Stackelberg game approach to constrained OSNR nash game in WDM optical networks

This paper formulates a Stackelberg (N + 1)-person non-cooperative game framework for OSNR optimization in optical networks. We introduce cost functions with differentiated prices for users and develop a cost function for the higher level Stackelberg player. In the design, we consider the capacity constraints in optical networks, i.e., that the total optical power does not exceed the link's capacity. We formulate a novel Stackelberg framework in OSNR game and characterize its Stackelberg equilibrium. Based on it, we give a closed form solution and develop an iterative algorithm for the optical network control problem and illustrate the game with a numerical example.

[1]  T. Basar,et al.  Hierarchical Network Games with Various Types of Public and Private Information , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[2]  T. Başar,et al.  Dynamic Noncooperative Game Theory , 1982 .

[3]  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.

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

[5]  P. Morris.  Introduction to Game Theory , 1994 .

[6]  T. Başar,et al.  A Stackelberg Network Game with a Large Number of Followers , 2002 .

[7]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[8]  L. Pavel,et al.  Application of robust L2 control to erbium doped fiber amplifier: Input and state uncertainty , 2006, 2006 IEEE Conference on Computer Aided Control System Design, 2006 IEEE International Conference on Control Applications, 2006 IEEE International Symposium on Intelligent Control.

[9]  Kumar N. Sivarajan,et al.  Optical Networks: A Practical Perspective , 1998 .

[10]  Tansu Alpcan,et al.  Power Control for Multicell CDMA Wireless Networks: A Team Optimization Approach , 2005, WiOpt.

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

[12]  Abdulsalam Yassine,et al.  Competitive game theoretic optimal routing in optical networks , 2002, SPIE/OSA/IEEE Asia Communications and Photonics.

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

[14]  Tim Roughgarden,et al.  Bounding the inefficiency of equilibria in nonatomic congestion games , 2004, Games Econ. Behav..

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

[16]  M. Osborne.  Introduction to Game Theory: International Edition , 2009 .

[17]  A. Rubinstein,et al.  Bargaining and Markets , 1991 .

[18]  Lacra Pavel,et al.  GEN02-1: Hierarchical Iterative Algorithm for a Coupled Constrained OSNR Nash Game , 2006, IEEE Globecom 2006.

[19]  Lacra Pavel,et al.  An extension of duality to a game-theoretic framework , 2007, Autom..

[20]  Lacra Pavel,et al.  A noncooperative game approach to OSNR optimization in optical networks , 2006, IEEE Transactions on Automatic Control.

[21]  J. Aitchison,et al.  Controlling a Semiconductor Optical Amplifier Using a State-Space Model , 2007, IEEE Journal of Quantum Electronics.

[22]  A. Rubinstein,et al.  Bargaining and Markets. , 1991 .

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

[24]  A. Berman,et al.  2. Nonnegative Matrices , 1994 .

[25]  Jean C. Walrand,et al.  High-performance communication networks , 1999 .

[26]  Quanyan Zhu,et al.  Solving constrained OSNR Nash game in WDM optical networks with a fictitious player , 2007, 2007 Fourth International Conference on Broadband Communications, Networks and Systems (BROADNETS '07).

[27]  Lacra Pavel.  OSNR optimization in optical networks: modeling and distributed algorithms via a central cost approach , 2006, IEEE Journal on Selected Areas in Communications.

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

[29]  F. Forghieri,et al.  Simple model of optical amplifier chains to evaluate penalties in WDM systems , 1998 .