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Discrete Dynamics in Nature and Society
Volume 2017 (2017), Article ID 2190724, 12 pages
Research Article

A Modified Total Crossing Time Model of Bidirectional Pedestrians at Signalized Crosswalks

1College of Transportation, Jilin University, Renmin Street 5988, Changchun, Jilin, China
2Hualan Design & Consulting Group, No. 39, Huadong Road, Nanning, Guangxi 530000, China

Correspondence should be addressed to Ningbo Cao

Received 18 November 2016; Revised 11 February 2017; Accepted 20 February 2017; Published 22 March 2017

Academic Editor: Stefan Balint

Copyright © 2017 Zhanzhong Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Since crosswalk width and pedestrian green time directly affect the safety of signalized crosswalks, modeling an exact total crossing time model to estimate those two variables is imperative. The total crossing time needed by a group of pedestrians to cross a signalized crosswalk contains the discharge time and the crossing time. The discharge time depends primarily on the maximum queue length, which is determined by pedestrian arrival rate, red interval, waiting position distribution, and the crosswalk width. Crossing time increases when interactions between bidirectional pedestrian flows become more serious. Thus, quantifying the impacts of the start-up process on the discharge time and the effects of the interactions on the crossing time is a prerequisite for optimizing the design of signalized crosswalks. This paper establishes a modified total crossing time model consisting of modified pedestrian discharge and crossing time. Discharge time is modeled by applying traffic wave theory, and crossing time is modeled based on drag force theory. The proposed models provide guidance for the design of crosswalk width and pedestrian green intervals.