We consider a repair facility consisting of one repairman and two arrival streams of failed items, from bases 1 and 2. The arrival processes are independent Poisson processes, and the repair times are independent and identically exponentially distributed. The item types are exchangeable, and a failed item from base 1 could just as well be returned to base 2, and vice versa. The rule according to which backorders are satisfied by repaired items is the longest queue rule: at the completion of a service (repair), the repaired item is delivered to the base that has the largest number of failed items.
We point out a direct relation between our model and the classical longer queue model. We obtain simple expressions for several probabilities of interest, and show how all two-dimensional queue length probabilities may be obtained. Finally, we derive the sojourn time distributions.
Original language | English |
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Place of Publication | Eindhoven |
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Publisher | Eurandom |
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Number of pages | 13 |
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Publication status | Published - 2011 |
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Name | Report Eurandom |
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Volume | 2011034 |
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ISSN (Print) | 1389-2355 |
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