Macroscopic Traffic Flow Characterization for Stimuli Based on Driver Reaction

The design and management of infrastructure is a significant challenge for traffic engineers and planners. Accurate traffic characterization is necessary for effective infrastructure utilization. Thus, models are required that can characterize a variety of conditions and can be employed for homogeneous, heterogeneous, equilibrium and non-equilibrium traffic. The Lighthill-Whitham-Richards (LWR) model is widely used because of its simplicity. This model characterizes traffic behavior with small changes over a long idealized road and so is inadequate for typical traffic conditions. The extended LWR model considers driver types based on velocity to characterize traffic behavior in non lane discipline traffic but it ignores the stimuli for changes in velocity. In this paper, an improved model is presented which is based on driver reaction to forward traffic stimuli. This reaction occurs over the forward distance headway during which traffic aligns to the current conditions. The performance of the proposed, LWR and extended LWR models is evaluated using the first order upwind scheme (FOUS). The numerical stability of this scheme is guaranteed by employing the Courant, Friedrich and Lewy (CFL) condition. Results are presented which show that the proposed model can characterize both small and large changes in traffic more realistically. Doi: 10.28991/cej-2021-03091632 Full Text: PD

On the Derivation of the Velocity and Fundamental Traffic Flow Diagram from the Modelling of the Vehicle-Driver Behaviors

reserved2This paper deals with derivation of the fundamental diagram by modelling the individual driver behavior that adjusts the velocity to the density of vehicles in order to respect the braking distance. A parameter is properly introduced to model the quality of the drivervehicle subsystem referred to the environmental conditions. Subsequently, it is shown how to use this result in order to model traffic flows by the macroscopic representation and by the kinetic theory.Bonzani, I.; L. Mussone, L.Bonzani, I.; Mussone, Lorenz

MCMC for a hyperbolic Bayesian inverse problem in motorway traffic flow

We study the LWR model: a hyperbolic conservation law used to model traffic flow on motorways. This is an old model dating back to the 1950s, but has been shown to be robust and is parametrised by the so-called Fundamental Diagram (FD) which provides the relationship between flow and density. We consider the boundary conditions as nuisance parameters to be estimated but neglect the initial conditions as their effect on data is quickly washed out. // The data we use to estimate the parameters in the model is MIDAS data on a section of motorway that does not include any on/off ramps, thus conforming with the nature of the model as a conservation law. Little statistically sound work has been done so far on this inverse problem to estimate the FD parameters as well as the boundary conditions. // We consider two families of FDs, Del Castillo’s FD and the exponential FD – which have 4 and 2 parameters respectively – and perform inference for these along with the boundary conditions. We assume as prior that the boundary conditions follow a log Ornstein Uhlenbeck process which corresponds surprisingly well to practitioners’ prior belief. // We use standard MCMC methods (Gibbs, RWMH, parallel tempering, functional preconditioned RWMH) to sample from the posterior distribution. For some models, the posterior is highly correlated, multimodal and non-Gaussian, so we introduce novel proposals and find that while these are underpinned by clear intuition and show great promise in preliminary studies, they do not seem to appreciably accelerate mixing judging from the studies carried out so far