Calibration of second order traffic models using continuous cross entropy method

Abstract

Second order macroscopic traffic flow models are often used to replicate non-linear traffic flow phenomena such as phantom traffic jams or traffic instabilities. In contrast to the (first order) Lighthill–Whitham–Richards (LWR) traffic model, which assumes an equilibrium speed-density relationship (or so-called fundamental diagram), the second order model uses one more dynamic equation to describe the evolution of the speed, therefore allows the speed to fluctuate around the equilibrium diagram. In general, in the second order model, a given model parameter set may exhibit traffic instabilities due to a small initial traffic perturbation (e.g. lane-changing or sudden deceleration). Therefore, small changes of parameter set in second order models will lead to completely different model performance, which consequently leads to a complex calibration effort and hence prohibits its real-life application as compared to the LWR model. So far relatively few calibration results for general macroscopic traffic flow models have been reported. To contribute to the state-of-the-art, this paper puts forward an effort to find global optimal parameters of a second order macroscopic traffic model using a stochastic optimization approach, namely cross entropy method (CEM). Basically, the CEM is set up to solve combinatorial optimization problems so the main novelty of this paper is to apply the CEM to solve continuous multi-extremal optimization problems in transportation through the use of the Kernel density estimation method. Numerical studies are carried out to show that the Kernel-based CEM can search for the global optimal model parameters in a second order model and is a promising method for the calibration of traffic models in general.