On Equilibrium in a Constant Retrial Queuing System with Reserved Time and Vacations

doi:10.1007/s40305-019-00290-9

Journal of the Operations Research Society of China ›› 2022, Vol. 10 ›› Issue (4): 785-800.doi: 10.1007/s40305-019-00290-9

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On Equilibrium in a Constant Retrial Queuing System with Reserved Time and Vacations

Lin-Lin Wang, Li-Wei Liu, Xu-Dong Chai, Zhen Wang

School of Science, Nanjing University of Science and Technology, Nanjing 210094, China

Received:2019-03-02 Revised:2019-11-15 Online:2022-12-30 Published:2022-11-09
Contact: Lin-Lin Wang,Li-Wei Liu,Xu-Dong Chai,Zhen Wang E-mail:wanglinlin502@163.com;lwliu@njust.edu.cn;690752860@qq.com;1721157913@qq.com

Abstract

Abstract: This paper investigates an M/M/1 constant retrial queue with reserved time and vacations. A new arriving customer will take up the server and accept service immediately if the server is idle. Otherwise, if the server is busy or on vacation, customers have to join a retrial orbit and wait for retry. Once a service is completed, the server will reserve a random time to seek a customer from the orbit at a constant retrial rate. If there is no arrivals (from the orbit or outside) during the idle period, to save energy, the server will take a vacation. This paper studies the fully unobservable case. First, the steady-state condition of the system is analyzed by using the Foster’s criterion, and the customers’ expected waiting time is obtained based on the generating function technique. And then, by introducing an appropriate revenue structure, the equilibrium strategies of customers and the socially optimal strategy are all derived. Furthermore, a comparison between them is made and the effect of some main system parameters is studied.

Key words: Queuing, Unobservable, Equilibrium strategies, Reserved time, Vacation, Retry

CLC Number:

60K25
91B50

Lin-Lin Wang, Li-Wei Liu, Xu-Dong Chai, Zhen Wang. On Equilibrium in a Constant Retrial Queuing System with Reserved Time and Vacations[J]. Journal of the Operations Research Society of China, 2022, 10(4): 785-800.

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On Equilibrium in a Constant Retrial Queuing System with Reserved Time and Vacations

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