Stability analysis of a single-lane microscopic car-following model is studied analytically from the perspective of delayed reactions of human drivers. In the literature, the delayed reactions of the drivers are modeled with discrete delays, which assume that drivers make their control decisions based on the stimuli they receive from a point of time in the history. We improve this model by introducing a distribution of delays, which assumes that the control actions are based on information distributed over an interval of time in history. Such an assumption is more realistic, as it takes into consideration the memory capabilities of the drivers and the inevitable heterogeneity of their delay times. We calculate exact stability regions in the parameter space of some realistic delay distributions. Case studies are provided demonstrating the application of the results.


Originally published in SIAM Journal on Applied Mathematics v.68 no.3 (2007), pp.738-759. DOI:10.1137/060673813


human drivers, memory effects, distributed delays, traffic flow stability

Subject Categories

Delivery of goods--Mathematical models.


Systems Engineering



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© 2007 Society for Industrial and Applied Mathematics

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Society for Industrial and Applied Mathematics

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