Repair systems with exchangeable items and the longest queue mechanism
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.
- Repair systems with exchangeable items and the longest queue mechanism
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Volume 73, Issue 3 , pp 295-316
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- Online ISSN
- Springer US
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- Repair system
- Longest queue
- Queue lengths
- Sojourn time
- Industry Sectors
- Author Affiliations
- 1. Department of Statistics, University of Haifa, Haifa, 31909, Israel
- 2. College of Engineering, ORT Braude, Karmiel, 20101, Israel
- 3. EURANDOM, Eindhoven, The Netherlands
- 4. Department of Mathematics and Computer Science, Technische Universiteit Eindhoven, Eindhoven, The Netherlands