LRW (Lighthill,

Whitham, Richard)

OR Continuum Model

・ Model suggests Preferred speeds

・ Different vehicles have different preferred speeds

・ Predicts abrupt speed change when a vehicle passes through a shockwave, an action that is unrealistic in real world.

・ LWR model fails to predict instabilities of stop-start traffic

・ LWR model assumes zero reaction time which does not happen in real world

PW Model: Payne-Whitham

・ Like LRW model, It does not remove all the shock waves

・ Vehicles are expected to adjust their speeds in relation to the rear vehicles, while in reality vehicles respond to thread

・ Proposed wave speeds are greater than traffic speeds. Again primarily because it derives the recommendations from rear vehicles

Kalman filtering


・ Velocity of an individual vehicle is assumed to correspond to the velocity at that given location

・ The velocity-to-density conversion, introduces error

・ Measurement error in the velocity