Directed and diffusive contributions to urban traffic flow patterns

– As a result of an extensive field trial in Frankfurt/Main, the urban traffic pattern is represented by a distribution of local entropy variables. This letter aims at reproducing this distribution by use of two arguments —a geometrical and a hierarchical one. A characteristic scaling relation for urban traffic is derived. Introduction: urban traffic patterns. – Vehicular traffic flow has for some time been in the focus of physical research. Initially, problems of the collective vehicle dynamics were tackled either by the hydrodynamic school of modelling [1–5], or by the computer-friendly school of cellular automata (CA) [6,7]. Meant to describe predominantly motorway phenomena where long road segments without structural attributes allow for the relaxation of complex vehiclevehicle interaction processes, the road network itself as a structural variable did not figure in these early works. In urban traffic the vehicular flow is, however, primarily shaped by properties of just this network rather than the vehicle-vehicle interactions: the (co-operative) design of traffic signals, individual route choice behaviour, the hierarchicity of different road classes and legal regulations determine the urban traffic patterns at least as much as the sheer transport volumes. Recently, several workers have addressed different facets of this spectrum of urban traffic, e.g.: the authors of [8] have presented a detailed analysis of the turning dynamics at non-signalled intersections; the authors of [9] and [10] investigated the interaction of geometrically interacting vehicle flows in a specially designed (urban) road network (with [11] as an important theoretical trail-blazer) and the authors of [12] introduced elements of game theory into the analysis of drivers’ route choice behaviour. The present letter makes use of a recent development in traffic monitoring: so-called floating car data (FCD) allow to track specially equipped vehicles continually (depending on configuration) over their trajectories in a considered road network. (From the physicists’ point of view, FCD are equivalent to tracer dynamics, i.e. to reconstructing a flow picture from information on the behaviour of representative particles.) In particular, turning relations at intersections are immediately accessible because of the vectorial character of FCD such that local origin-destination matrices (ODM) can be directly measured. Given a sufficient spatio-temporal density of the FCD, it is thus principally possible to map the complete