Stability of traffic flow with distributed delays modeling the memory effects of the drivers

Rifat Sipahi, Fatihcan M. Atay, and Silviu-Iulian Niculescu

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Submission date: 02. Nov. 2006
published in: SIAM journal on applied mathematics, 68 (2007) 3, p. 738-759 
DOI number (of the published article): 10.1137/060673813
Bibtex
with the following different title: Stability of traffic flow behavior with distributed delays modeling the memory effects of the drivers
MSC-Numbers: 34K20, 34K60, 93D20
Keywords and phrases: traffic, delay, memory

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 human 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 addresses the inevitable heterogeneity of the drivers’ variations in 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.