Transportation research board natl research council
Traffic flow theory and highway capacity and quality of services 2004 issue:1883 pages:21-30
The structural properties of the shock- and rarefaction-wave solutions of a macroscopic, second-order nonlocal continuum traffic flow model, namely, Helbing's model, are analyzed. It is shown that this model has two families of characteristics for the shock-wave solutions: one characteristic is slower and the other one is faster than the average vehicle speed. Corresponding to the slower characteristic are one-shock and one-rarefaction waves, the behavior of which is similar to that of shock and rarefaction waves in the first-order Lighthill-Whitham-Richards model. Corresponding to the faster characteristic are two-shock and two-rarefaction waves, which behave differently from the previous type in the sense that the information in principle travels faster than average vehicle speed, but in Helbing's model this inconsistency is solved by the addition of a nonlocal term. For the Helbing model the shocks do not produce negative states as other second-order models do. The formulas for the solution of the Riemann problem associated with this model in the equilibrium case are also derived.