Investigation of stochastic variation of parameters for a macroscopic traffic model

ABSTRACT This paper proposes a novel approach to include stochastic variation in the framework of a macroscopic traffic model. Simultaneously, the effects of insufficient data quality and consequent inaccurate identification are investigated. The traffic density distribution over time and space provides a deeper understanding of the evolution of jams, which in turn is vital for the development of traffic network control algorithms. Model parameters are estimated using both Eulerian and Lagrangian sensing. Instead of using deterministic model parameters directly, this work proposes to use stochastic model parameters. Therefore, in addition to the estimated mean of model parameters, a corresponding covariance matrix is estimated as well. The utilized traffic model supports arbitrary Fundamental Diagrams defined by (a combination of) model parameters. Using an analytic approach to define the resulting variation in the Fundamental Diagram is generally impossible, due to the nonlinear combination of random variables in the parameterization of the Fundamental Diagram. A general approach to deal with complex combinations of random variables in the definition of Fundamental Diagrams and, consequently, in the traffic model, is proposed. The core idea is to utilize Monte Carlo Simulation to create a discretized lookup table for the density–speed relationship. Thereby computational effort is significantly reduced, while preserving the ability of the traffic model to reflect variation in the driving behavior. The proposed approach is validated via simulation with state-of-the-art software and Monte Carlo Simulations.