Robustness and delay effects on network games

Abstract

This chapter presents results on robustness of network control algorithms derived from game-theoretic formulations in the presence of time delay. Mesh optical networks are distributed over large surface areas. Any realistic OSNR model must account for these delays. Sufficiently large time delays may destabilize the closed-loop systems that implement these game-theoretic-inspired control algorithms. These algorithms need to have been appropriately adjusted so as to ensure closed-loop stability in the presence of time delays. We consider delay effects in network games without constraints, followed by games with constraints. Then we study a delayed primal–dual algorithm and perform a two time-scale stability analysis. We conclude by considering robustness and delay effects combined.