Consistency of Input-Output Model and Shockwave Analysis in Queue and Delay Estimations

This paper investigates the consistency between the simple input-output model and the shockwave analysis method as applied to traffic bottleneck problems. Mathematical derivations considering changes in arriving demand and discharge rate have shown that these models are consistent in queue and delay estimations, as both methods produce identical results at anytime during the congestion propagation and dissipation processes. Earlier findings on the inconsistency of these two methods are attributed to the lack of consideration of the baseline factor, which is dependent on the level of background traffic. Numerical examples are presented to illustrate the importance of the baseline factor, to ensure consistency regardless of the use of different flow-density relationships.