Robust signal timing optimization with environmental concerns

1. Background Because of its negative effects on health and living conditions, air pollution has long emerged as one of the most acute problems in many metropolitan areas. A major source of this pollution is the emissions from vehicular traffic (see e.g., Cai et al., 2009; Sharma et al., 2010; Environmental Protection Agency, 2011). They contribute considerably to the level of, e.g., carbon monoxide (CO), nitrogen oxides (NOx), and volatile organic compounds (VOCs) in the environment. In order to achieve a more sustainable mobility, reducing traffic emissions has been an ongoing endeavor of many governmental authorities over the past two decades. However, many emission reducing programs implemented thus far are passive in nature because they regulate only the rates (e.g., grams per mile) at which a vehicle generates these hazardous air pollutants. Depending on the amount of driving or the mode of driving, cars meeting an emission standard can generate as much air pollutants as cars not meeting the standard. More proactive strategies that aim to reduce the mileage vehicles traveled or improve the efficiency of the transportation network have recently gained more and more attention (e.g. Yin and Lawphongpanich, 2006; Cambridge Systematics, 2009). Traffic signals at intersections impose significant impact on traffic emissions because they interrupt traffic flow (for good reasons) and create additional deceleration, idle and acceleration driving modes to the otherwise cruise driving mode. Traffic emissions are very sensitive to the driving modes. For example, accelerating vehicles produce 350% more CO than those in the cruise driving mode (Environmental Protection Agency, 2002). Previous studies have investigated the impacts of signal 56 L. Zhang et al. / Transportation Research Part C 29 (2013) 55–71 timing on vehicular emissions. Rakha et al. (2000) showed that efficient signal coordination can reduce emissions up to 50% in a highly simplified scenario. Hallmark et al. (2000) evaluated signal coordination strategy on CO emission reduction with an activity-specific approach, where the vehicle activity profile was obtained with handheld laser range-finding devices. Unal et al. (2003) directly collected emission data using a portable, on-road vehicle date measurement device, to show that signal coordination was able to reduce pollutant emissions by approximately 10–20%. Coelho et al. (2005) integrated a mesoscopic traffic model and the modal emission approach to investigate the impact of various speed control signal settings on vehicle emissions. Li et al. (2009) integrated a comprehensive modal emission model (Barth et al., 2000) and PARAMICS to evaluate vehicular emissions at signalized intersections. Hirschmann and Fellendorf (2010) developed a simulation toolbox to estimate pollutant emissions under different signal control strategies, and simulation results show 5–12% emission reduction depending on pollutant types and signal control strategies. Madireddy et al. (2011) recently examined a signal coordination strategy that reduces vehicle emissions by about 10% on a real arterial. Tao et al. (2011) also used field data to evaluate the effectiveness of signal coordination on reducing vehicle emissions during both peak and non-peak hours. Previous studies have also attempted to develop signal timing optimization models to minimize both congestion and emissions. Li et al. (2004) optimized the cycle length and green splits for an isolated intersection to minimize a weighed sum of the delay, fuel consumption and emission. Liao and Machemehl (1996), Stevanovic et al. (2009) and Park et al. (2009) developed signal timing optimization models to minimize the fuel consumption and vehicle emission based on microscopic simulation. More recently, Ma and Nakamura (2010) developed an analytical procedure to obtain the optimized cycle length against vehicle emissions for isolated intersections. These studies consider tailpipe emissions instead of roadside air pollution concentrations, which decide the local air quality. In other words, dispersion of air pollutants is not captured in their models. The tradeoff between delays and emissions in street canyons should be very different from that in open rural environments, because the dispersion procedure of air pollutants relies heavily on the surface roughness (e.g., Wieringa, 1993). Since air pollutants are more difficult to disperse in the former, they likely lead to higher pollution concentrations and worse air quality in the area adjacent to the streets. Much research has been carried out to investigate the impact of terrain conditions on atmospheric dispersion (e.g., McElroy, 1969; Briggs, 1973; Bowne, 1974; Dennis, 1978). Nowadays, most air dispersion models available are capable of modeling different terrains, and many of them are specifically developed for estimating concentrations near roadways, e.g. the CAR model (Eerens et al., 1993), the CALINE model (California Department of Transportation, 1989), the HYROAD model (Carr et al., 2002) and the ADMS-Roads model (Cambridge Environmental Research Consultants, 2006). Moreover, previous signal timing optimization studies either use a highly simplified approach to compute traffic emissions or rely on microscopic driving-cycle-based emission models. The former approach, which is adopted in Li et al. (2004) and Ma and Nakamura (2010), estimates emissions based on average traffic condition at the link or intersection level, and thus fails to capture spatially and temporally varying traffic state and may underestimate the emissions due to accelerations and decelerations (Lin and Ge, 2006). The latter approach requires instantaneous vehicle information to calculate individual vehicle emissions for each modeling time step. To obtain such detailed information, researchers have turned to microscopic traffic simulation (e.g., Park et al., 2009). When such an emission estimation component is incorporated into an optimization framework, the resulting microscopic-simulation-based optimization model will be computationally intensive for real network optimization. In contrast, this paper presents a signal timing optimization model for coordinated signal control along arterials to minimize traffic delay and roadside air pollutant concentrations. The model is macroscopic and computationally tractable. At the same time, it can model traffic dynamics to capture the impact of time-dependent traffic characteristics on emissions. More specifically, the macroscopic cell transmission model (CTM) developed by Daganzo (1994, 1995) is adopted to describe traffic dynamics. CTM represents urban streets as a set of consecutive cells and propagates traffic flow through these cells based on the fundamental diagram and signal status. The computation is very efficient. Based on the CTM representation of traffic dynamics, traffic delay may be estimated with reasonable accuracy. More importantly, the driving mode of the vehicles in each cell at each time interval can be identified as deceleration, idle, acceleration or cruise. Subsequently, the time-dependent cell emission rates for air pollutants such as CO and NOx can be determined using the modal emissions approach (e.g., Frey et al., 2001). With the emission rate of each cell, a Gaussian plume dispersion model (e.g., Turner, 1994) is further utilized to capture the dispersion of air pollutants and compute the roadside pollutant concentrations. For a given wind direction and speed, a measure of total human emissions exposure is calculated to represent the potential adverse impacts by the roadside pollutant concentrations. Given a set of scenarios of wind direction and speed, we define a risk measure, i.e., the mean excess exposure, as the mean of the total human emissions exposures incurred by high-consequence wind scenarios. In financial engineering, the risk measure is known as conditional value-at-risk or CVaR (Rockafellar and Uryasev, 2000). With the above consideration, a bi-objective signal timing optimization model is developed to determine cycle length, offsets, green splits and phase sequences to simultaneously minimize traffic delay and the mean excess exposure. A geneticalgorithm-based solution approach (Yin, 2002) is adopted to solve the timing optimization problem for a set of Pareto optimal solutions. The solutions form an efficient frontier that presents explicit tradeoffs between the total delay of the corridor and the mean excess exposure of the roadside area. Based on the decision maker’s consideration of social costs of delays and emissions, an optimal timing plan can be selected. For the remainder, Section 2 briefly introduces the CTM description of traffic dynamics in a signalized arterial. Section 3 elaborates the cell-based modal emissions approach to compute the cell emission rates, the cell-based Gaussian plume dispersion model to capture air pollutant dispersion and the definition of mean excess exposure. Section 4 presents the biL. Zhang et al. / Transportation Research Part C 29 (2013) 55–71 57 objective signal timing optimization model and develops a simulation-based genetic algorithm to solve the bi-objective timing optimization model. Section 5 is a numerical example to demonstrate the model and the solution algorithm, followed by concluding remarks in the last section. 2. Modeling traffic dynamics via cell-transmission model We attempt to determine timing plans for a series of coordinated traffic signals along a local arterial, which share a common cycle length, and prescribe offset, green splits and phase sequence for each signal in coordination. We assume that the traffic demand for the arterial is given, and do not consider the impact of signal timing on drivers’ route choices. Modeling traffic dynamics is particularly important for signal timing optimization due to the need for accurately evaluating various feasible timing plans. The evaluation process should be efficient such that the optimization procedure can be computationally tractable. This paper adopts CTM to describe traffic dynamics, such as shockwave, and queue formation and dissipation. CTM is a finite differencing solution scheme for the first-order hydrodynamic theory of traffic flow, i.e., the Lighthill–Whitham–Richards (LWR) model. Mathematically the model can be stated as the following equations: 1 To @k @t þ @q @x 1⁄4 0 ð1Þ q 1⁄4 f ðk; x; tÞ ð2Þ where k and q denote traffic density and flow respectively, which may vary across location x and time t. Eq. (1) is the flow conservation equation and Eq. (2) defines the traffic flow at location x and time t as a function (denoted as f) of the density, the so-called fundamental diagram. For a homogeneous roadway, Daganzo (1994) suggested using the following timeinvariant flow–density relationship: q 1⁄4 minfVk;Q ;Wðkjam kÞg where kjam is the jam density; Q is the inflow capacity; V is the free-flow speed and W is the backward wave speed. By dividing the whole network into homogeneous cells with the cell length equal to the duration of a time step multiplied by the free-flow speed, the results of the LWR model can be approximated by a set of recursive equations in the simplest case: niðt þ 1Þ 1⁄4 niðtÞ þ yi 1ðtÞ yiðtÞ ð3Þ yiðtÞ 1⁄4 minfniðtÞ;QiðtÞ;x 1⁄2Niþ1;max niþ1ðtÞ g ð4Þ where ni(t) is the number of vehicles in cell i during time step t; yi(t) is the number of vehicles that leave cell i during time step t; Ni,max is the maximum number of vehicles that can be accommodated by cell i; x is equal toW/V; Qi(t) is the minimum of the capacity flows of cell i and i + 1. Eq. (3) ensures the flow conservation and Eq. (4) determines the outflow for each cell at each time step. CTM has been extensively employed in the literature for modeling traffic dynamics in various applications, e.g. signal timing optimization (e.g., Lo, 1999; Lo et al., 2001; Lin andWang, 2004; Karoonsoontawong andWaller, 2009, 2010; Zhang et al., 2010; Li, 2011), dynamic traffic assignment (e.g., Ziliaskopoulos, 2000; Lo, 2001), dynamic network design (e.g., Karoonsoontawong and Waller, 2006), and evacuation planning (e.g. Xie et al., 2010; Ben-Tal et al., 2011). This paper adopts the CTM implementation that Zhang et al. (2010) proposed for a general signal-controlled arterial network. In their implementation, all the cells comprising the network are categorized into seven groups: ordinary, origin, destination, non-signalized diverge, non-signalized merge, signalized diverge and signalized merge cells, as shown in Fig. 1 from (a) to (g) correspondingly. Fig. 1a denotes an ordinary cell (cell i) whose flow propagation is described by Eqs. (3) and (4). Using a technique recently proposed by Pavlis and Recker (2009), the equations can be equivalently converted into a linear system of equalities and inequalities with integer variables. Fig. 1b is an origin cell (cell i) with the inflow fixed as the exogenous demand input, denoted as di in the figure. The flow propagation for this type of cells is similar to Eqs. (3) and (4). The destination cell, as shown in Fig. 1c, is also similar to the ordinary cell, but the outflow is unlimited, implying that all the vehicles currently residing in the cell are able to flow out of the system at the next time step. Fig. 1d illustrates a non-signalized diverge cell where the geometry or capacity changes and traffic diverge into different lanes for their respective destinations. In the figure, traffic in cell i diverges into cells j1 and j2 according to some pre-determined proportion parameters. Fig. 1e shows non-signalized merge, where the traffic in upstream cells i1 and i2 merge into the downstream cell j. The merging flow rates are determined based on the traffic condition and priority setting at the merge point. Fig. 1f sketches a signalized diverge cell, where the sign S indicates a traffic signal. A signalized diverge occurs within a signalized intersection. Traffic from one direction enters the intersection during a green phase and then leaves the intersection while diverging into two or more directions of traffic. Lastly, Fig. 1g presents an example of traffic merge under signal control. According to the signal settings, three streams of simplify the notation, we here use the same t to indicate the discretized time interval. i+1 ni n i+1 yi-1 yi i