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Multiserver Retrial Queue with Two-Way Communication and Synchronous Working Vacation

Author

Listed:
  • Tzu-Hsin Liu

    (Department of Finance, Chaoyang University of Technology, 168, Jifeng East Road, Wufeng District, Taichung City 41349, Taiwan)

  • Kuo-Ching Chiou

    (Department of Finance, Chaoyang University of Technology, 168, Jifeng East Road, Wufeng District, Taichung City 41349, Taiwan)

  • Chih-Ming Chen

    (Ph.D. Program of Business Administration in Industrial Development, Department of Business Administration, Chaoyang University of Technology, 168, Jifeng East Road, Wufeng District, Taichung City 41349, Taiwan)

  • Fu-Min Chang

    (Department of Finance, Chaoyang University of Technology, 168, Jifeng East Road, Wufeng District, Taichung City 41349, Taiwan)

Abstract

This work investigates a two-way communication retrial queue with synchronous working vacation and a constant retrial policy. During the idle time, a server makes an outgoing call after a random length. The service time of the incoming call and outgoing call obeys exponential distribution with different rates. If the incoming call finds all servers to be unavailable, it may or may not enter orbit. All servers immediately go on vacation simultaneously as soon as they find an empty system after the service finishes. During vacation, the servers can provide a service to those incoming calls, but this is at a lower-speed rate. The stationary probability distribution and the ergodic condition are obtained utilizing the matrix geometric technique. Some system characteristics are developed. Using MATLAB software, the variation in average orbit length, idle ratio, and the average number of servers in different server states is plotted for different values of the incoming/outgoing call rate and retrial rate. We further propose a multi-objective optimization model from which the optimal rate of outgoing calls and optimal vacation rate are explicitly obtained.

Suggested Citation

  • Tzu-Hsin Liu & Kuo-Ching Chiou & Chih-Ming Chen & Fu-Min Chang, 2024. "Multiserver Retrial Queue with Two-Way Communication and Synchronous Working Vacation," Mathematics, MDPI, vol. 12(8), pages 1-14, April.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:8:p:1163-:d:1374758
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    References listed on IDEAS

    as
    1. Muthukrishnan Senthil Kumar & Aresh Dadlani & Kiseon Kim, 2020. "Performance analysis of an unreliable M/G/1 retrial queue with two-way communication," Operational Research, Springer, vol. 20(4), pages 2267-2280, December.
    2. Dong-Yuh Yang & Chia-Huang Wu, 2019. "Performance analysis and optimization of a retrial queue with working vacations and starting failures," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 25(5), pages 463-481, September.
    3. Konak, Abdullah & Coit, David W. & Smith, Alice E., 2006. "Multi-objective optimization using genetic algorithms: A tutorial," Reliability Engineering and System Safety, Elsevier, vol. 91(9), pages 992-1007.
    4. Jeongsim Kim & Bara Kim, 2016. "A survey of retrial queueing systems," Annals of Operations Research, Springer, vol. 247(1), pages 3-36, December.
    5. Se Won Lee & Bara Kim & Jeongsim Kim, 2022. "Analysis of the waiting time distribution in M/G/1 retrial queues with two way communication," Annals of Operations Research, Springer, vol. 310(2), pages 505-518, March.
    6. Sundararaman Muthusamy & Narasimhan Devadoss & Sherif I. Ammar & Filippo Cacace, 2022. "Reliability and Optimization Measures of Retrial Queue with Different Classes of Customers under a Working Vacation Schedule," Discrete Dynamics in Nature and Society, Hindawi, vol. 2022, pages 1-17, October.
    7. M. Sundararaman & D. Narasimhan & P. Rajadurai & Antonio Di Crescenzo, 2024. "Performance Analysis of Two Different Types of Waiting Queues with Working Vacations," Journal of Mathematics, Hindawi, vol. 2024, pages 1-19, January.
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