California Partners for Advanced Transportation Technology

This paper presents a simple representation of traffic on a highway with a single entrance and exit. The representation can be used to predict traffic's evolution over time and space, including transient phenomena such as the building, propagation and dissipation of queues. The easy-to-solve difference equations used to predict traffic's evolution are shown to be the discrete analog of the differential equations arising from a special case of the hydrodynamic model of traffic flow. The proposed method automatically generates appropriate changes in density at locations where the hydrodynamic theory would call for a shockwave; i.e. a jump in density such as those typically seen at the end of every queue. The complex side calculations required by classical methods to keep track of shockwaves are thus eliminated. The paper also shows how the equations can mimic the real-life development of stop-and-go traffic within moving queues. The model predicts that the oscillation pattern is independent of the initial impulse from downstream (as one would expect), and that oscillations should not increase delay unless they result in car stalls or other incidents. The results in this paper can be used for simple traffic engineering analyses. Most importantly, they are a fundamental building block for traffic prediction over networks. The ability to make such predictions can lead to better strategies for ramp metering and incident detection. A sequel to this paper will examine highway networks. The representation's simplicity should make it possible to keep track of each vehicle's final destination throughout a simulation, even for complex networks. This capability should help improve traffic control packages and dynamic traffic assignment methods.