Transient study of a queueing system with one unreliable server, batch arrivals, two types of verification, loss and vacation

This paper studies a transient regime for an unreliable queue with repairs, two delays, geometric loss and Bernoulli schedule server vacations. The server takes always a vacation when during the service, no customer arrives and the queue is empty. The customer whose service is interrupted stays in the service, waiting for delay, repair and second delay (verification), after that, he completes his service. Using a supplementary variable method, transient solutions, performance and reliability measures and stochastic decomposition of the system are determined. Numerical results are sketched out to illustrate the effect of the system parameters on the main performances.