Exploring the Behavior of LWR Continuum Models of Traffic Flow in Presence of Shock Waves

LWR (Lighthill-Whitham-Richards) models represent the behavior of traffic streams through the continuity equation and an assumed equilibrium speed-density relationship. Such models assume traffic streams to be always in equilibrium. That is it assumes that the speed and density values at any point in the stream at any time are according to the equilibrium relation. This paper shows that in the presence of shocks this assumption is not valid for every equilibrium speed-density relation.