A queueing model with start-up/close-down times and retrial customers

We consider a queueing system with Poisson arrivals and arbitrarily distributed service times, vacation times, and start-up and close-down times. The model accepts two types of customers - the ordinary and the retrial customers - and the server takes a single vacation each time he becomes free. For such a model the stability conditions and the system state probabilities are investigated both in a transient and in the steady state. Numerical results are finally obtained and used to observe system performance for various values of the parameters.