European Journal of Molecular & Clinical Medicine

Abstract

An one server retrial lineup system operating in a uncertain environment subject to server failure along with repair is analysed. The environment is in any one of the m + 1 states 0, 1, 2,…, m. The environmental state 0 denotes to the state that the server is undergoing repair. The mean is exponential to the repair time. Throughout repair time, customer is not allowed to join the orbit. Instantaneously once the repair, the system drives to phase i, i 1 with probability , where Σ =1. When the environment is in stage 1, the model acts like an queue with service and arrival rate and respectively There is no waiting room and any arriving customer who discovers the server idle joins for service; else (in case of busy server) goes to an orbit of infinite capacity and retries for service with rate v. The system resides in phase for a random intermission of time is exponential with mean and at the end of the sojourn period, a catastrophe occurs washing out the customers (if any) in the orbit and also the customer (if any) undergoing service and the system moves to phase 0: The system steady-state behaviour is derived.