Recent Advances in Nonlinear Dynamics and Synchronization

Abstract

The efficient and reliable operation of material flows in transportation networks is a subject of broad economic interest. Important applications include the control of signalized intersections in urban road systems and the planning and scheduling of logistic processes. Traditional approaches to operating material flow networks are however known to have severe disadvantages: centralized controllers suffer from their high computational demands that make an on-line control hardly possible in larger networks, whereas a decentralized control using clearing policies leads under rather general conditions to instabilities. A particular solution for optimizing flows on a network that has attracted considerable interest in the case of urban traffic networks over the last 50 years is synchronizing sequences of traffic lights so that "green waves" emerge. However, the practical applicability of this very basic synchronization strategy is unfortunately restricted to only few special cases. More recent synchronization approaches to optimizing transportation networks suggest a mutual adjustment of the service periods of neighboring facilities by exclusively local information transfer, yielding self-organized phase synchronization. Traditionally, these concepts have been motivated by theoretical results on the dynamics of coupled phase oscillators, which model the switching cycle of traffic lights at signalized intersections. The corresponding results are thoroughly reviewed in this chapter. As an alternative approach that may help to overcome the problems of standard central as well as decentralized controllers and make an adaptive and purely demand-driven traffic light control practically applicable, a self-organization mechanism of conflicting flows is proposed that is inspired by oscillatory phenomena of pedestrian and animal flows at intersections or bottlenecks. For this purpose, a permeability function is introduced that allows to sequentially serve the different possible flow directions at an intersection in a fully demand-dependent way. The self-organized optimization achieved by the presented approach is demonstrated to be closely linked to synchronization of the oscillatory service dynamics at the different intersections in the network. For regular grid topologies, different synchronization regimes are present depending on the inertia of the switching from one service state to the next one. The dependence of this observation on the regularity of the considered network is tested. The reported results contribute to an improved understanding of the conditions that have to be present for efficiently operating material flow networks by a decentralized control, which is of major importance for future implementations in real-world traffic or production systems. © 2009 Springer-Verlag Berlin Heidelberg.