A non-equilibrium traffic model devoid of gas-like behavior

The validity of existing higher-order continuum models has been seriously challenged in recent literature. A primary objection to these models is that they exhibit gas-like behavior, that is, they predict that vehicles from behind can influence the behavior of vehicles in front, as elucidated by Daganzo [Transp. Res. B 29 (1995) 277]. Considerable efforts devoted to remove this deficiency (del Castillo et al. [In: C.-F. Daganzo (Ed.), Transportation and Traffic Theory, Elsevier Science, Amsterdam, 1993, p. 387], Zhang [Transp. Res. B 32(7) (1998) 485; Transp. Res. B 33(6) (1999) 387; Transp. Res. B 34 (2000) 583]) have met with only partial success. In this paper we present a non-equilibrium traffic model shown to be devoid of the gas-like behavior that plagues other higher-order models. The system of partial differential equations that describes this model is hyperbolic and has two characteristic fields: one is genuinely nonlinear and the other is linearly degenerate. The first field gives rise to shock and rarefaction waves that are similar to those of the Lighthill–Whitham–Richards (LWR) model, while the second field produces contact discontinuities. All these waves travel no faster than traffic; thus the trajectory of a vehicle cannot be influenced by what happens behind it. The model is also shown to exhibit correct queue-end behavior and is able to explain some of the observed traffic phenomena that challenge old models.