A batch arrival unreliable server delaying repair queue with two phases of service and Bernoulli vacation under multiple vacation policy. Issue 2 (4th March 2018) - Choudhury, Gautam; Deka, Mitali
Abstract: This paper deals with an M X / G /1 unreliable queue with two phases of service and Bernoulli vacation schedule under multiple vacation policy, where after each vacation completion or service completion, the server takes sequence of vacations until a batch of new customer arrive. Further concept of the delay time is also introduced. We assume that customers arrive to the system according to a Poisson process with rate . While the server is working with any phase of service, it may breakdown at any instant and the service channel will fail for a short interval of time. After completion of both phases of service, the server either goes for a vacation with probability p (0 ≤  p  ≤ 1) or may continue to serve the next unit, if any, with probability q (= 1 –  p ). Otherwise; it remains in the system until a customer arrives. For this model, we derive queue size distributions at various epochs, busy period distribution, waiting time distribution under the steady-state condition. Next, we derive reliability function and related reliability indices of this model. Finally, some numerical examples are presented for illustrative purpose.