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

摘要

We consider an analytical signal control problem on a signalized networkwhose traffic flow dynamic is described by the Lighthill-Whitham-Richards (LWR)model (Lighthill and Whitham, 1955; Richards, 1956). This problem explicitlyaddresses traffic-derived emissions as side constraints. We seek to tackle thisproblem using a mixed integer mathematical programming approach. Such a classof problems, which we call LWR-Emission (LWR-E), has been analyzed before tocertain extent. Since mixed integer programs are practically efficient to solvein many cases (Bertsimas et al., 2011b), the mere fact of having integervariables is not the most significant challenge to solving LWR-E problems;rather, it is the presence of the potentially nonlinear and nonconvexemission-related constraints/objectives that render the program computationallyexpensive. To address this computational challenge, we proposed a novelreformulation of the LWR-E problem as a mixed integer linear program (MILP).This approach relies on the existence of a statistically valid macroscopicrelationship between the aggregate emission rate and the vehicle occupancy ofthe same link. This relationship is approximated with certain functional formsand the associated uncertainties are handled explicitly using robustoptimization (RO) techniques. The RO allows emissions-related constraintsand/or objectives to be reformulated as linear forms under mild conditions. Tofurther reduce the computational cost, we employ the link transmission model todescribe traffic dynamics with the benefit of fewer (integer) variables andless potential traffic holding. The proposed MILP explicitly captures vehiclespillback, avoids traffic holding, and simultaneously minimizes travel delayand addresses emission-related concerns.