Performance analysis of a complex queueing system with vacations in random environment

oleh: Jianjun Li, Liwei Liu

Format: Article
Diterbitkan: SAGE Publishing 2017-08-01

Deskripsi

This article studies a complex queueing system with vacations in a multi-phase random environment. When the system is in operative phase i , i = 1 , 2 , … , n , customers are served one by one. Whenever the system becomes empty at a service completion instant, the server starts a vacation, causing the system to move to vacation phase. When a vacation ends, if the system is empty, another begins. Otherwise, the system moves from the vacation phase to some operative phase i with probability q i , i = 1 , 2 , … , n . Using the method of probability generating function, we obtain the distribution for the steady-state queue length at arbitrary epoch. We also derive the distributions for the stationary sojourn time and the length of the server’s working time in a service cycle, respectively. Finally, we present some special cases and numerical examples.