Journal
SIAM JOURNAL ON APPLIED MATHEMATICS
Volume 60, Issue 3, Pages 916-938Publisher
SIAM PUBLICATIONS
DOI: 10.1137/S0036139997332099
Keywords
traffic flow; conservation laws
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We introduce a new second order model of traffic flow. As noted in [C. Daganzo, Requiem for second-order fluid with approximation to traffic flow, Transportation Res. Part B, 29 (1995), pp. 277-286], the previous second order models, i.e., models with two equations (mass and momentum), lead to nonphysical effects, probably because they try to mimic the gas dynamics equations, with an unrealistic dependence on the acceleration with respect to the space derivative of the pressure. We simply replace this space derivative with a convective derivative, and we show that this very simple repair completely resolves the inconsistencies of these models. Moreover, our model nicely predicts instabilities near the vacuum, i.e., for very light traffic.
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