Repair systems with exchangeable items and the longest queue mechanism

Repair systems with exchangeable items and the longest queue mechanism

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Article ID: iaor20131216
Volume: 73
Issue: 3
Start Page Number: 295
End Page Number: 316
Publication Date: Mar 2013
Journal: Queueing Systems
Authors: , ,
Keywords: queues: theory
Abstract:

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.

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