1. Introduction
Transportation is one of the major producers of greenhouse gases [
1], which are responsible for climate change. Therefore, reducing emissions in the transportation sector seems necessary. Emission reduction can be made by changing traffic composition to less pollutant vehicles such as electric vehicles. However, electric vehicles’ wide adoption is hindered by issues such as their charging times, driving range, and charging infrastructures [
2,
3,
4]. With that in mind, emission reduction through traffic management seems more applicable. Emission control strategies such as re-routing can reduce the emission made by transportation [
5]. The first step for developing such strategies is estimating the current emission level to take subsequent actions to reduce it. There are two main approaches to emission estimation: macroscopic [
6] and microscopic [
7,
8]. The former refers to emission estimation at a larger scale, e.g., at the network level, and the latter refers to emissions estimation of each vehicle.
While microscopic models are highly accurate and considered the ground truth for emission estimation in the literature [
7,
8], they are not suitable for large-scale applications. Microscopic models need second-by-second vehicle trajectory data for emission estimation [
9], which is financially expensive to acquire. The fine resolution of microscopic emission models challenges their scalability, as many trajectories are needed. Fitting the microscopic emission model to many vehicle trajectories in the network requires high computational power. Then the estimated emission levels need to be aggregated to get the network emission.
On the other hand, macroscopic models [
6,
10] are more computationally efficient for large-scale networks but usually offer lower accuracy compared to microscopic methods [
11]. Macroscopic model inputs such as network speed and density are less computationally and financially expensive to collect. Loop detectors, already available in many cities, can provide the inputs for macroscopic models. Mesoscopic models stand between microscopic and macroscopic models. For example, VT-Meso [
12] constructs synthetic driving cycles for each link instead of tracking individual vehicles and aggregates the emission levels. The driving cycle construction is based on the assumption that all drivers accelerate and decelerate at a constant rate. However, finding a platoon of vehicles with a similar acceleration and deceleration rate to apply the model to them might not be accessible in practice [
13].
Previous studies found that emission levels correlate with macroscopic traffic network state characteristics, such as density, speed, and flow [
9,
13]. Recently, [
14] combined MFD, COPERT III model [
15], and VT-CPEM model [
16] to develop CE-MFD (Carbon Emission MFD). In that study, the electric and regular vehicle flows were calculated by multiplying the network flow from the MFD by each vehicle type’s penetration rate. Then, each vehicle type’s flow was fed to the related macroscopic emission model (Copert for regular vehicles and VT-CPEM for electric vehicles). Eventually, CE-MFD was developed based on the total emission of vehicles (summation of both electric and regular vehicle emissions). While this approach simplifies the emission calculation, the drawbacks of macroscopic models such as [
15] were discussed and presented here are in place. Also, there was no comparison with the microscopic emission models to quantify the accuracy of CEI-MFD.
The emission MFD (e-MFD) concept was recently introduced by Saedi et al. (2020) [
13]. The e-MFD shows the emission level as a function of the network traffic state (i.e., density, speed, or flow). These inputs can be collected from the existing infrastructure, like loop detectors, making them more accessible to many cities. The advantage of e-MFD is the simplicity and lower computation costs while offering close to microscopic emission estimation results. A recent real case study validated the existence of the e-MFD relationship [
9] using vehicle trajectories recorded by drones.
Table 1 shows the summary of the previous literature.
Congestion distribution in the network was found to be an essential factor affecting the overall traffic network performance [
21,
22]. Knoop et al. (2015) used the standard deviation of density for measuring congestion distribution. They showed that the increase in the standard deviation of density, maintaining the density level, negatively impacts the traffic flow in the traffic network [
21]. Recently, Ref. [
13] showed that emission rates and flow are highly correlated. Based on what was discussed above, congestion distribution could improve the accuracy and stability of e-MFD in different scenarios. To the authors’ knowledge, no study has incorporated congestion distribution. Also, the literature did not study the stability of e-MFD under different circumstances, such as the change in demand and accidents. In this study, we aim to answer the following questions:
Does network congestion distribution have any relationship with emission rate?
Will the inclusion of congestion distribution term (as the standard deviation of density) improve the accuracy of the e-MFD model?
Will the congestion distribution term enable e-MFD to handle exceptional circumstances, such as evacuation and accidents in the network, with high estimation accuracy?
This study comprehensively analyzes e-MFD stability and proposes a new e-MFD model. In addition to what has been proposed in the previous study [
13], the proposed model considers the traffic congestion homogeneity using the standard deviation of density [
21,
22]. It is worth mentioning that this is the first study to consider congestion distribution as an independent variable for emission estimation modelling. The developed model and the previous one [
13] were tested on a grid network in three experimental scenarios: day-to-day stability, directional demand to mimic evacuation situations, and blockage on high-density links to mimic accidents. The developed model outperformed the previous e-MFD under the same test conditions. A quantitative comparison between the models was performed. In addition, the models were calibrated for Blacksburg, VA, USA network, and the validation results were compared. Results showed that the new heterogeneity-aware e-MFD outperformed the previous model.
The developed model adds no computational complexity to the previous model, relying solely on existing data collection devices such as loop detectors. The developed model can be used in congestion prevention and energy management programs by homogeneously distributing traffic flow throughout the network.
The rest of the paper is organized as follows: first, in the
Section 2, the tools used for emission estimation are introduced; secondly, in
Section 3, our modelling setup is introduced; thirdly, in
Section 4 our modelling results for our case studies are presented and discussed. Then, a discussion of the results is provided. Finally, the concluding remarks, policy recommendations, and future research directions are provided.
5. Discussion
Our results showed that separating the free-flow and congestion branches and including the standard deviation of density could improve the estimation results of the e-MFD. Previous literature showed the standard deviation of density impacts the flow [
21,
22] and the inclusion of this term could lead to calibrating a more accurate MFD. However, standard deviation of density impact depends on the level of density [
22]. Moreover, similar to [
22,
30] suggestion for MFD, we used the third power of density in our e-MFD. However, we opted to drop the first and the second power from our e-MFD since they were not statistically significant in our calibration trials. Saedi model showed underestimation for the free-flow branch of e-MFD and overestimation for the congested branch of e-MFD in both numerical experiments. Interestingly, when we solely imported the standard deviation of density without the dummy variable for free-flow, we observed the same behaviour for the free-flow branch of our model. Therefore, we suggest incorporating the dummy variable and the standard deviation of density in the e-MFD. This suggestion is in harmony with the dependence of standard deviation of density impact on flow to the congestion level [
21,
22]. As [
13] stated, macroscopic emission rates correlate highly with the flow. However, this relationship is not strictly linear and can have different slopes for free-flow and congested phases. While the original single modal e-MFD was not able to capture those different slopes, we showed that by accounting for the traffic state (free-flow and congested) and including the standard deviation of density, the calibrated model stayed more flexible in different scenarios and across different congestion levels (for example,
Figure 7F).
We observed more considerable differences between the performance of our model and the previous model for the grid network compared to Blacksburg network. This less considerable difference in model performance can be attributed to the availability of alternative routes in Blacksburg network (US 460 highway that passes by Blacksburg). Contrarily, in a grid network, density’s standard deviation grows quickly due to the limited routing options and the nucleation effect [
21]. While the grid network results highlight our model’s superiority for urban networks with more homogeneous structures (CBD, downtown alike structures), our model stays relevant and offers better estimation results compared to Saedi model. Around 10% improvement in
without the need for any new hardware installation or data collection) for the less homogeneous networks (CBD + highways). We speculate that partitioning the network [
33] into more homogeneous sub-networks could improve the estimation accuracy and make emission control more feasible. Future research work can explore the potential benefits of network partitioning in improving e-MFD performance.
6. Conclusions
Previous studies showed that congestion distribution plays a critical role in traffic state estimation [
22,
30]. However, the potential benefits of this important variable in improving the emission estimation model’s accuracy were not explored. In this paper, we presented an enhanced version of the emission macroscopic fundamental diagram (e-MFD), which included the standard deviation of the density as an independent variable, along with density and speed. Our observations suggested e-MFD is bi-modal (free flow and congested branch). With that in mind, we added a dummy variable for separating the free-flow and congested branches to our e-MFD model.
The original e-MFD showed promising, and accurate results [
13]. However, the stability of the e-MFD was not explored. Also, we showed the e-MFD accuracy could be improved by adding the standard deviation of density, which was missing in previous studies. We tested the performance of our model in two case studies, a synthetic grid network and Blacksburg, VA network. Also, three challenging scenarios were selected to test the stability of the model in the grid network. First, the day-to-day stability was done by testing the developed model against unseen simulated data with different random seeds. The stability in directional demand pattern scenarios and accident scenarios were the two other experimental scenarios considered for testing the stability of the proposed model. The contributions of the current study are twofold: Offering an advanced version of e-MFD, which performs better than the original e-MFD in emission estimation without requiring new data collection. Also, we tested the stability of the original e-MFD and our e-MFD and showed the higher stability of our model. Moreover, this study highlights the critical role of network congestion homogeneity, which is crucial in maintaining network performance close to the desired state. Our model can be used in realistic cases for emission by importing the speed, density, and standard deviation of density, which are all easily accessible from loop detectors. We achieved higher emission estimation accuracy by adding only one single variable to the existing model, which can be obtained from loop detectors. This research highlighted the critical role of navigation in emission reduction as well. Our correlation analysis showed lower emission rates could be expected by keeping density’s standard deviation low through better navigation and more homogeneous congestion distribution. Furthermore, the model could be used for emission reduction in hierarchical traffic controllers [
22,
34], which were proven to be very effective in improving network performance. Such controllers use the congestion level and congestion homogeneity of each region presented in the proposed model.
In this paper, we considered some simplifying assumptions which could be relaxed in future research, such as: adding different vehicle types and conducting a sensitivity analysis of our model for different vehicle combinations. This analysis will help the network managers to optimize the network modal share to achieve minimum pollution. For example, previous studies showed that the effect of public transportation lines on regional emission levels could be considerable [
35]. Another interesting research frontier could be removing the full-coverage assumption we made in this paper. In real life, a limited number of network links are equipped with loop detectors, and we acknowledge this partial coverage could impact our model’s performance. However, finding the critical links (similar to [
36] about MFD) to capture network state with limited coverage could solve this issue. Furthermore, the e-MFD of a network can be utilized to develop advanced emission mitigation systems. In such a system, the network’s emissions level is monitored and predicted with e-MFD to search for the most efficient traffic management strategies, such as cooperative signal control, dynamic routing, and variable speed limit, to minimize the total network-level emissions.