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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Main Authors: Yanling Huang, Ruiling Tian, Junting Su
Format: Article
Language:English
Published: MDPI AG 2025-06-01
Series:Mathematics
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Online Access:https://www.mdpi.com/2227-7390/13/11/1856
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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.
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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