Analysis of a GI/M/1 queue in a multi-phase service environment with disasters

In this paper, we study a single server GI/M/1 queue in a multi-phase service environment with disasters, where the disasters occur only when the server is busy serving customers. Whenever a disaster occurs in an operative service phase, all present customers are forced to leave the system simultaneously, the server abandons the service and an exponential repair time is set on. After the system is repaired, the server resumes his service and moves to service phase i immediately with probability qi,i = 1,2,...,N. Using the matrix analytic approach and semi-Markov process, we obtain the stationary queue length distribution at both arrival and arbitrary epochs. After introducing tagged customers and the concept of a cycle, we also derive the sojourn time distribution, the duration of a cycle, and the length of the server’s working time in a service cycle. In addition, numerical examples are presented to illustrate the impact of some critical model parameters on performance measures