Analysis of a M/M/1 Queueing System with Two-Phase, N-Policy, Server Failure and Second Optional Batch Service with Customers impatient behaviour

In this paper an M/M/1 queueing system with server vacation, Startup, breakdowns and second optional service with impatient customer behavior is considered. All the customers will be given unique type of individual service in the first phase and then second phase service will be provided on option of the customer. We obtain some important system characteristics, such as the number of customers in the system, the probability that the server is idle, busy and broken down states, the expected waiting time in the system. Sensitivity analysis is also conducted with various parameters on system's performance measures.