Estimation of delay induced by downstream operations at signalized intersections over extended control time

Analytical macroscopic models are presented to quantify delay at signalized intersections for extended control periods (multiple cycles) attributable to downstream time-variable congestion. Each of the models consists of an upstream demandestimation algorithm, a downstream queue build-up prediction algorithm, a shockwave propagation and dissipation tracking algorithm, and an algorithm that carries traffic aftereffect of a cycle's control into the following cycle. Model inputs are basic traffic flow properties, signal control parameters, and link geometry. The models are modular and can be incorporated into any size system for one or multiple cycles. The models were tested on a hypothetical system of closely spaced intersections and under different traffic flow, control, and geometric conditions. Results show that delay induced by downstream traffic operations on an upstream intersection can be significant and that it may change with time and reach steadiness once traffic flow, downstream queues, and signal control measures stabilize and start replicating over time. Green ratios of neighboring intersections exert a significant influence on delay. For certain green ratios and geometric combinations, offsets can exert appreciable influence as well. The delay values and their temporal variation compared well with those from a microscopic simulation model.