Analysis of the M/G/1 queue in multi-phase random environment with disasters

Abstract

This paper studies an M/G/1 queue in a multi-phase random environment. When in operative phase i, i=1,2,…,n, the system is subject to disastrous interruptions, causing all present customers (waiting and served) to leave the system. At an exponential failure instant, the server abandons the service and the system goes directly to repair phase. After an exponential repair time, the system moves to operative phase i with probability qi, i=1,2,…,n. Using the supplementary variable technique, we obtain the distribution for the stationary queue at an arbitrary epoch. We also derive results of the cycle analysis, the sojourn time distribution and the length of the server's working time in a service cycle. In addition, some special cases and numerical examples are presented.