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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Khalil, H.K.: Nonlinear Systems, 3rd edn. Prentice Hall, New York (2002)
Paganini, F., Wang, Z., Doyle, J.C., Low, S.H.: Congestion control for high performance, stability, and fairness in general networks. IEEE/ACM Trans. Netw. 13(1), 43–55 (2005)
Stefanovic, N.: Robust power control of optical networks with time-delays. Ph.D. thesis, University of Toronto, Toronto, Canada (2010)
Stefanovic, N., Pavel, L.: Link level power control of optical networks with time-delay. In: Proceedings of the 46th IEEE Conference on Decision and Control, December, pp. 5198–5203 (2007)
Stefanovic, N., Pavel, L.: A Lyapunov–Krasovskii stability analysis for game-theoretic based power control in optical networks. In: Proceedings of GameComm 2008, October (2008)
Stefanovic, N., Pavel, L.: Robust power control of optical links with time-delay. In: Proceedings of European Control Conference, Budapest, Hungary, August (2009)
Stefanovic, N., Pavel, L.: Robust power control of single sink optical networks with time-delays. In: Proceedings of the 48th IEEE Conference on Decision and Control, Shanghai, China, December, pp. 2034–2039 (2009)
Stefanovic, N., Pavel, L.: A stability analysis with time-delay of primal-dual power control in optical links. Automatica 45(5), 1319–1325 (2009)
Stefanovic, N., Pavel, L.: A Lyapunov–Krasovskii stability analysis for game-theoretic based power control in optical links. J. Telecommun. Syst. 47(1), 19–33 (2011)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2012 Springer Science+Business Media New York
About this chapter
Cite this chapter
Pavel, L. (2012). Robustness and Delay Effects on Network Games. In: Game Theory for Control of Optical Networks. Static & Dynamic Game Theory: Foundations & Applications. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-8322-1_11
Download citation
DOI: https://doi.org/10.1007/978-0-8176-8322-1_11
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-8321-4
Online ISBN: 978-0-8176-8322-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)