A robust optimization approach for dynamic traffic signal control with emission considerations

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Title: A robust optimization approach for dynamic traffic signal control with emission considerations
Authors: Han, K
Liu, H
Gayah, V
Friesz, TL
Yao, T
Item Type: Journal Article
Abstract: We consider an analytical signal control problem on a signalized network whose traffic flow dynamic is described by the Lighthill–Whitham–Richards (LWR) model (Lighthill and Whitham, 1955; Richards, 1956). This problem explicitly addresses traffic-derived emissions as constraints or objectives. We seek to tackle this problem using a mixed integer mathematical programming approach. Such class of problems, which we call LWR-Emission (LWR-E), has been analyzed before to certain extent. Since mixed integer programs are practically efficient to solve in many cases (Bertsimas et al., 2011b), the mere fact of having integer variables is not the most significant challenge to solving LWR-E problems; rather, it is the presence of the potentially nonlinear and nonconvex emission-related constraints/objectives that render the program computationally expensive. To address this computational challenge, we proposed a novel reformulation of the LWR-E problem as a mixed integer linear program (MILP). This approach relies on the existence of a statistically valid macroscopic relationship between the aggregate emission rate and the vehicle occupancy on the same link. This relationship is approximated with certain functional forms and the associated uncertainties are handled explicitly using robust optimization (RO) techniques. The RO allows emissions-related constraints and/or objectives to be reformulated as linear forms under mild conditions. To further reduce the computational cost, we employ a link-based LWR model to describe traffic dynamics with the benefit of fewer (integer) variables and less potential traffic holding. The proposed MILP explicitly captures vehicle spillback, avoids traffic holding, and simultaneously minimizes travel delay and addresses emission-related concerns.
Issue Date: 4-May-2015
Date of Acceptance: 1-Apr-2015
DOI: 10.1016/j.trc.2015.04.001
ISSN: 0968-090X
Publisher: Elsevier
Start Page: 3
End Page: 26
Journal / Book Title: Transportation Research Part C - Emerging Technologies
Volume: 70
Copyright Statement: © 2015, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
Keywords: Logistics & Transportation
09 Engineering
08 Information And Computing Sciences
15 Commerce, Management, Tourism And Services
Publication Status: Published
Appears in Collections:Faculty of Engineering
Civil and Environmental Engineering

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