On the asymptotic optimality of the cμ/θ rule under ergodic cost

Authors:
Rami Atar;Chanit Giat;Nahum Shimkin
Affiliations:
Department of Electrical Engineering, Technion--Israel Institute of Technology, Haifa, Israel 32000;Department of Electrical Engineering, Technion--Israel Institute of Technology, Haifa, Israel 32000;Department of Electrical Engineering, Technion--Israel Institute of Technology, Haifa, Israel 32000
Venue:
Queueing Systems: Theory and Applications
Year:
2011

Citing 2
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Queueing Systems: Theory and Applications

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Abstract

We consider an overloaded multi-server multi-class queueing model where customers may abandon while waiting to be served. For class i, service is provided at rate μ i , and abandonment occurs at rate θ i . In a many-server fluid regime, we show that prioritizing the classes in decreasing order of c i μ i /θ i asymptotically minimizes an ergodic holding cost, where c i denotes the equivalent holding cost per unit time for class i.