Lyapunov-Based Design of a Distributed Wardrop Load-Balancing Algorithm With Application to Software-Defined Networking

Abstract

This paper presents an original discrete-time, distributed, non-cooperative load balancing algorithm, based on mean field game theory, which does not require explicit communications. The algorithm is proved to converge to an arbitrarily small neighborhood of a specific equilibrium among the loads of the providers, known as Wardrop equilibrium. Thanks to its characteristics, the algorithm is suitable for the Software Defined Networking (SDN) scenario, where service requests coming from the network nodes, i.e., the switches, are managed by the so-called SDN Controllers, playing the role of providers. The proposed approach is aimed at dynamically balancing the requests of the switches among the SDN Controllers to avoid congestion. The paper also suggests the adoption of SDN Proxies to improve the scalability of the overall SDN paradigm and presents an implementation of the algorithm in a proof-of-concept SDN scenario, which shows the effectiveness of the proposed solution with respect to the current approaches.

Wardrop Equilibrium in Discrete-Time Selfish Routing With Time-Varying Bounded Delays

“…The present work extends the results of previous works from the authors [24], [25] and the ones available in literature mainly in two directions: (i) the asymptotic analysis and algorithm design are extended to the multi-commodity case, which is not explicitly discussed in the cited works, enabling the application to more realistic scenarios; (ii) the agents of the various commodities are provided with a measure of the network state subject to heterogeneous, time-varying, unknown but bounded delays; in this respect, differently from [20], which only analyses the tolerance to delays of the algorithm developed therein, here the delays are explicitly considered and compensated within the algorithm development.…”

“…The LaSalle invariance principle for discrete-time nonlinear in [24]. In this paper, strictly increasing functions are assumed for the sake of simplicity.…”

“…However, by using these standard migration policies in the discrete-time, it can be shown that convergence cannot be guaranteed even in the delay-free case, however small the sampling time is chosen [20]. In [24], a modified better response policy to achieve an -Wardrop equilibrium in the discrete-time, single-commodity case (corresponding to a ( , 0)-Wardrop equilibrium, as per definition (4)) is proposed:…”

“…Here, we further modify the migration policy of [24] by considering the latency measures instead of the current latency values to cope with the delays:…”

“…Note that, due to equation (26), is now an additional controller design parameter. In [24], a time-varying tolerance law is proposed for the single-commodity delay-free case, where [ ] is proportional, by a parameter 0 < < 1, to the current maximum latency mismatch. Taking inspiration from that idea, the proposed timevarying tolerance law and the controller gain are defined as…”