Games with coupled propagated constraints in optical networks with multi-link topologies

Authors:
Yan Pan;Lacra Pavel
Affiliations:
Department of Electrical and Computer Engineering, University of Toronto, 10 King's College Road, Toronto, ON, M5S 3G4, Canada;Department of Electrical and Computer Engineering, University of Toronto, 10 King's College Road, Toronto, ON, M5S 3G4, Canada
Venue:
Automatica (Journal of IFAC)
Year:
2009

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Abstract

We consider games in optical networks in the class of m-player games with coupled utilities and constraints. Nash equilibria of such games can be computed based on recent extension of duality to a game theoretical framework. This work extends previous results on games with coupled constraints in optical links to multi-link topologies. Coupled constraints in optical networks are propagated along links, which introduces additional complexities for analysis. Specifically, convexity of the propagated constraints is no longer automatically ensured. We show that convexity is satisfied for single-sink multi-link topologies. The general case of multi-links with arbitrary sources and sinks is dealt with by a partitioned game with stages. We exploit the single-sink structure of each stage and the ladder-nested form of the game and we discuss iterative computation of equilibria based on a three-level hierarchical algorithm and prove its convergence under certain conditions.