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

RAMI ATAR; Chanit Giat; Nahum Shimkin

doi:https://doi.org/10.1007/s11134-010-9206-x

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

RAMI ATAR, Chanit Giat, Nahum Shimkin

Technion - Israel Institute of Technology

Research output: Contribution to journal › Article › peer-review

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_iμ_i/θ_i asymptotically minimizes an ergodic holding cost, where c_i denotes the equivalent holding cost per unit time for class i.

Original language	English
Pages (from-to)	127-144
Number of pages	18
Journal	Queueing Systems
Volume	67
Issue number	2
DOIs	https://doi.org/10.1007/s11134-010-9206-x
State	Published - Feb 2011

Keywords

Asymptotic optimality
Ergodic cost
Fluid limits
Multi-class queues
Queues with abandonment

All Science Journal Classification (ASJC) codes

Statistics and Probability
Computer Science Applications
Management Science and Operations Research
Computational Theory and Mathematics

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https://doi.org/10.1007/s11134-010-9206-x

Cite this

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title = "On the asymptotic optimality of the cμ/θ rule under ergodic cost",

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 μi, and abandonment occurs at rate θi. In a many-server fluid regime, we show that prioritizing the classes in decreasing order of ciμi/θi asymptotically minimizes an ergodic holding cost, where ci denotes the equivalent holding cost per unit time for class i.",

keywords = "Asymptotic optimality, Ergodic cost, Fluid limits, Multi-class queues, Queues with abandonment",

author = "RAMI ATAR and Chanit Giat and Nahum Shimkin",

note = "Funding Information: Research supported in part by grants 2006379 and 2008466 from the United States–Israel Binational Science Foundation, grant 1349/08 from the Israel Science Foundation, and the Technion{\textquoteright}s fund for promotion of research.",

year = "2011",

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doi = "https://doi.org/10.1007/s11134-010-9206-x",

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T1 - On the asymptotic optimality of the cμ/θ rule under ergodic cost

AU - ATAR, RAMI

AU - Giat, Chanit

AU - Shimkin, Nahum

N1 - Funding Information: Research supported in part by grants 2006379 and 2008466 from the United States–Israel Binational Science Foundation, grant 1349/08 from the Israel Science Foundation, and the Technion’s fund for promotion of research.

PY - 2011/2

Y1 - 2011/2

N2 - 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 μi, and abandonment occurs at rate θi. In a many-server fluid regime, we show that prioritizing the classes in decreasing order of ciμi/θi asymptotically minimizes an ergodic holding cost, where ci denotes the equivalent holding cost per unit time for class i.

AB - 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 μi, and abandonment occurs at rate θi. In a many-server fluid regime, we show that prioritizing the classes in decreasing order of ciμi/θi asymptotically minimizes an ergodic holding cost, where ci denotes the equivalent holding cost per unit time for class i.

KW - Asymptotic optimality

KW - Ergodic cost

KW - Fluid limits

KW - Multi-class queues

KW - Queues with abandonment

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U2 - https://doi.org/10.1007/s11134-010-9206-x

DO - https://doi.org/10.1007/s11134-010-9206-x

M3 - مقالة

SN - 0257-0130

VL - 67

SP - 127

EP - 144

JO - Queueing Systems

JF - Queueing Systems

IS - 2

ER -

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

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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