Fluid M/M/1 catastrophic queue in a random environment

Abstract

Our main objective in this study is to investigate the stationary behavior of a fluid catastrophic queue of M/M/1 in a random multi-phase environment. Occasionally, a queueing system experiences a catastrophic failure causing a loss of all current jobs. The system then goes into a process of repair. As soon as the system is repaired, it moves with probability qi ≥ 0 to phase i. In this study, the distribution of the buffer content is determined using the probability generating function. In addition, some numerical results are provided to illustrate the effect of various parameters on the distribution of the buffer content.