Effects of parameters on Nash games with OSNR target

This paper studies efficiency in a Nash game with optical signal-to-noise ratio (OSNR) target. Instead of looking from the view point of degree of efficiency ("price of anarchy"), we investigate the effects of parameters in individual cost functions. We show that the aggregate cost function in the game-theoretic formulation is not automatically convex and the optimal solution of the associated constrained optimization problem is not immediate. Then we build the relation between these two formulations by indicating that the individual cost function Ci(ui) in the system optimization formulation has an approximate interpretation with the one Ji(u) in the game-theoretic formulation. We compare simulation results from both a system optimization and a user optimization (game-theoretic) approach for a single optical link. It is well known that the Nash equilibria of a game may not achieve full efficiency. We show the effects of pricing mechanisms on system performance. We also show that OSNR target can be achieved and efficiency can be possibly improved by appropriate selection of parameters.

[1]  Lacra Pavel,et al.  Global Convergence of An Iterative Gradient Algorithm for The Nash Equilibrium in An Extended OSNR Game , 2007, IEEE INFOCOM 2007 - 26th IEEE International Conference on Computer Communications.

[2]  Cem U. Saraydar,et al.  Efficient power control via pricing in wireless data networks , 2002, IEEE Trans. Commun..

[3]  Eitan Altman,et al.  CDMA Uplink Power Control as a Noncooperative Game , 2002, Wirel. Networks.

[4]  Frank Kelly,et al.  Rate control for communication networks: shadow prices, proportional fairness and stability , 1998, J. Oper. Res. Soc..

[5]  G. Perakis,et al.  The Price of Anarchy when Costs Are Non-separable and Asymmetric , 2004, IPCO.

[6]  F. Forghieri,et al.  Simple model of optical amplifier chains to evaluate penalties in WDM systems , 1996, Optical Fiber Communications, OFC..

[7]  Eitan Altman,et al.  A survey on networking games in telecommunications , 2006, Comput. Oper. Res..

[8]  Ronald L. Wasserstein,et al.  Monte Carlo: Concepts, Algorithms, and Applications , 1997 .

[9]  Pradeep Dubey,et al.  Inefficiency of Nash Equilibria , 1986, Math. Oper. Res..

[10]  Christos H. Papadimitriou,et al.  Worst-case equilibria , 1999 .

[11]  T. Basar,et al.  A game-theoretic framework for congestion control in general topology networks , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[12]  John N. Tsitsiklis,et al.  Efficiency loss in a network resource allocation game: the case of elastic supply , 2005, IEEE Trans. Autom. Control..

[13]  T. Basar,et al.  Differentiated Internet pricing using a hierarchical network game model , 2004, Proceedings of the 2004 American Control Conference.

[14]  Frank Kelly,et al.  Charging and rate control for elastic traffic , 1997, Eur. Trans. Telecommun..

[15]  L. Pavel,et al.  OSNR optimization in optical networks: extension for capacity constraints , 2005, Proceedings of the 2005, American Control Conference, 2005..

[16]  A. Ozdaglar,et al.  Costs of Competition in General Networks , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[17]  Tim Roughgarden,et al.  Selfish routing and the price of anarchy , 2005 .

[18]  T. Alpcan,et al.  A Distributed Optimization Approach to Constrained OSNR Problem , 2008 .

[19]  Cem U. Saraydar,et al.  Pricing and power control in a multicell wireless data network , 2001, IEEE J. Sel. Areas Commun..