A Proposed Definition of Traffic Flow in Continuous Transportation Models

Abstract

The paper deals with the problem of how to define traffic flow in a continuous transportation model. A hydrodynamic analogy with continuously distributed sources and sinks, where a continuum of vector fields represents the communication system, is used. Traffic is defined as an integral of the moduli of all these vector fields. The definition is seen to provide for conservation of traffic. The measure is compared to those obtained by counting ‘cordon crossings’. It is seen that a measure obtained in this way agrees with the one proposed if the cordon crossings are weighted by the reciprocals of the cosines of the incidence angle.