Queueing Systems with Multi Interruptions of the Main Server : Queueing Systems with Server Vacations, Extended Vacations, Breakdowns, Delayed Repairs and Stand-bys

This work investigates a batch arrival queueing system with a Bernoulli scheduled vacation and random system breakdowns. It is assumed that the repair process does not start immediately after the breakdown. Consequently there maybe a delay in starting repairs. After every service completion the server may go on an optional vacation. When the original vacation is completed the server has the option to go on an extended vacation. It is assumed that the system is equipped with a stand-by server to serve the customers during the vacation period of the main server as well as during the repair process.