Pedestrian Delay at Signalized Intersections with a Two-Stage Crossing Design

usually staggered to separate the two crossings as shown in Figure 2. Staggered crossings are designed to force pedestrians to face the upcoming traffic and to avoid the confusion that pedestrians may see the further pedestrian signal indication when they are supposed to follow the first-stage signal. Staggered crossings are implemented widely in the United Kingdom and Japan and are recommended by FHWA studies (2, 3). Delay is a key factor when evaluating the level of service for pedestrians at intersections (4). The commonly used pedestrian delay model in the Highway Capacity Manual (HCM) (5) was developed by Pretty (6) for one-stage crossings based on uniform arrival rates and fixed pedestrian timing. Pedestrian delay for one-stage crossings was also analyzed by other researchers with simulations and mathematical models (7). Although the two stages of a signalized two-stage crossing are controlled separately, the total pedestrian delay should not be calculated by simply adding up the analytical delays from both stages as if they were independent. The pedestrian arrivals are not random after the first-stage crossing, so the arrival patterns need to be carefully analyzed on the basis of the signal timing design in order to estimate the pedestrian delays. Noland (8), Ishaque (9), and Ishaque and Noland (10) used microsimulation to investigate pedestrian delays from staggered crossings with various pedestrian and vehicle volumes and focused on analyzing the trade-offs between pedestrian and vehicle delays in the hypothetical network. Few studies were found to provide analytical pedestrian delay models for signalized two-stage crossings. Following the same delay definition from the HCM procedure, this paper analyzes pedestrian crossings and proposes mathematical solutions to calculate the average pedestrian delay at two-stage crossings. The paper is organized in the following manner. First, the current pedestrian delay model in the HCM is discussed. Second, pedestrian delays for two-stage crossings are analyzed; this is followed by a discussion of a general pedestrian delay model developed on the basis of this analysis. A validation is then conducted by comparing results from the proposed model with simulation model results. Finally, conclusions and recommendations for future studies are provided.