{
  "id": "1211.4865",
  "version": "v3",
  "published": "2012-11-19T23:37:07.000Z",
  "updated": "2016-03-24T12:35:59.000Z",
  "title": "A robust optimization approach for dynamic traffic signal control with emission considerations",
  "authors": [
    "Ke Han",
    "Hongcheng Liu",
    "Vikash Gayah",
    "Terry L. Friesz",
    "Tao Yao"
  ],
  "comment": "35 pages, 7 figures, 4 tables",
  "doi": "10.1016/j.trc.2015.04.001",
  "categories": [
    "math.OC"
  ],
  "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 side constraints. We seek to tackle this problem using a mixed integer mathematical programming approach. Such a 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 of 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 the link transmission 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.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-06-20T11:31:25.000Z",
      "title": "A Robust Optimization Approach for Dynamic Traffic Signal Control with Emission Constraints",
      "abstract": "We consider an adaptive 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). Such problem explicitly considers traffic-derived emission as side constraints. We seek to tackle this problem using a mixed integer mathematical programming approach. Such a problem class, which we call LWR-Emission (LWR-E), has been analyzed before to certain extent. Since mixed integer programs are practically efficient to compute in many cases (Bertsimas et al., 2011), the mere fact of having integer variables is not the most significant challenge to computing solutions of MIPs; rather, it is the presence of the nonlinear and nonconvex emission-related constraints that render the program computationally expensive. To address this issue, we proposed an efficient and practical way of solving the LWR-E problem, by formulating it as a mixed integer linear program (MILP). This methodology relies on the existence of a strong correlation between the aggregate vehicle emissions rate and certain macroscopic traffic quantities, such as the number of vehicles on a link. This correlation is fitted by a function and deviations from this function are treated as parameter uncertainty. We then apply robust optimization techniques to reformulate the emissions-related constraints into convex and tractable forms. To further reduce the computational cost, we employ the link transmission model to represent traffic dynamics. The final proposed MILP explicitly captures vehicle spillback, avoids traffic holding and features time-varying signal cycle and splits, as well as the aforementioned emissions constraints.",
      "comment": "32 pages, 8 figures, 5 tables",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2016-03-24T12:35:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "90B20",
      "90C11",
      "90B10"
    ],
    "keywords": [
      "dynamic traffic signal control",
      "robust optimization approach",
      "emission constraints",
      "explicitly captures vehicle spillback",
      "integer mathematical programming approach"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1211.4865H"
    }
  }
}