Abstract
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.
Keywords
human drivers, memory effects, distributed delays, traffic flow stability
Subject Categories
Delivery of goods--Mathematical models.
Disciplines
Systems Engineering
Publisher
SIAM
Publication Date
12-20-2007
Rights Information
© 2007 Society for Industrial and Applied Mathematics
Rights Holder
Society for Industrial and Applied Mathematics
Permanent URL
Recommended Citation
Sipahi, Rifat; Atay, Fatihcan M.; and Niculescu, Silviu-Julian, "Stability of traffic flow behavior with distributed delays modeling the memory effects of the drivers" (2007). . Paper 10. http://hdl.handle.net/2047/d10009395
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Notes
Originally published in SIAM Journal on Applied Mathematics v.68 no.3 (2007), pp.738-759. DOI:10.1137/060673813