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In car-following models, the driver reacts according to his physical andpsychological abilities which may change over time. However, most car-followingmodels are deterministic and do not capture the stochastic nature of humanperception. It is expected that purely deterministic traffic models may produceunrealistic results due to the stochastic driving behaviors of drivers. Thispaper is devoted to the development of a distinct car-following model where astochastic process is adopted to describe the time-varying random accelerationwhich essentially reflects the random individual perception of driver behaviorwith respect to the leading vehicle over time. In particular, we apply coupledLangevin equations to model complex human driver behavior. In the proposedmodel, an extended Cox-Ingersoll-Ross (CIR) stochastic process will be used todescribe the stochastic speed of the follower in response to the stimulus ofthe leader. An important property of the extended CIR process is to enhance thenon-negative properties of the stochastic traffic variables (e.g. non-negativespeed) for any arbitrary model parameters. Based on stochastic processtheories, we derive stochastic linear stability conditions which, for the firsttime, theoretically capture the effect of the random parameter on trafficinstabilities. Our stability results conform to the empirical results that thetraffic instability is related to the stochastic nature of traffic flow at thelow speed conditions, even when traffic is deemed to be stable fromdeterministic models.

Langevin method for a continuous stochastic car-following model and its stability conditions