Games with coupled propagated constraints in optical networks: The multi-link case

Abstract

This work extends previous results on games with coupled constraints in optical links to general multi-link topologies. Nash equilibria of such games can be computed based on recent extension of duality to a game theoretical framework. Unlike capacity constraints in flow control, coupled constraints in optical networks are propagated along links. This introduces additional complications for analysis. Specifically, convexity of the propagated constraints is no longer automatically ensured. We show that convexity is satisfied for the special case of multi-links with a single sink. The general case of multi-links with arbitrary sources and sinks is dealt with by a partitioned (modified) game with stages. We exploit the single sink structure of each stage and the ladder-nested form of the game.