An analysis of stability with time-delay of link level power control in optical networks

We study the effects of time-delay on the stability of optical networks. A link level power control scheme adjusts the OSNR value of the signals toward channel OSNR optimization. We utilize the OSNR model from [Pavel, L. (2006). A noncooperative game approach to OSNR optimization in optical networks. IEEE Transactions on Automatic Control, 51(5), 848–852] along with its game-theoretic based control algorithm. Time-delay is incorporated into the closed loop system, for the general network case where every link has a unique time-delay. We derive sufficient conditions for stability under arbitrary time-delays and network configurations. The results are verified via extensive simulations.