An extended coordinate descent method for distributed anticipatory network traffic control

• Published in: Transportation research. Part B: methodological 2015-10, Vol.80, p.107-131
• Main Authors: Rinaldi, Marco, Tampère, Chris M.J.
• Format: Article
• Language: English
• Subjects: Anticipatory; Anticipatory network traffic control; Control distribution; Descent; Distributed optimization; Mathematical analysis; Mathematical models; Network control; Networks; Optimization; Transportation
• ISSN: 0191-2615; 1879-2367
• DOI: 10.1016/j.trb.2015.06.017

•We pursue and attain network-wide anticipatory control by coordinating local controllers.•The control decomposition scheme optimizes the different controllers separately.•The scheme is guaranteed to converge under specific assumptions.•Our algorithm can be shown to converge to a local optimum in non-convex conditions.•We reformulate our objective function by separating its sensitivity.•This allows to distinguish separate roles in network-wide information gathering.•We couple the scheme with Dial's B algorithm for static assignment.•Optimal control is computed alongside static assignment in the same iterating loop. Anticipatory optimal network control can be defined as the practice of determining the set of control actions that minimizes a network-wide objective function, so that the consequences of this action are taken in consideration not only locally, on the propagation of flows, but globally, taking into account the user’s routing behavior. Such an objective function is, in general, defined and optimized in a centralized setting, as knowledge regarding the whole network is needed in order to correctly compute it. This is a strong theoretical framework but, in practice, reaching a level of centralization sufficient to achieve said optimality is very challenging. Furthermore, even if centralization was possible, it would exhibit several shortcomings, with concerns such as computational speed (centralized optimization of a huge control set with a highly nonlinear objective function), reliability and communication overhead arising. The main aim of this work is to develop a decomposed heuristic descent algorithm that, demanding the different control entities to share the same information set, attains network-wide optimality through separate control actions.