Stability of Traffic Flow Behavior with Distributed Delays Modeling the Memory Effects of the Drivers

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 bas...

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Bibliographic Details
Published in:SIAM journal on applied mathematics 2007-01, Vol.68 (3), p.738-759
Main Authors: Sipahi, Rifat, Atay, Fatihcan M., Niculescu, Silviu-Iulian
Format: Article
Language:English
Subjects:
Computer Science
Control theory
Decision making
Eigenvalues
Flow velocity
Memory
Method of characteristics
Modeling
Motor vehicle traffic
System theory
Traffic congestion
Traffic delay
Traffic flow
Traffic models
Vehicles
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Summary: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.
ISSN:0036-1399
1095-712X
DOI:10.1137/060673813