ISEN 689 Fall 2007: Large-Scale Stochastic Optimization Semester Project Report Regulating Traffic Flows under Air Quality Constraints: Two-Stage Stochastic Optimization Application Student: Xiugang Li Instructor: Dr. L. Ntaimo Dec. 11, 200711. Abstract The air pollution from vehicles is one of the significant problems faced by the developed country such as the United States, and by the developing country such as China in which motor vehicles increase very rapidly. In a metropolitan area, the air pollutant concentrations are significant largely due to heavy traffic flows and traffic congestions. Once the concentrations exceed the limits, it is difficult to adjust the traffic flows to comply with the air quality standards. Therefore, it is necessary and very beneficial to regulate traffic flows in order to comply with the air quality standards during the planning stage considering the uncertainties of traffic flows, such as turning ratio. This is especially important for sensitive and large exposure locations such as hospitals, schools, gas stations in heavy traffic areas. In this paper the authors develop an approach to regulate the traffic flows under air quality constraints with two-stage stochastic programming. The cloverleaf interchange is modeled as an example of uninterrupted traffic flow network. The model is formulated based on the assumption of constant emission factors for a highway link and the assumption of worst wind conditions. The traffic turning ratio on one entrance is assumed to be constant, and the ratio on other entrances may have various values with probabilities. The L-shaped algorithm is implemented to solve this two-stage random recourse model. The results show that L-shaped algorithm solves the model efficiently. The derived maximum flow rate is a very useful reference for transportation planners to regulate the traffic flows during the planning stage.22. Introduction and Literature Review The air pollution from vehicles is one of the significant problems faced by the developed country such as the United States (U.S.), and by the developing country such as China in which motor vehicles increase very rapidly. According to the published air quality data (U.S. Environmental Protection Agency, 2007), the monitored pollutant concentrations exceeded the limits of the National Ambient Air Quality Standards (U.S. Environmental Protection Agency, 2004) in many metropolitan areas. Areas that have failed to meet federal standards for ambient air quality are designated as nonattainment areas. In Texas the nonattainment areas include Houston-Galveston-Brazoria (HGB), Dallas–Fort Worth (DFW), Beaumont–Port Arthur (BPA), San Antonio (SA), and El Paso (ELP). Vehicle emissions have significant negative impacts on health. Carbon Monoxide (CO) can cause harmful health effects by reducing oxygen delivery to the body's organs (U.S. Environmental Protection Agency, 2006). Ozone can cause a variety of health problems such as chest pain and coughing (U.S. Environmental Protection Agency, 2006). Fine particles can affect the heart and lungs and cause serious health effects, and oxides of nitrogen (NOx) can cause the disease of lung (U.S. Environmental Protection Agency, 2006). The Ambient Air Quality Standards (U.S. Environmental Protection Agency, 2004) set limits to protect public health, including the health of sensitive populations such as asthmatics, children, and the elderly, and to protect public welfare, including protection against decreased visibility, damage to animals, crops, vegetation, and buildings. In a metropolitan area, the air pollutant concentrations are significant largely due to heavy traffic flows and traffic congestions. Once the concentrations exceed the limits, it is difficult to adjust the traffic flows to comply with the air quality standards. Therefore, it is necessary and very beneficial to develop strategies to regulate traffic flows in order to comply with the air quality standards during the planning stage considering the impacts of traffic flow, land use, traffic management, and air quality control. This is especially important for sensitive and large exposure locations such as hospitals, schools, gas stations in heavy traffic areas.3Currently highway capacity is defined as the maximum hourly flow rate at which vehicles or persons can reasonably be expected to traverse a point or uniform section of a lane or roadway during a given time period under prevailing roadway, traffic, and control conditions (Garber and Hoel, 2002) . The calculating method is described in the Highway Capacity Manual (Transportation Research Board, 2000). In addition to highway capacity, Li et al. (2005) define traffic capacity under air quality constrains as the maximum hourly flow rate at which vehicles or persons can reasonably be expected to traverse a point or uniform section of a lane or roadway during a given time period without generating air pollutions exceeding limits of air quality standard. Li et al. (2005) developed a methodology to estimate the traffic capacity under air quality constraints for a highway link. In this paper the authors extend the methodology for an uninterrupted traffic flow network, such as a cloverleaf interchange. Furthermore the uncertainties of traffic-flow turning ratios are considered in the proposed two-stage random-recourse stochastic programming model to regulate the traffic flows under air quality constraints. Stochastic programming has been applied successfully in many fields (Birge and Louveaux, 1997; Ntaimo and Sen, 2005), including the application in transportation (Powell and Topaloglu, 2003). One of the advantages of stochastic programming is to provide an adapted way to deal with the uncertainties in the modeling process. Many algorithms have been proposed to solve stochastic programming, such as L-shaped algorithm (Van Slyke and Wets, 1969) and the extensions including multi-cut algorithms (Birge and Louveaux, 1988), regularized decomposition method (Ruszczynski, 1986), and stochastic decomposition (Higle and Sen, 1996). In this paper, the L-shaped algorithm is implemented to solve the formulated model. 3. Formal Problem Statement 3.1 Problem Description The cloverleaf interchange is one of the examples of uninterrupted traffic-flow network. Shown in Figure 1, the cloverleaf interchange connects two major two-direction highways, and has very heavy traffic especially during traffic