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This book aims to investigate the stochastic evolution modeling for highway traffic flow to reveal the mechanism of complex and dynamic traffic congestion．We will first review the existing studies on stochastic traffic flow approaches and probabilistic distributions of headway/spacing．Motivated both by the availability of vehicle trajectory data，and by the need for traffic congestion reduction，the goal of this book is to develop a framework of stochastic traffic flow evolution analysis by using Eulerian and Lagrangian field measurements that empirically reveal the important characteristics of traffic congestion．
We aim to emphasize the features of headway/spacing/velocity distributions，which establish a tight connection between microscopic and macroscopic traffic flow approaches．We also target to adapt these empirical observations into stochastic modeling problems by proposing a Markov car-following model and a stochastic fundamental diagram model，because the randomness explicitly embedded in these models could be reasonably explained as the outcome of the unconscious and also inaccurate perceptions of space and/or time interval that people have．We will study a behavioral or psychological mechanism that is different from other approaches to explain the stochastic traffic flow features．
We aim to develop a traffic flow breakdown probability model and its corresponding phase diagram approach to explore the phenomena that occur with continuous oscillations and lead to a wide range of spatial-temporal traffic congestion near on-ramp bottlenecks．We will study the transition process from perturbations to traffic jams in the metastable traffic flow，and the varying features of traffic flow breakdown by using vehicle trajectory data．This model will benefit the optimal control models of active traffic management by minimizing traffic flow breakdown probability and maximizing the expectation of stochastic traffic capacity．