NDLI: Closed Form Solutions for Symmetric Water Filling Games

Content Provider	IEEE Xplore Digital Library
Author	Altman, E. Avrachenkov, K. Garnaev, A.
Copyright Year	2008
Description	Author affiliation: INRIA, Sophia Antipolis (Altman, E.; Avrachenkov, K.)
Abstract	We study power control in optimization and game frameworks. In the optimization framework there is a single decision maker who assigns network resources and in the game framework users share the network resources according to Nash equilibrium. The solution of these problems is based on so-called water-filling technique, which in turn uses bisection method for solution of non-linear equations for Lagrange multipliers. Here we provide a closed form solution to the water-filling problem, which allows us to solve it in a finite number of operations. Also, we produce a closed form solution for the Nash equilibrium in symmetric Gaussian interference game with an arbitrary number of users. Even though the game is symmetric, there is an intrinsic hierarchical structure induced by the quantity of the resources available to the users. We use this hierarchical structure to perform a successive reduction of the game. In addition to its mathematical beauty, the explicit solution allows one to study limiting cases when the crosstalk coefficient is either small or large. We provide an alternative simple proof of the convergence of the iterative water filling algorithm. Furthermore, it turns out that the convergence of Iterative water filling algorithm slows down when the crosstalk coefficient is large. Using the closed form solution, we can avoid this problem. Finally, we compare the non-cooperative approach with the cooperative approach and show that the non-cooperative approach results in a more fair resource distribution.
Starting Page	673
Ending Page	681
File Size	227825
Page Count	9
File Format	PDF
ISBN	9781424420254
ISSN	0743166X
DOI	10.1109/INFOCOM.2008.117
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2008-04-13
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Closed-form solution Filling Water resources Nash equilibrium Crosstalk Iterative algorithms Power control Nonlinear equations Lagrangian functions Interference
Content Type	Text
Resource Type	Article
Subject	Computer Science Electrical and Electronic Engineering

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4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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