Abstract: 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.

Key words: input-output model, shockwave, bottleneck, queue, delay

摘要： 简单输入输出模型与冲击波分析是研究交通瓶颈问题的两种常用方法，本文着重分析两者的一致性。在数学推导中考虑到达需求与流出率的变化时，两者对于排队和延误的预测结果是一致的。在不同的交通和边界条件下，两者在拥堵形成至消散的任意时刻所得排队长度，拥堵时间等结果均是一致的。以往认为两种方法不一致的研究忽略了一些与背景交通密切相关的基本因素。实例分析说明正是这些基本因素使得这两种分析方法在不同流量－密度关系下都具有一致性。

关键词: 输入输出模型, 冲击波, 瓶颈, 排队, 延误