Model Validation and Strategy Analysis in Retrial Queues with Delayed Vacations and Feedback Based on Monte Carlo Simulation
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 servic...
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MDPI AG
2025-06-01
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| Series: | Mathematics |
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| author | Yanling Huang Ruiling Tian Junting Su |
| author_facet | Yanling Huang Ruiling Tian Junting Su |
| author_sort | Yanling Huang |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-9ba26cc4cc394d0380f9f1bc73904254 |
| institution | DOAJ |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-9ba26cc4cc394d0380f9f1bc739042542025-08-20T03:11:32ZengMDPI AGMathematics2227-73902025-06-011311185610.3390/math13111856Model Validation and Strategy Analysis in Retrial Queues with Delayed Vacations and Feedback Based on Monte Carlo SimulationYanling Huang0Ruiling Tian1Junting Su2School of Science, Yanshan University, Qinhuangdao 066004, ChinaSchool of Science, Yanshan University, Qinhuangdao 066004, ChinaSchool of Science, Yanshan University, Qinhuangdao 066004, ChinaInspired 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.https://www.mdpi.com/2227-7390/13/11/1856delayed vacationsretrial queuecustomer behaviorcost optimizationMonte Carlo simulation |
| spellingShingle | Yanling Huang Ruiling Tian Junting Su Model Validation and Strategy Analysis in Retrial Queues with Delayed Vacations and Feedback Based on Monte Carlo Simulation Mathematics delayed vacations retrial queue customer behavior cost optimization Monte Carlo simulation |
| title | Model Validation and Strategy Analysis in Retrial Queues with Delayed Vacations and Feedback Based on Monte Carlo Simulation |
| title_full | Model Validation and Strategy Analysis in Retrial Queues with Delayed Vacations and Feedback Based on Monte Carlo Simulation |
| title_fullStr | Model Validation and Strategy Analysis in Retrial Queues with Delayed Vacations and Feedback Based on Monte Carlo Simulation |
| title_full_unstemmed | Model Validation and Strategy Analysis in Retrial Queues with Delayed Vacations and Feedback Based on Monte Carlo Simulation |
| title_short | Model Validation and Strategy Analysis in Retrial Queues with Delayed Vacations and Feedback Based on Monte Carlo Simulation |
| title_sort | model validation and strategy analysis in retrial queues with delayed vacations and feedback based on monte carlo simulation |
| topic | delayed vacations retrial queue customer behavior cost optimization Monte Carlo simulation |
| url | https://www.mdpi.com/2227-7390/13/11/1856 |
| work_keys_str_mv | AT yanlinghuang modelvalidationandstrategyanalysisinretrialqueueswithdelayedvacationsandfeedbackbasedonmontecarlosimulation AT ruilingtian modelvalidationandstrategyanalysisinretrialqueueswithdelayedvacationsandfeedbackbasedonmontecarlosimulation AT juntingsu modelvalidationandstrategyanalysisinretrialqueueswithdelayedvacationsandfeedbackbasedonmontecarlosimulation |