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Queueing Syst (2011) 67: 127144 DOI 10.1007/s11134-010-9206-x

Summary: Queueing Syst (2011) 67: 127144
DOI 10.1007/s11134-010-9206-x
On the asymptotic optimality of the c/ rule
under ergodic cost
Rami Atar Chanit Giat Nahum Shimkin
Received: 12 January 2010 / Revised: 17 October 2010 / Published online: 29 December 2010
Springer Science+Business Media, LLC 2010
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 i, and abandonment occurs at rate i. In a many-server fluid regime, we show
that prioritizing the classes in decreasing order of cii/i asymptotically minimizes
an ergodic holding cost, where ci denotes the equivalent holding cost per unit time
for class i.
Keywords Queues with abandonment Ergodic cost Multi-class queues
Asymptotic optimality Fluid limits
Mathematics Subject Classification (2000) 68M20 90B36 93E20
1 Introduction
We consider a parallel server queueing model with I customer classes and multiple
servers. Each server is capable of serving any one of the customers, and each cus-
tomer has a single service requirement. Customers arrive according to independent


Source: Atar, Rami - Department of Electrical Engineering, Technion, Israel Institute of Technology


Collections: Engineering