A sensitivity-based approach for adaptive decomposition of anticipatory network traffic control

Anticipatory optimal network control is defined as the problem of determining the set of control actions that minimizes a network-wide objective function. This not only takes into account local consequences on the propagation of flows, but also the global network-wide routing behavior of the users. Such an objective function is, in general, defined in a centralized setting, as knowledge regarding the whole network is needed to correctly compute it. Reaching a level of centralization sufficient to attain network-wide control objectives is however rarely realistic in practice. Multiple authorities are influencing different portions the network, separated either hierarchically or geographically. The distributed nature of networks and traffic directly influences the complexity of the anticipatory control problem. This is our motivation for this work, in which we introduce a decomposition mechanism for the global anticipatory network traffic control problem, based on dynamic clustering of traffic controllers. Rather than solving the full centralized problem, or blindly performing a full controller-wise decomposition, this technique allows recognizing when and which controllers should be grouped in clusters, and when, instead, these can be optimized separately. The practical relevance with respect to our motivation is that our approach allows identification of those network traffic conditions in which multiple actors need to actively coordinate their actions, or when unilateral action suffices for still approximating global optimality. This clustering procedure is based on well-known algebraic and statistical tools that exploit the network's sensitivity to control and its structure to deduce coupling behavior. We devise several case studies in order to assess our newly introduced procedure's performances, in comparison with fully decomposed and fully centralized anticipatory optimal network control, and show that our approach is able to outperform both centralized and decomposed procedures.