Speed-Density Relationship: From Deterministic to Stochastic

Traffic flow is a many-car system with complex and stochastic movement. It is difficult to describe the system dynamics solely by using deterministic tools. Therefore, a stochastic speed-density relationship is proposed here as a further step forward to overcome the well known drawbacks of deterministic models. Modeling results show that by taking care of second order statistics (i.e., mean and variance) a stochastic speed-density model is suitable for describing the observed phenomenon as well as matching the empirical data. Starting from here, a stochastic fundamental diagram of traffic flow could be established. The stochastic speed-density relationship model can potentially be used for real-time on-line prediction and to explain phenomenons in a similar manner.

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