Modeling the Stochastic Traffic Flow with Markov Jump Linear Hyperbolic Systems

In this paper, we present a new stochastic model on the basis of the switching problem of two modes in the ARZ traffic flow model - Markov jump traffic flow model. The model is a continuous time model, it can accurately capture the state switching of the freeway segment at different times and describes the evolution of traffic flow on the freeway. Compared with the deterministic ARZ model, the model proposes the switching of two modes satisfy Markov stochastic processe and uses Markov state transition rate matrix to describe this processe, which improve the accuracy of the model. In the last part of the paper, some NGSIM data are substituted into the Markov jump traffic flow model for numerical evolution, the reliability and accuracy of the model are verified by comparing with the actual data.