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M/M/1 machine repairmanproblem withbulk-repair using general bulk service rule

A. Banerjee, U. C. Gupta


In this paper, we consider a M/M/1//N machine repairman problem where the failed machines are repaired in batches of minimum size ‘a’ with a maximum threshold value ‘b’. We obtain several probability distributions of interest, such as, the joint distribution of the number of down machines in the queue and with the repairman, the distribution of the number of the down machines in the queue, number of the machines under repair with the repairman, and thenumberofworking machines.Various useful performance measures, such as,average system (queue) length,averagewaiting timeofafailed machinein the queue as well as in the system, average number of operating machines, probability that the repairman is idle, have been obtained. Finally, influence of certain model parameters on keyperformence measureshave beeninvestigated.


Finite-source, Bulk-repair, Machine repairman, Queue.

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