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. (C) 2001 Elsevier Science Ltd. All rights reserved.