The control of vehicular pollutant emissions, particularly nitrogen oxides (NOx), at urban signalized intersections is a critical challenge for sustainable transportation management. These nodes, characterized by frequent vehicle stops, accelerations, and idling under diverse traffic conditions, are hotspots for elevated emissions. The proliferation of hybrid electric vehicles (HEVs), especially plug-in types, introduces new dynamics into the traffic stream, as their emission profiles differ significantly from conventional internal combustion engine vehicles and vary based on their operational mode. Traditional signal timing models, primarily focused on traffic efficiency metrics like delay and capacity, often overlook these environmental impacts and the heterogeneity of the vehicle fleet. This paper addresses this gap by developing an integrated optimization model for intersection signal timing that explicitly minimizes average vehicle NOx emissions within a mixed traffic environment comprising conventional and hybrid electric vehicles.
The core of the methodology lies in accurately quantifying the NOx emissions for different vehicle types under the specific driving cycles induced by signal control. The Vehicle Specific Power (VSP) model serves as the fundamental framework, translating vehicle dynamics (speed, acceleration) into an instantaneous power demand per unit mass, which is strongly correlated with emission rates. For conventional Light-Duty Gasoline Vehicles (LDGVs) and Heavy-Duty Diesel Trucks (HDDTs), NOx emission factors are mapped to predefined VSP bins based on established models and real-world data.
The novel contribution focuses on modeling the hybrid electric vehicle. Recognizing the distinct operational states of a plug-in hybrid electric vehicle, we differentiate between its Charge-Depleting (CD) mode, where the electric motor plays a primary or substantial role, and its Charge-Sustaining (CS) mode, where the internal combustion engine is the dominant power source. For each mode, a cubic polynomial relationship between VSP and the instantaneous NOx emission factor is derived from real-world measurements using a Portable Emission Measurement System (PEMS), as illustrated in the testing setup below.
The driving trajectory of a vehicle approaching and departing a signalized intersection is decomposed into four distinct regimes: deceleration to a stop, idling during red, acceleration to cruise speed after green, and cruising away from the intersection. To enhance realism, vehicle motion during deceleration and acceleration is modeled as variable acceleration rather than constant. The total NOx emitted by a vehicle during its passage through the intersection is the sum of emissions from these four phases. For a hybrid electric vehicle, the calculation depends on its operational mode (CD or CS), which is assumed constant for the trip segment. The average NOx emission per vehicle, \(\bar{E}\), for the intersection is then calculated as a flow-weighted average across all vehicle types (LDGV, HDDT, hybrid electric vehicle) and all traffic movements.
The signal timing optimization model is formally defined with the following key elements. The primary decision variables are the signal cycle length, \(C\), and the effective green times for each phase, \(g_i\). The model’s notations are summarized in Table 1.
| Symbol | Description | Unit |
|---|---|---|
| \(i, j\) | Index for signal phase and approach lane | – |
| \(\alpha, \beta\) | Indices for vehicle class and energy type (fuel, hybrid) | – |
| \(\bar{E}\) | Average NOx emission per vehicle at the intersection | g/pcu |
| \(e_{\delta, \alpha, \beta}\) | NOx emission factor for vehicle type (\(\alpha, \beta\)) in regime \(\delta\) (1: decel, 2: accel, 3: idle, 4: cruise) | g/s |
| \(D_{ij}\) | Average delay for vehicles in phase \(i\), approach \(j\) | s/pcu |
| \(\bar{h}\) | Average number of stops per vehicle at the intersection | stops/pcu |
| \(q_{\alpha,\beta, ij}\) | Traffic flow of vehicle type (\(\alpha, \beta\)) on approach \(j\) in phase \(i\) | pcu/h |
| \(S_{ij}\) | Saturation flow rate | pcu/h |
| \(L, v_0\) | Intersection approach length and vehicle initial speed | m, m/s |
| \(\omega, \xi\) | Proportion of hybrid electric vehicles operating in CD and CS mode (\(\omega + \xi = 1\)) | % |
| \(C, g_i\) | Decision variables: Cycle length and green time for phase \(i\) | s |
The objective is to minimize the average NOx emission per vehicle:
$$
\min F(C, g_i) = \bar{E} = \frac{\sum_{i=1}^{n} \sum_{j=1}^{m} \sum_{\alpha} \sum_{\beta} (E_{1,\alpha,\beta} + E_{2,\alpha,\beta} + E_{3,\alpha,\beta} + E_{4,\alpha,\beta}) \cdot q_{\alpha,\beta, ij} }{ \sum_{i=1}^{n} \sum_{j=1}^{m} \sum_{\alpha} \sum_{\beta} q_{\alpha,\beta, ij} }
$$
The emission terms \(E_{\delta,\alpha,\beta}\) are computed as described, integrating the respective VSP-based emission factors over the time or distance of each driving regime, multiplied by the expected number of stops, \(\bar{h}\). The calculation for a hybrid electric vehicle, for example in acceleration regime, would be:
$$
E_{2,1,2} = \left( \omega \int_{0}^{t_{2,1}} e’_{2,1,2}(VSP(t)) \,dt + \xi \int_{0}^{t_{2,1}} e”_{2,1,2}(VSP(t)) \,dt \right) \cdot \bar{h}
$$
where \(e’\) and \(e”\) represent the emission factor functions for CD and CS modes, respectively, and \(t_{2,1}\) is the acceleration duration for a light-duty vehicle.
The optimization is subject to constraints ensuring traffic efficiency does not degrade beyond acceptable limits and that signal timing parameters are practical:
$$
\begin{aligned}
\text{s.t.} \quad & \bar{D} \leq D_0, \\
& \bar{h} \leq h_0, \\
& \sum_{i=1}^{n} (g_i + \eta_i) = C, \\
& C_{\text{min}} \leq C \leq C_{\text{max}}, \\
& g_{i,\text{min}} \leq g_i \leq g_{i,\text{max}}, \\
& y_i \leq g_i / C \leq 0.9.
\end{aligned}
$$
Here, \(D_0\) and \(h_0\) are the pre-optimization average delay and stop frequency, \(\eta_i\) is the lost time per phase, and \(y_i\) is the flow ratio for the critical lane group in phase \(i\).
The model is applied to a real-world three-phase signalized intersection during an evening peak period. The traffic composition includes LDGVs, HDDTs, and hybrid electric vehicles. The VSP-based emission factors for conventional vehicles are assigned according to Table 2. For the hybrid electric vehicle, the polynomial models from PEMS data are used.
| Bin | VSP Range (kW/t) for LDGV | NOx Factor for LDGV (g/s) | VSP Range (kW/t) for HDDT | NOx Factor for HDDT (g/s) |
|---|---|---|---|---|
| 1 | < -2 | 0.000140 | < -2 | 0.056211 |
| 2 | [-2, 0) | 0.000460 | [-2, 0) | 0.072015 |
| 3 | [0, 1) | 0.001056 | [0, 1) | 0.065285 |
| 4 | [1, 4) | 0.001182 | [1, 4) | 0.120160 |
| 5 | [4, 7) | 0.001345 | [4, 7) | 0.155863 |
| 6 | [7, 10) | 0.001557 | [7, 10) | 0.200919 |
| 7 | [10, 13) | 0.001958 | [10, 13) | 0.222891 |
| 8 | [13, 16) | 0.002642 | [13, 16) | 0.256654 |
| 9 | [16, 19) | 0.003205 | [16, 19) | 0.247437 |
| 10 | [19, 23) | 0.002766 | ≥ 19 | 0.228228 |
| 11 | [23, 28) | 0.002080 | – | – |
| 12 | [28, 33) | 0.001501 | – | – |
| 13 | [33, 39) | 0.000488 | – | – |
| 14 | ≥ 39 | 0.000725 | – | – |
A Genetic Algorithm (GA) is employed to solve the optimization problem. The chromosome is encoded as \([g_1, g_2, g_3, C]\). The algorithm initializes a population of feasible signal timing plans, evaluates each plan’s fitness (i.e., the objective function \(\bar{E}\)), and iteratively applies selection, crossover, and mutation operations to evolve the population towards an optimal solution.
The analysis reveals that the optimal cycle length identified by the proposed model is 140 seconds, compared to the existing 160-second cycle. At this optimum, the model achieves a 31.29% reduction in average vehicle NOx emissions. Notably, this environmental benefit is coupled with significant improvements in traffic efficiency: average vehicle delay decreases by 43.99% and the average number of stops drops by 28.88%. This performance surpasses that of the conventional Webster delay-minimization model, which, when applied to the same case, yielded a lower reduction in NOx emissions (26.22%) for the same optimal cycle. The results underscore that explicitly incorporating emissions, particularly from diverse vehicle types like the hybrid electric vehicle, into the signal timing objective leads to control strategies that synergistically enhance both environmental and operational performance.
A critical finding from the emission breakdown is the overwhelming contribution of Heavy-Duty Diesel Trucks (HDDTs) to the total intersection NOx burden, accounting for over 93% of emissions across all evaluated cycle lengths. This highlights the disproportionate impact of freight traffic on urban air quality at intersections and emphasizes the need for targeted policies.
Sensitivity analyses were conducted on key parameters. First, varying traffic demand levels shows that both average delay and NOx emissions increase non-linearly with volume, while the average number of stops decreases due to traffic saturation effects. Second, adjusting the proportion of left-turning vehicles in a shared through-left phase reveals a non-monotonic impact on emissions and delay, with an optimal proportion around 40% for this specific intersection geometry. Exceeding this significantly degrades performance. Third, and most pertinent to vehicle technology transition, increasing the market penetration rate of hybrid electric vehicles demonstrates a clear and substantial linear reduction in average NOx emissions. This confirms the positive environmental impact of fleet electrification, even at the level of hybrid electric vehicles, and shows that signal timing optimization can amplify this benefit.
In conclusion, this study presents a robust methodology for designing intersection signal timings that holistically address the dual goals of emission reduction and traffic efficiency in a mixed vehicle fleet. By developing a detailed VSP-based emission model that accounts for the unique dual-mode operation of plug-in hybrid electric vehicles and integrating it into a signal optimization framework, the proposed model offers a practical tool for traffic engineers and policymakers. The findings advocate for adaptive signal control that responds not just to traffic volume but to fleet composition, and underscore the significant air quality co-benefits of promoting hybrid electric vehicle adoption. Future work should integrate real-time state-of-charge information for hybrid electric vehicles and expand the framework to coordinate signals across urban networks for greater system-wide environmental gains.