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

Tzu-Hsin Liu, Kuo-Ching Chiou, Chih-Ming Chen () and Fu-Min Chang ()
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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

Mathematics, 2024, vol. 12, issue 8, 1-14

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.

Keywords: two-way communication; synchronous working vacation; retrial queue; optimization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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