Abstract
Delay is a critical measure when evaluating level of service under interrupted flow conditions and is widely used to assess operational improvements and optimize traffic signals. However, existing delay models often fail to capture the effects of arrival interruptions, which are prevalent at closely spaced intersections, and are typically limited to specific facility types. To address this limitation, this paper proposes a generalized analytical delay model that explicitly accounts for the effects of arrival interruptions caused by upstream signals on delays at downstream signals. The model consists of two components that maintain consistency between delay terms while reflecting both the duration and timing of arrival interruptions. The model was evaluated against the Highway Capacity Manual (HCM) method at internal approaches of a typical diamond interchange and closely spaced arterial intersections. While the HCM model produced reasonable estimates under good progression conditions, it tended to overestimate delays under poor progression. This overestimation was attributed to double-counting of the effects of arrival interruptions; the variation in arrival rates was reflected through the progression factor, while capacity was simultaneously reduced. In contrast, the proposed model avoids this type of redundancy, demonstrating improved accuracy. Results show that it provided more reliable delay estimates across both facility types and various offset scenarios, with errors ranging from −4.6 to 1.9 s compared with VISSIM simulations or field measurements. The model is expected to support more robust delay estimations and informed decision-making under diverse traffic conditions and network configurations.