Abstract

This work studied a queuing system with four different main server interruptions and a stand-by server replaces the main server during any potential stop. The main server has five statues in this system where it is either services the customers( active) or it does not work because of one of the four reason; original vacation, extended vacation, it is broken-down but the repairs did not start yet (delay time) and broken-down servers under repairs. The arrivals are assumed to attend the system in batches. All the distributions of the service, vacation, extended vacation, repairs and delay times all follow general distributions while the breakdown times and the stand-by service times are  exponentially distributed.

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