Open Access

Unifying View on Min-Max Fairness, Max-Min Fairness, and Utility Optimization in Cellular Networks

EURASIP Journal on Wireless Communications and Networking20072007:034869

DOI: 10.1155/2007/34869

Received: 23 March 2006

Accepted: 3 November 2006

Published: 21 February 2007

Abstract

We are concerned with the control of quality of service (QoS) in wireless cellular networks utilizing linear receivers. We investigate the issues of fairness and total performance, which are measured by a utility function in the form of a weighted sum of link QoS. We disprove the common conjecture on incompatibility of min-max fairness and utility optimality by characterizing network classes in which both goals can be accomplished concurrently. We characterize power and weight allocations achieving min-max fairness and utility optimality and show that they correspond to saddle points of the utility function. Next, we address the problem of the difference between min-max fairness and max-min fairness. We show that in general there is a (fairness) gap between the performance achieved under min-max fairness and under max-min fairness. We characterize the network class for which both performance values coincide. Finally, we characterize the corresponding network subclass, in which both min-max fairness and max-min fairness are achievable by the same power allocation.

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Authors’ Affiliations

(1)
Heinrich Hertz Chair for Mobile Communications, Faculty of Electrical Engineering and Computer Science (EECS), Berlin University of Technology
(2)
German-Sino Lab for Mobile Communications (MCI), Fraunhofer Institute for Telecommunications

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Copyright

© Holger Boche et al. 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.