A simplified theory of kinematic waves in highway traffic. Part II: Queueing at freeway bottlenecks

For a freeway having various entrance and exit ramps, the methods described in Part I are used to relate the cumulative flow curve at any junction to the net cumulative entrance flow at this junction, and the cumulative flow curves for the freeway at the next upstream junction and/or the next downstream junction. If the type of flow-density relations typical of freeway traffic are idealized by a triangular shaped curve with only two wave speeds, one for free-flowing traffic (positive) and the other for congested traffic (negative), then the relationship is easy to evaluate. The cumulative flow curve at the junction is simply the lower envelope of a translation of the cumulative curve from upstream and a different translation of the cumulative curve from downstream. This relationship is the basic building block for a freeway flow prediction model described in Part III.