in queueing systems with server vacations/failures," European Journal of Operational Research, Elsevier, vol. 299(3), pages 960-976.
    3. Xianyue Shi & Liwei Liu, 2023. "Equilibrium Joining Strategies in the Retrial Queue with Two Classes of Customers and Delayed Vacations," Methodology and Computing in Applied Probability, Springer, vol. 25(2), pages 1-27, June.
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    5. Wei Sun & Shiyong Li, 2014. "Equilibrium and optimal behavior of customers in Markovian queues with multiple working vacations," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 694-715, July.
    6. Wang, Jinting & Zhang, Feng, 2013. "Strategic joining in M/M/1 retrial queues," European Journal of Operational Research, Elsevier, vol. 230(1), pages 76-87.
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