M~X/G/1Repairable Queueing System In Which Customers Who Arrive During The Second Type Failure Times Don’t Enter System

In this paper, we study the M~X/G/1repairable queueing system, inwhich the service station is likely to failure in both busy periods and idle periods, andwe assume the failure rates are different but the customers who arrive during the secondtype failure times don’t enter the system. By using some mathematical tools such astotal probability decomposition technique, Laplace transform, Laplace-Stieltjestransform and so on, we discuss the queueing indices and reliability indices of thesystem from any initial state. By inference, calculation and proof, we obtained thetransient distribution and the steady distribution of the queue-length in this system, theprobability that the service station is in the “generalized busy time”, the unavailabilityof the service station and the expected failure number during0, t. Addition, we alsodiscuss some special cases of the system.