Discrete Time Geo/G/1 Queue with Multiple Adaptive Vacations |
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| Authors: | Zhang Zhe George Tian Naishuo |
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| Affiliation: | (1) Department of Finance, Marketing and Decision Sciences, College of Business and Economics, Western Washington University, Bellingham, WA 98225-9077, USA;(2) Faculty of Business Administration, Simon Fraser University, Burnaby, BC, V5A 1S6, Canada;(3) Department of Mathematics and Physics, Yanshan University, Qinhuangdao, 066004, China |
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| Abstract: | This paper treats the discrete time Geometric/G/1 system with vacations. In this system, after serving all customers in the system, the server will take a random maximum number of vacations before returning to the service mode. The stochastic decomposition property of steady-state queue length and waiting time has been proven. The busy period, vacation mode period, and service mode period distributions are also derived. Several common vacation policies are special cases of the vacation policy presented in this study. |
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| Keywords: | discrete-time queueing system vacation stochastic decomposition busy period |
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