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1 introduction  1.1  motivation  1.2  objectives  1.3  contributions  1.4  organization2 literature review  2.1  introduction  2.2  historical development of traffic flow theory    2.2.1  macroscopic modeling    2.2.2  mesoscopic modeling    2.2.3  microscopic modeling    2.2.4  stochastic modeling  2.3  probabilistic headway/spacing distributions    2.3.1  simple univariable distributions    2.3.2  compositional distributions    2.3.3  mixed distributions    2.3.4  random matrix model  2.4  summary3 empirical observations of stochastic and dynamic evolutions of traffic flow  3.1  introduction  3.2  characteristics of headway/spacing/velocity  3.3  congested platoon oscillations  3.4  time-frequency properties  3.5  summary4 a markov model based on headway/spacing distributions  4.1  introduction  4.2  a markov model for headway/spacing distributions    4.2.1  background    4.2.2  markov-process simulation models    4.2.3  simulation results    4.2.4  discussions   4.3  asymmetric stochastic tau theory in car-following    4.3.1  asymmetric stochastic extension of the tau theory    4.3.2  testing results    4.3.3  discussions5 stochastic fundamental diagram based on headway/spacing distributions  5.1  introduction  5.2  newell's simplified model and its stochastic extension  5.3  the homogeneous platoon model    5.3.1  basic idea    5.3.2  summation of lognormal random variables    5.3.3  average headway distribution    5.3.4  model validation    5.3.5  sensitivity analysis  5.4  the heterogeneous platoon model    5.4.1  average headway distribution    5.4.2  validation    5.4.3  boundaries of congested flows  5.5  summary6 traffic flow breakdown model based on headway/spacing distributions  6.1  introduction  6.2  nonparametric lifetime statistics approach  6.3  queueing models for breakdown probability    6.3.1  backgrounds    6.3.2  some previous models    6.3.3  g/g/1 queueing model    6.3.4  discussions    6.3.5  model validation    6.3.6  summary  6.4  phase diagram analysis    6.4.1  backgrounds    6.4.2  the spatial-temporal queueing model    6.4.3  the analytical solution for phase diagram    6.4.4  numerical example  6.5  discussions7 conclusions and future workappendix a: linear stability analysis of the higher-order macroscopic modelappendix b: linear stability analysis of the multi-anticipative car-following modelsreferencesindex