Cost optimisation of single server retrial queue with standby server, extended vacation and delayed repair

This paper analyses a steady-state queueing system with repeated attempts, coupled with a standby server during vacation periods. Clients arrive in batches according to a compound Poisson process. If the server is idle upon batch arrival, one client receives immediate service; the rest join the orbit. Otherwise, the entire batch joins the orbit. After each service completion, the server may take a vacation and may extend the vacation with a certain probability. During vacations of the main server, a standby server serves clients. The server is subject to breakdown at a random amount of time, and the repair starts after some delay. After repair, service resumes for interrupted clients. Using the supplementary variable method, the equilibrium condition of the system is derived, and the stochastic decomposition law is verified. The system's probabilities and performance metrics are obtained. The optimal standby rate is determined through cost analysis to minimise expenses for the proposed model.