Dynamic representation of the fundamental diagram via Bayesian networks for estimating traffic flows from probe vehicle data

Area-wide measurements of traffic flow are usually not possible with today's common sensor technologies. However, such information is essential for (urban) traffic planning and control. Hence, in order to support traffic managers, this paper analyses an approach for deriving traffic flows from probe vehicle speeds, which are potentially available with a wide spatial coverage. The idea is to apply the speed-flow function as known from macroscopic traffic flow theory. In this context, a stochastic representation of the fundamental diagram via Bayesian networks is proposed which also considers the temporal dependencies and transitions between the appearing traffic states. The paper describes the relevant theoretical concepts in comparison to the traditional approach of fitting deterministic curves to empirical speed-flow relations. Moreover, it analyses the findings of an extensive validation in context of traffic flow estimation via probe vehicle data using real traffic measurements provided by about 600 local detectors and about 4,300 taxi probes in Berlin, Germany.