1.3　Contributions

This book contains several contributions to the state of art in stochastic traffic flow modeling based on headway/spacing distributions．

• A microscopic unified Markov-process car-following model：stochastic behaviors in unconscious and inaccurate perceptions of headway/spacing．
  We link two research directions of road traffic，the mesoscopic headway distribution model and the microscopic vehicle interaction model，together to account for the empirical headway/spacing distributions．A unified car-following model（a Markov-headway model for high velocity and a Markov-spacing model for low velocity）will be proposed to simulate different driving scenarios，including traffic on highways and at intersections．The parameters of this model are directly estimated from the Next Generation Simulation（NGSIM）trajectory data．Empirical headway/spacing distributions are viewed as the outcomes of stochastic car-following behaviors and the reflections of the unconscious and inaccurate perceptions of space and/or time intervals that people may have．This explanation can be viewed as a natural extension of the well-known psychological car-following model（the action point model）．The psychological explanation by the asymmetric stochastic extension of the Tau theory will be also presented．Furthermore，the fast simulation speed of this model will benefit transportation planning and surrogate testing of traffic signals．
• A macroscopic stochastic fundamental diagram model：characterizing scattering features in flow-density plots using a stochastic platoon model．
  Fundamental diagram is observed as wide scattering in the congested flow regime that requires a stochastic mechanism to explain this feature．Based on the Newell's simplified car-following model，we discuss the implicit but tight connection between the microscopic spacing/headway distributions and the macroscopic scattering feature of flow-density plot．We examine microscopic driving behaviors that are retrieved from the NGSIM trajectory database and study the asymmetric driving behaviors that result in a family of velocity-dependent lognormal type headway/spacing distributions．Then，we propose a stochastic platoon model to characterize the distribution of points in spacing-velocity plot．Extending the Newell's simplified car-following model，we finally discuss the distribution of points in the flow-density plot．
• A traffic flow breakdown model for highway ramp bottlenecks：empirical observations，queueing theory and phase diagram analysis．
  We will incorporate the queueing theory to describe traffic breakdown phenomena caused by ramping vehicle perturbations．The traffic breakdown probability directly corresponds with the probability that this jam queue dissipates in a given time period．The proposed queueing theory based model emphasizes the size evolution of a jam queue（local congested vehicle cluster）instead of its spatial evolutions．This model will capture the stochastic nature of traffic flow dynamics and therefore accounts for the probability of breakdown phenomena．
  We will propose a simple spatial-temporal queueing model based on Newell's simplified car-following model to quantitatively address some typical congestion patterns that were observed around on/off-ramps．Particularly，we examine three prime factors that play important roles in ramping traffic scenarios：the time for a vehicle to join a jam queue，the time for this vehicle to depart from this jam queue，and the time interval for the ramping vehicle to merge into the mainline．The analytically derived phase diagram will be compared with the simulation results．We will show that the new queueing model not only reserves the merits of Newell's model on the microscopic level but also helps quantify the contributions of these parameters in characterizing macroscopic congestion patterns．

In summary，from an academic point of view，our study advances the knowledge on stochastic traffic flow modeling in both microscopic car-following models and macroscopic fundamental diagram contexts；from a practice point of view，this study reveals the numerous underlying aspects of empirical traffic measurements，including the complex，dynamic and stochastic phenomena of highway traffic flow． HL8yNW/QDn8XOck/N8m7Z4/xW51ISTofmAJx+LocrWdDPIcKrkmyAgeXMSfYCOqH