The cμ/θ rule

Rami Atar; Chanit Giat; Nahum Shimkin

3rd International ICST Conference on Performance Evaluation Methodologies and Tools

Research Article

The cμ/θ rule

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@INPROCEEDINGS{10.4108/ICST.VALUETOOLS2008.4386,
    author={Rami Atar and Chanit Giat and Nahum Shimkin},
    title={The cμ/θ rule},
    proceedings={3rd International ICST Conference on Performance Evaluation Methodologies and Tools},
    publisher={ICST},
    proceedings_a={VALUETOOLS},
    year={2010},
    month={5},
    keywords={Multi-class multi server queues many servers asymptotic regime asymptotically optimal control fluid limits},
    doi={10.4108/ICST.VALUETOOLS2008.4386}
}

Rami Atar
Chanit Giat
Nahum Shimkin
Year: 2010
The cμ/θ rule
VALUETOOLS
ICST
DOI: 10.4108/ICST.VALUETOOLS2008.4386

Rami Atar¹^,*, Chanit Giat¹^,*, Nahum Shimkin¹^,*

1: Department of Electrical Engineering Technion — IIT Haifa 32000, Israel

*Contact email: atar@ee.technion.ac.il, gchanit@tx.technion.ac.il, shimkin@ee.technion.ac.il

Abstract

We consider a multi-class queueing system with customer abandonment. For class i, the holding cost per unit time, the service rate and the abandonment rate are denoted by ci, μi and θi, respectively. Our results show that under a manyserver fluid scaling and heavy traffic conditions, a routing policy that assigns non-preemptive priority to classes according to their index ciμi/θi, is asymptotically optimal for minimizing the overall long run average holding cost.

Keywords: Multi-class multi server queues many servers asymptotic regime asymptotically optimal control fluid limits

Published: 2010-05-16
Publisher: ICST
Modified: 2010-05-16

: http://dx.doi.org/10.4108/ICST.VALUETOOLS2008.4386