Flow of traffic on freeways and limited access highways can be represented as a series of kinemetic waves. Solutions to these systems of equations become problematic under congested traffic flow conditions, and under complicated (real-world) networks. A simplified theory of kinematics waves (KWaves) was previously proposed. Simplifying elements includes translation of the problem to moving coordinate system, adoption of triangular speed-density relationships, and adoption of restrictive constraints at the on- and off-ramps. However, these simplifying assumptions preclude application of this technique to most practical situations. By directly addressing the limitations of the original theory, this article proposes a simplified Kwaves model for network traffic (N-KWaves). Several key constraints of the original theory are relaxed. For example, the original merge model, which gives full priority to on-ramp traffic, is relaxed and replaced with a capacity-based weighted queuing (CBWFQ) merge model. The original diverge model, which blocks upstream traffic as a whole when a downstream queue exceeds the diverge, is also relaxed and replaced with a contribution-based weighted splitting (CBWS) diverge model. Based on the above, the original theory is reformulated and extended to address network traffic. Central to the N-KWaves model is a five-step computational procedure based on a generic building block. It is assumed that a freeway network can be represented by the combination of some special cases of the generic building block. An empirical field study showed satisfactory results. The N-KWaves model is best suited for modeling traffic operation in a regional freeway network and has a strong connection to Intelligent Transportation Systems (ITS).
The authors are grateful to an anonymous referee of this journal whose insightful comments and constructive suggestions greatly improved the quality of this article.