A study of G. F. Newell's 'simplified theory of kinematic waves in highway traffic'

Recently G. F. Newell (1993a, 1993b & 1993c) has developed a "simplified theory of kinematic waves in highway traffic" which is capable of predicting multi-destination traffic flow patterns while preserving the physical reality of traffic phenomena being modelled. The primary objective of this research was to test the accuracy of Newell's theory and the adequacy of an important simplifying assumption, a triangular flow versus density relationship. To accomplish this objective, a computer algorithm and program were developed to mechanize Newell's graphical methods.; The accuracy of the computer algorithm was tested and illustrated through three numerical examples simple enough to be solved by hand using two conventional techniques--the cumulative arrival and departure technique and the shock wave technique. The computer algorithm produced the same answers as those obtained from these two techniques. This confirms that the three methods are consistent.; The accuracy of Newell's model was then empirically tested with real data collected from freeways in the San Francisco Bay Area. There were considerable difficulties in obtaining the correct capacity at some bottlenecks from an extremely small sample of actual 15-minute queue discharge counts, and the predicted queueing pattern was quite sensitive to capacity, as is the real pattern. The accuracy of the model's results also was adversely affected by the use of 15-minute traffic counts, which are too coarse to reflect the real traffic variations.; The model performed consistently very well when congestion was severe, but dealt less well with light congestion. It did a good job in describing queueing propagation and dissipation processes with rapidly varying traffic flows and with several upstream entrance and exit ramps. This good performance supports the use of the triangular q-k relationship in modelling freeway congestion. However, the model had difficulty in predicting the traffic state (i.e., congested or uncongested) when the real densities were in the range {dollar}kin(30, 50){dollar} veh/mile, probably due to the fact that the triangular q-k relationship does not work well at high flows. The empirical testing results are very encouraging, reveal many promising characteristics of Newell's model, and support its validity.