REQUIEM FOR 2ND-ORDER FLUID APPROXIMATIONS OF TRAFFIC FLOW

Although the ''first order'' continuum theory of highway traffic propo sed by Lighthill and Whitham (1955) and Richards (1956)-the LWR model- can predict some things rather well, it is also known to have some def iciencies. In an attempt to correct some of these, ''higher order'' th eories have been proposed starting in the early 70s. Unfortunately, th e usefulness of these improvements can be questioned. This note descri bes the logical flaws in the arguments that have been advanced to deri ve higher order continuum models, and shows that the proposed high ord er modifications lead to a fundamentally flawed model structure. The m odifications can actually make things worse. As an illustration of thi s, it is shown that any continuum model of traffic flow that smooths o ut all discontinuities in density will predict negative flows and nega tive speeds (i.e., ''wrong way travel'') under certain conditions. Suc h unreasonable predictions are made by all existing models formulated as a quasilinear system of partial differential equations in speed, de nsity, and (sometimes) other variables but not by the LWR model. The n ote discusses the available empirical evidence and ends with a (hopefu lly positive) commentary on what can be accomplished with first-order models.