# The Impact of Violations of Bicycles and Pedestrians on Vehicle Emissions at Signalized Intersections

Authors: Jianchang Huang; Guohua Song; Jianbo Zhang; Chenxu Li; Qiumei Liu; Lei Yu
Journal: Journal of Advanced Transportation
 (2020)

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## Abstract

An intersection is a typical emission hot spot in the urban traffic network. And frequent violations such as running the red light have been a critical social problem at signalized intersections in developing countries. This article aimed to quantify the impact of violations (behaviors which will block the fleet) on emissions at signalized intersections. Increased emissions of vehicles affected by violations are of two levels: (1) trajectory level for the first four affected vehicles and (2) traffic flow level for the subsequent vehicles. At the trajectory level, the study focuses on the second-by-second activities of the first four affected vehicles. First, the trajectory model of the first affected vehicle is developed. Then, the trajectory of the other three vehicles is constructed using the Gipps car-following model. At the traffic flow level, a linear emission model is developed to describe the relationship between emission factors and idling time in the one-stop (vehicle stop once) and two-stop (vehicle stop twice) scenarios based on the global position system (GPS)-collected data at 44 intersections in Beijing. Based on the linear emission model, increased emissions at the traffic flow level are calculated as knowing the number of stops and idling time before and after violations. The analysis of the subsequent vehicles is divided into unsaturated and saturated conditions. Under the unsaturated condition, the emissions have barely increased due to the increase of idling time for one-stop vehicles caused by the violations. Under the saturated conditions, the emission increment increases sharply as the one-stop vehicle gradually transforms to a two-stop vehicle because of violations, and the maximum emission increment reaches 45% in half an hour in the case. The increment of emissions decreases steadily as the proportion of two-stop vehicles reaches 100% after violations, while the proportion before violations keeps increasing.


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## Body

## 1. Introduction

In recent years, urban vehicle pollution has threatened human health. Air pollutants can cause pulmonary and cardiovascular diseases and chronic obstructive pulmonary disease, and decrease lung function [1]. According to the WHO report, air pollution resulted in 3.7 million premature deaths worldwide in 2012 [2]. In the United States, motorized vehicles are responsible for 57% of emissions [3].An intersection is a typical emission hot spot in the urban traffic network [4], especially in a densely populated metropolis like Beijing. Extensive studies have been carried out on vehicle emissions around intersections, and illustrate that high emissions at intersections mainly resulted from unstable traffic operation and stop-and-go vehicle activity [5–7] and lead to high pollutant exposure, particularly to pedestrians and cyclists around the intersections.When vehicles, pedestrians, and cyclists arrive at the intersection, each traffic subject follows the corresponding rules and passes through the intersection orderly. However, violation behaviors, one of the core factors, are frequently observed in developing countries such as China [8]. Frequent violations will not only aggravate traffic risk but also worsen the stop-and-go condition of vehicles. Four typical violations at intersections are shown in Figure 1 frequent violations of pedestrians and bicycles block the vehicle fleet, aggravating stop-and-go behaviors at intersections. In this article, the critical problem of quantifying emission increments caused by violations has been discussed.Figure 1
Violations at signalized intersections under mixed traffic in Beijing. (a) Crossing the intersection diagonally. (b) Running the red light. (c) Waiting in front of the motorway. (d) Intruding into the lane.
(a)
(b)
(c)
(d)Motor vehicles, bicycles, and pedestrians are three typical traffic components of mixed traffic flow intersections. Their relationships are variable and complex due to the conflict in time and space. Existing studies indicated that violations were frequently observed in developing countries and had a significant impact on driving operation [7]. Researches on the impact of violations on emissions can be summarized into two categories: (1) intersection emission estimation and (2) violation characteristics and impact analysis.In terms of intersection emission estimation, existing studies indicated that steady speed, shortest delays, and fewest stops are the best operations for emission reduction [9, 10]; nonsmooth traffic operations and stop-and-go activity were the main reasons for high emissions at intersections; and much more time was spent in the acceleration mode after highly interrupted movements of vehicles [11–13]. During the acceleration period, an engine operates at a high level, which leads to excessive fuel consumption and emissions [14, 15]. In existing studies, extensive studies have been carried out on vehicle emission around intersections. Rakha and Ding analyzed the impact of stops on vehicle fuel consumption and emissions and found that vehicle fuel consumption was more sensitive to cruise-speed levels [13]. Papson et al. used a time-in-mode model with MOVES to analyze vehicle emissions at congested and uncongested signalized intersections [16]. Zhang et al. developed the SIDRA model to estimate intersection emissions with MOVES, and acceleration mode included constant acceleration and linearly decreasing acceleration (3). Gokhale and Pandian developed a semi-empirical box model to predict CO concentration based on the assumed traffic flow pattern at intersections [17]. Braven et al. estimated vehicle emissions at a signalized intersection by using VISSIM [18].In terms of violation characteristic analysis, it can be summarized into two categories. (1) Violation characteristics mainly include two aspects: (a) for the influencing factors (waiting time, group size of pedestrians, gender, nonmotor vehicle type, and so on), existing studies indicated that these factors had an obvious impact on intersection violations [19–21], and (b) for the frequency model, violation probability model [22] and violation waiting time model [23] were developed to predict the frequency of violations. (2) Impact of interference has an impact on vehicles, both at the trajectory level and the traffic flow level. At the trajectory level, Przybyla established a dynamic car-following model for driving distraction [24]. At the traffic flow level, interference has an impact on vehicle speed [25] and further influences intersection capacity [26–28].The mechanism of the trajectory and emission characteristics affected by interference has not been fully understood. Further investigation is thus necessary. Hence, this article was aimed at quantifying the impact of violations on emissions at intersections. The content of this article is divided based on the following two aspects. (1) Variations in vehicle operating affected by violations. Variations of vehicle headways and trajectories are analyzed based on manual investigation data. (2) Based on the analysis above, increased emissions of vehicles affected by violations included two levels: (a) modeling at the trajectory level for second-by-second activities of the first four affected vehicles and (b) modeling at the traffic flow level for the aggregated parameters (number of stops and idling time) of the subsequent vehicles after the first four vehicles. A numerical simulation is conducted to assess the impact of violations on emissions based on the existing study.


## 2. Materials and Methods

In this study, violations are defined as the behavior that will block the vehicle fleet. Pedestrians and cyclists are the objectives of violations.Increased emissions of vehicles affected by violations include two levels (see Figure2): (1) trajectory level for the first four affected vehicles and (2) traffic flow level for the subsequent vehicles. At the trajectory level, the study focused on second-by-second activities of the first four affected vehicles. First, the trajectory model of the first affected vehicle is developed. Then, the trajectory of the other three vehicles is constructed by using the Gipps car-following model. At the traffic flow level, a linear emission model that can describe the relationship between emission factors and idling time in the one-stop and two-stop scenarios is developed by using Global Position System (GPS)-collected data at 44 intersections in Beijing. Increased emissions are calculated by the number of stops and idling time before and after violations based on the linear emission model. Finally, a case study is conducted to assess the impact of violations on vehicle emissions at signalized intersections.Figure 2
Overview of the methodology.


### 2.1. Data Collection

This article includes two types of data. (1) Manual investigation data are used for describing the vehicle operating characteristics under violation. (2) Emission data are used for developing the linear emission model, which can explain the relationship between emission factors and idling time in the one-stop and two-stop scenarios.


#### 2.1.1. Manual Investigation Data

Video data of 8 signalized intersections under mixed traffic were collected in Beijing, China, which are used to model the operating of vehicles affected by violations. The data include intersection attributes and violation data.(1)
Intersection attributes(a)
Channelization information(b)
Signal information(2)
Violation data: Violation data were acquired from videos frame by frame, which included three parts.(a)
Trajectories data. The crosswalk grid is constructed by crosswalks in the four directions of the intersection (see Figure3). Based on the crosswalk grid in the video, positions of vehicles at each time step are collected, and 10 groups of trajectories are collected under the influence of violations.(b)
Headway. 171 groups of time headway are collected from video, and each group includes five headways of vehicle fleet after the violation with a precision of 0.02 s.(c)
Idling time of the first affected vehicle. The time precision is 0.02 s, and 66 groups of data are collected.Figure 3
Intersection crosswalk grid in the video.


#### 2.1.2. Emission Data

The emission data includes two parts.(1)
Emission rate. Vehicle emission data are derived from the local emission rate model for light-duty gasoline vehicles [29, 30]. The emission standard of China IV was selected to provide the emission rates for LDVs, which is more common in Beijing compared with other emission standards.(2)
Global positioning system (GPS) trajectory data. 1666 valid trajectories of data, whose range is 200 meters of the intersection radius, were selected from 44 arterial and collector intersections in Beijing. Vehicle specific power (VSP, kW/ton) is estimated after data quality control [31]. Other details about the data are listed as follows:(i)
Date, from April 25th, 2004, to April 16th, 2013;(ii)
Time, from 5:00 to 23:00; and(iii)
Speed, from 0 to 133 km/h (for the whole trajectory to ensure accuracy of the GPS device), with a precision of 0.1 km/h [32].


### 2.2. Variations of Vehicle Operating Affected by Violations

Increased emissions of vehicles affected by violations included two levels: (1) trajectory level for the first four affected vehicles and (2) traffic flow level for the subsequent vehicles. At the trajectory level, the study focused on second-by-second activities of the first four affected vehicles. At the traffic flow level, the study focused on the number of stops and idling time before and after violations of the subsequent vehicles after the first four vehicles. Increased emissions of the two levels are the total increased emissions under the violation condition.The characteristics of headway under violations are shown in Figure4. When the violation occurs, the headway of the first affected vehicle will increase obviously. From the first affected vehicle to the fourth, the headways gradually return to be stable. The impact of violations on the vehicle fleet disappears after the fourth vehicle. As a result, the first four vehicles are determined as vehicles affected by violations in the trajectory level.(1)tlost=∑i=14thead,after,i−thead,before,i,where tlost (s) is the total lost time of violation behaviors. i is the ith vehicle after the violation location. thead,after (s) is the headway after the violation, and thead,before (s) is the time headway before the violation.Figure 4
Time headway after violations (with the first and third quantiles).Vehicles trajectories under the violation are shown in Figure5. The x-axis is time, and the y-axis is the distance. The negative y-axis is the location of the queuing vehicles, and the positive y-axis is downstream of the intersection.Figure 5
Vehicle trajectories affected by the violation.The red point represents the location and time of the violation.τ is the reaction time plus braking time, and Sτ is the corresponding distance. The first affected vehicle will return to normal speed after the process of deceleration-idling-acceleration. The second vehicle starts to decelerate after the reaction time of Dr since the first affected vehicle began to decelerate. The deceleration of the second vehicle is less than the first vehicle as the interference decreases as the impact of the violation spreads in the vehicle fleet. The second vehicle begins to accelerate after the reaction time of Ar since the first affected vehicle accelerated. When the y-axis of Dr and Ar is the same, the second affected vehicle will have a second stop; the process of the second vehicle is deceleration-idling-acceleration; if not, the process is deceleration-acceleration.The interference is gradually transmitted to the rear of the vehicle fleet, as described above. When the speed is low enough, the subsequent vehicles will extend the idling time to eliminate the interference as the fifth vehicle. Then, the subsequent vehicles will pass the intersection with the saturated time headway.


### 2.3. Trajectory Level

At the trajectory level, the objective is the first four affected vehicles after the violation. It is necessary to divide the model into two parts: (1) the trajectory model for the first vehicle and (2) the car-following model for the other three vehicles.


#### 2.3.1. The First Affected Vehicle

The trajectory of the first affected vehicle can be described when the following two factors are determined: (1) idling time and (2) acceleration and deceleration data.For the idling time, sixty-six groups of idling time data in violation situations are collected. The average idling time is 2.08 s (standard deviation is 3.03).For the acceleration and deceleration data, a corresponding relationship between vehicle speed and acceleration is developed in the low-speed range based on GPS trajectory data (see Figure6).Figure 6
Speed and corresponding acceleration in the low-speed range (with the first and third quantiles). (a) Speed distribution under low-speed range of queuing. (b) Acceleration distribution under low-speed range of queuing.
(a)
(b)As shown in Figure6, based on the GPS trajectory data of 44 intersections, a total of 18,709 pieces of valid data of the first 10-s deceleration and 10-s acceleration around the idling time are extracted. At low speed, each speed corresponds to a group of accelerations. In other words, the process of acceleration and deceleration in violation conditions can be totally described after knowing the initial speed before violations. The acceleration of the first affected vehicle can be calculated as equations (2)–(3):(2)as,t=randomarangevs,t,when  acceleration or deceleration,(3)a=0,v=0,when idling,where Vs,t are the speeds in the acceleration and deceleration states at time t; the states are acceleration and deceleration when s is a and d, respectively. arange (Vs,t) are the corresponding acceleration range of Va,t and Vd,t. Each corresponding acceleration range has a database in which random values are taken by numerical simulation.


#### 2.3.2. The Rear Three Vehicles of the First Four Affected Vehicles

The rear three vehicles decelerate after the sudden stop of the first affected vehicle. At the intersection, acceleration of the rear vehicle is closely related to the speed of the preceding vehicle, the speed of the rear vehicle, and the distance between the two vehicles. The Gipps car-following model can not only fulfill the above requirement but also generate rather realistic VSP distributions among the car-following models [33], which are calculated as equations (4)–(6):(4)vnt+τ=minvnacct+τ,vndect+τ,(5)vnacct+τ=vnt+2.5⋅anτ1−vntvnd0.025+vntvnd,(6)vndect+τ=−τdn+τ2d2+dn2⋅xn−1t−xnt−Sn−1−τvnt+vn−1t2dn−1.where an (m/s2) is the maximum desired acceleration of the following vehicle; dn (m/s2) is the maximum desired deceleration of the following vehicle; d^n−1 (m/s2) is the estimation of the maximum desired deceleration of the leading vehicle; T (s) is the apparent reaction time; Sn−1 is the effective length of a vehicle, which consists of the vehicle length and the minimum distance between the vehicles; θ is the additional delay for braking, which is 0.5; and α, β, and γ are parameters, which are 2.5, 0.025, and 0.5, respectively.


#### 2.3.3. Emission Increment at Trajectory Level

At the trajectory level, the study focused on second-by-second activities of the first four affected vehicles. Two different models are developed: one is the trajectory model of the first vehicle, while the other is the Gipps car-following model of the three rear vehicles. The trajectory model of four vehicles affected has been developed above; thus, increased emission factors of the four vehicles can be calculated as follows:(7)EFincreased,trajectory,x=3600⋅∑iERi⋅VSPBini,trajectory,xveffected,x−∑iERi⋅VSPBini,normal,xvnormal,x,x=1,2,3,4,where EFincreased,trajectory,x (g/km) is the increased emission factors of the xth affected vehicle, VSP Bini,trajectory,x is the time fraction in the ith VSP bin of trajectory after violations, and Veffected,x (km/h) is the average speed after violations.


### 2.4. Traffic Flow Level

At the traffic flow level, a linear emission model that can describe the relationship between emission factors and idling time in the one-stop and two-stop scenarios is developed by using GPS-collected data at 44 intersections in Beijing. Increased emissions are calculated by the number of stops and idling time before and after violations based on the linear emission model.


#### 2.4.1. Linearly Emission Model

In this section, a linear emission model which can describe the relationship between emission factors and idling time in the one-stop and two-stop scenarios is developed. The emission model is developed based on the emission rate data and 85 VSP distributions, which are constructed based on the number of stops and idling time.(1) VSP Distribution. Based on field measurements from the available research on emissions, there are three typical trajectories for a vehicle passing through an intersection (see Figure 7): (a) No stop, (b) one stop, and (c) multiple stops at the intersection (30, 31). It is hypothesized that each of these speed profiles generates different levels of emissions, with type three generating the highest amount of emission due to longer idling time and more acceleration and deceleration circles.Figure 7
Three types of GPS trajectories at mixed-flow intersection.The equation for calculating VSP is provided by equation (8). VSP values are binned at an interval of 1 kW/ton. This article analyzes the VSP bins of −20 kW/ton to 20 kW/ton. More than 98% of the VSP data are in this range.(8)VSPt=A⋅vt+B⋅vt2+C⋅vt3m+at+g⋅sinθ⋅vt,where at (m/s2) is the acceleration, g (m/s2) is the acceleration due to gravity, which is 9.8 m/s2; and sinθ is the road grade. A  (kw·s/m), B  (kw·s2/m2), and C  (kw·s3/m3) are road load coefficients, representing rolling resistance, rotational resistance, and aerodynamic drag, respectively; the values of A, B, and C are 0.156461, 0.0020002, and 0.000493, respectively. m (ton) is the vehicle weight, and the value is 1.4788 ton.Based on GPS trajectory data, idling time rarely exceeds 150 s for one-stop vehicles, or 275 s for two-stop vehicles. Thus, 85 VSP distributions are developed based on the number of stops, idling time, and division of upstream and downstream (see Table1).Table 1
Information of the eighty-five VSP distributions.
Serial number
Spatial position
Number of stops
Idling time (s)
1
Downstream of intersection
0
0
2
Upstream of intersection
0
0∼2
3
Upstream of intersection
1
2∼5
4
Upstream of intersection
1
5∼10
5
Upstream of intersection
1
10∼15
……
30
Upstream of intersection
1
135∼140
31
Upstream of intersection
1
140∼145
32
Upstream of intersection
1
145∼150
33
Upstream of intersection
2
10∼15
34
Upstream of intersection
2
15∼20
35
Upstream of intersection
2
20∼25
……
83
Upstream of intersection
2
260∼265
84
Upstream of intersection
2
265∼270
85
Upstream of intersection
2
270∼275(2) Emission Rates. Vehicle emission rate data were derived from the local emission rate model for light-duty gasoline vehicles (see Figure 8), and the type of gasoline emission standard is China IV.Figure 8
Mean emission rates in each VSP bin.(3) Emission Factors. Idling time and number of stops are the most important changes under the violation. Therefore, the eimssion factors have two key parameters: number of stops and the idling time based on GPS data (see Figure 8). The downstream emission factor is constant, as there is no stop. The emission factors are calculated as follows:(9)EFv=3600⋅∑iERiVSPBiniv,where EFv (g/km) is the emission factor at the average speed of v (km/h). ERi (g/s) is the mean emission rate of the ith VSP Bin. VSPBini is the fraction in the ith VSP Bin.The emission factors increase linearly with the increase in idling time, as shown in Figure9. The difference in emission factors between one-stop and two-stop vehicles is small under the same idling time. It is because the two-stop vehicle keeps a low speed and low acceleration, while the corresponding VSP value is concentrated around zero, and the corresponding emission rate is also small. But the range of the idling time of one-stop and two-stop vehicles is obviously different. The emission factor model is shown as follows:(10)EFc,i=ac,i⋅tidling+bc,i,c=1,2,i=1,2,3,4,where EFi, EFj (g/km) are emissions of types i and j. When i = 1, 2, 3, 4, EFi is the emission factor of CO2, CO, NOX, and HC of one-stop vehicles, respectively. When c = 1, 2, EFj is the emission factor of one-stop and two-stop vehicles, respectively. tidling is the idling time of the vehicle. ai and bi are parameters.Figure 9
Emission factor model based on the number of stops and idling time.
(a)
(b)


#### 2.4.2. Variations of Vehicles Operating at Traffic Flow Level

At the traffic flow level, the study focused on the number of stops and idling time for the subsequent vehicles after the first four vehicles, which is divided into two scenarios (see Figure10).(1)
Unsaturated condition of the vehicle fleet after being disturbed by violations;(2)
Saturated condition of the vehicle fleet after being disturbed by violations.Figure 10
Characteristics of subsequent vehicles after violations.As shown in Figure10, the total lost time of the first four affected vehicles is 4 s in the unsaturated condition. The idling time of subsequent vehicles increases by 4 s, and the number of stops is still one. Under the saturated condition, two vehicles will transform from one stop to two stops due to the increased idling time. And the idling time of two-stop vehicles increases by 4 s. Suppose that the maximum number of stops for all vehicles is two. Subsequent vehicles are divided into three types: (type A) one-stop vehicle, the increase in idling time is equal to the total lost time, (type B) transformation from one-stop vehicle to two-stop vehicle, and (type C) two-stop vehicle, the increase in idling time is equal to the total lost time of cycles.Under the unsaturated condition, the subsequent vehicles are all type A. Under the saturated condition, vehicles that passing through the intersection are types A, B, and C at the beginning. As cycles pass, type A vehicles will disappear first, followed by type B vehicles. After all vehicles transform to two-stop vehicles, vehicles passing through the intersection are all type C.As shown in Figure11, VSP distributions of vehicles with and without violations are divided into three conditions, which corresponds to types A, B, and C (see Figure 11). For types A and C, the number of stops of affected vehicles is constant. Thus, the difference in VSP distributions of vehicles with and without violations is small. For type B, the number of stops transforms from one to two, and the idling time increment is the sum of the lost time and the red-light time. The frequency of VSP distributed above 0 kW/ton will be much highly affected by violations.Figure 11
VSP distributions of vehicles with and without violations. (a) One-stop vehicle (type A). (b) The vehicle transforms from one stop to two stops (type B). (c) Two-stop vehicle (type C).
(a)
(b)
(c)Take equation (10) as a reference. The emission model has been developed based on the number of stops and idling time. The operation change of subsequent vehicles, which are after the first four affected vehicles, is reflected in the number of stops and idling time. Therefore, increased emissions of the subsequent vehicles can be obtained by the emission model above. Based on equation (11), the numerical simulation method is used to calculate the emissions under violation conditions.(11)EFincreased,flow,y=acAfter,i⋅tafter+bcAfter,i−acBefore,i⋅tbefore+bcBefore,i,where EFincreased,flow,y (g/km) is the increased emission factors of subsequent vehicles. y is the yth vehicle of vehicles going through the intersection in the cycle. tafter is the idling time after violations, and tbefore (s) is the idling time without violations. cAfter and cBefore are stopping numbers before and after violations, respectively.


### 2.5. Increased Emissions Affected by Violations

The analysis of emissions affected by violations includes two levels. At the trajectory level, the study focused on second-by-second activities of the first four affected vehicles. At the traffic flow level, the study focused on the aggregated parameters (number of stops and idling) for the subsequent vehicles after the first four vehicles, and the conditions are divided into two categories: unsaturated and saturated conditions of the vehicle fleet disturbed by violations.The sum of the increased emissions on these two levels is the total emission at intersections affected by violations, which can be calculated as follows:(12)AE=∑x=ee+3EFincreased,trajectory,x+∑x=e+4nEFincreased,flow,x∑i=1nEFi+EFdownstream·D,where AE (%) is the increased emission increment of the cycle. e is the eth vehicle, which is the location of the first affected vehicle. n is the vehicle number of the cycle. EFincreased,trajectory,x (g/km) is the increased emission factors of the first four affected vehicles. EFincreased,flow,y (g/km) is the increased emission factors of the subsequent vehicles after the first four affected vehicles. EFi (g/km) is the normal emission factors of vehicles. EFdownstream (g/km) is the emission factors downstream of the intersection. D (km) is the distance of the study range, which is 200 meters.


## 2.1. Data Collection

This article includes two types of data. (1) Manual investigation data are used for describing the vehicle operating characteristics under violation. (2) Emission data are used for developing the linear emission model, which can explain the relationship between emission factors and idling time in the one-stop and two-stop scenarios.


### 2.1.1. Manual Investigation Data

Video data of 8 signalized intersections under mixed traffic were collected in Beijing, China, which are used to model the operating of vehicles affected by violations. The data include intersection attributes and violation data.(1)
Intersection attributes(a)
Channelization information(b)
Signal information(2)
Violation data: Violation data were acquired from videos frame by frame, which included three parts.(a)
Trajectories data. The crosswalk grid is constructed by crosswalks in the four directions of the intersection (see Figure3). Based on the crosswalk grid in the video, positions of vehicles at each time step are collected, and 10 groups of trajectories are collected under the influence of violations.(b)
Headway. 171 groups of time headway are collected from video, and each group includes five headways of vehicle fleet after the violation with a precision of 0.02 s.(c)
Idling time of the first affected vehicle. The time precision is 0.02 s, and 66 groups of data are collected.Figure 3
Intersection crosswalk grid in the video.


### 2.1.2. Emission Data

The emission data includes two parts.(1)
Emission rate. Vehicle emission data are derived from the local emission rate model for light-duty gasoline vehicles [29, 30]. The emission standard of China IV was selected to provide the emission rates for LDVs, which is more common in Beijing compared with other emission standards.(2)
Global positioning system (GPS) trajectory data. 1666 valid trajectories of data, whose range is 200 meters of the intersection radius, were selected from 44 arterial and collector intersections in Beijing. Vehicle specific power (VSP, kW/ton) is estimated after data quality control [31]. Other details about the data are listed as follows:(i)
Date, from April 25th, 2004, to April 16th, 2013;(ii)
Time, from 5:00 to 23:00; and(iii)
Speed, from 0 to 133 km/h (for the whole trajectory to ensure accuracy of the GPS device), with a precision of 0.1 km/h [32].


## 2.1.1. Manual Investigation Data

Video data of 8 signalized intersections under mixed traffic were collected in Beijing, China, which are used to model the operating of vehicles affected by violations. The data include intersection attributes and violation data.(1)
Intersection attributes(a)
Channelization information(b)
Signal information(2)
Violation data: Violation data were acquired from videos frame by frame, which included three parts.(a)
Trajectories data. The crosswalk grid is constructed by crosswalks in the four directions of the intersection (see Figure3). Based on the crosswalk grid in the video, positions of vehicles at each time step are collected, and 10 groups of trajectories are collected under the influence of violations.(b)
Headway. 171 groups of time headway are collected from video, and each group includes five headways of vehicle fleet after the violation with a precision of 0.02 s.(c)
Idling time of the first affected vehicle. The time precision is 0.02 s, and 66 groups of data are collected.Figure 3
Intersection crosswalk grid in the video.


## 2.1.2. Emission Data

The emission data includes two parts.(1)
Emission rate. Vehicle emission data are derived from the local emission rate model for light-duty gasoline vehicles [29, 30]. The emission standard of China IV was selected to provide the emission rates for LDVs, which is more common in Beijing compared with other emission standards.(2)
Global positioning system (GPS) trajectory data. 1666 valid trajectories of data, whose range is 200 meters of the intersection radius, were selected from 44 arterial and collector intersections in Beijing. Vehicle specific power (VSP, kW/ton) is estimated after data quality control [31]. Other details about the data are listed as follows:(i)
Date, from April 25th, 2004, to April 16th, 2013;(ii)
Time, from 5:00 to 23:00; and(iii)
Speed, from 0 to 133 km/h (for the whole trajectory to ensure accuracy of the GPS device), with a precision of 0.1 km/h [32].


## 2.2. Variations of Vehicle Operating Affected by Violations

Increased emissions of vehicles affected by violations included two levels: (1) trajectory level for the first four affected vehicles and (2) traffic flow level for the subsequent vehicles. At the trajectory level, the study focused on second-by-second activities of the first four affected vehicles. At the traffic flow level, the study focused on the number of stops and idling time before and after violations of the subsequent vehicles after the first four vehicles. Increased emissions of the two levels are the total increased emissions under the violation condition.The characteristics of headway under violations are shown in Figure4. When the violation occurs, the headway of the first affected vehicle will increase obviously. From the first affected vehicle to the fourth, the headways gradually return to be stable. The impact of violations on the vehicle fleet disappears after the fourth vehicle. As a result, the first four vehicles are determined as vehicles affected by violations in the trajectory level.(1)tlost=∑i=14thead,after,i−thead,before,i,where tlost (s) is the total lost time of violation behaviors. i is the ith vehicle after the violation location. thead,after (s) is the headway after the violation, and thead,before (s) is the time headway before the violation.Figure 4
Time headway after violations (with the first and third quantiles).Vehicles trajectories under the violation are shown in Figure5. The x-axis is time, and the y-axis is the distance. The negative y-axis is the location of the queuing vehicles, and the positive y-axis is downstream of the intersection.Figure 5
Vehicle trajectories affected by the violation.The red point represents the location and time of the violation.τ is the reaction time plus braking time, and Sτ is the corresponding distance. The first affected vehicle will return to normal speed after the process of deceleration-idling-acceleration. The second vehicle starts to decelerate after the reaction time of Dr since the first affected vehicle began to decelerate. The deceleration of the second vehicle is less than the first vehicle as the interference decreases as the impact of the violation spreads in the vehicle fleet. The second vehicle begins to accelerate after the reaction time of Ar since the first affected vehicle accelerated. When the y-axis of Dr and Ar is the same, the second affected vehicle will have a second stop; the process of the second vehicle is deceleration-idling-acceleration; if not, the process is deceleration-acceleration.The interference is gradually transmitted to the rear of the vehicle fleet, as described above. When the speed is low enough, the subsequent vehicles will extend the idling time to eliminate the interference as the fifth vehicle. Then, the subsequent vehicles will pass the intersection with the saturated time headway.


## 2.3. Trajectory Level

At the trajectory level, the objective is the first four affected vehicles after the violation. It is necessary to divide the model into two parts: (1) the trajectory model for the first vehicle and (2) the car-following model for the other three vehicles.


### 2.3.1. The First Affected Vehicle

The trajectory of the first affected vehicle can be described when the following two factors are determined: (1) idling time and (2) acceleration and deceleration data.For the idling time, sixty-six groups of idling time data in violation situations are collected. The average idling time is 2.08 s (standard deviation is 3.03).For the acceleration and deceleration data, a corresponding relationship between vehicle speed and acceleration is developed in the low-speed range based on GPS trajectory data (see Figure6).Figure 6
Speed and corresponding acceleration in the low-speed range (with the first and third quantiles). (a) Speed distribution under low-speed range of queuing. (b) Acceleration distribution under low-speed range of queuing.
(a)
(b)As shown in Figure6, based on the GPS trajectory data of 44 intersections, a total of 18,709 pieces of valid data of the first 10-s deceleration and 10-s acceleration around the idling time are extracted. At low speed, each speed corresponds to a group of accelerations. In other words, the process of acceleration and deceleration in violation conditions can be totally described after knowing the initial speed before violations. The acceleration of the first affected vehicle can be calculated as equations (2)–(3):(2)as,t=randomarangevs,t,when  acceleration or deceleration,(3)a=0,v=0,when idling,where Vs,t are the speeds in the acceleration and deceleration states at time t; the states are acceleration and deceleration when s is a and d, respectively. arange (Vs,t) are the corresponding acceleration range of Va,t and Vd,t. Each corresponding acceleration range has a database in which random values are taken by numerical simulation.


### 2.3.2. The Rear Three Vehicles of the First Four Affected Vehicles

The rear three vehicles decelerate after the sudden stop of the first affected vehicle. At the intersection, acceleration of the rear vehicle is closely related to the speed of the preceding vehicle, the speed of the rear vehicle, and the distance between the two vehicles. The Gipps car-following model can not only fulfill the above requirement but also generate rather realistic VSP distributions among the car-following models [33], which are calculated as equations (4)–(6):(4)vnt+τ=minvnacct+τ,vndect+τ,(5)vnacct+τ=vnt+2.5⋅anτ1−vntvnd0.025+vntvnd,(6)vndect+τ=−τdn+τ2d2+dn2⋅xn−1t−xnt−Sn−1−τvnt+vn−1t2dn−1.where an (m/s2) is the maximum desired acceleration of the following vehicle; dn (m/s2) is the maximum desired deceleration of the following vehicle; d^n−1 (m/s2) is the estimation of the maximum desired deceleration of the leading vehicle; T (s) is the apparent reaction time; Sn−1 is the effective length of a vehicle, which consists of the vehicle length and the minimum distance between the vehicles; θ is the additional delay for braking, which is 0.5; and α, β, and γ are parameters, which are 2.5, 0.025, and 0.5, respectively.


### 2.3.3. Emission Increment at Trajectory Level

At the trajectory level, the study focused on second-by-second activities of the first four affected vehicles. Two different models are developed: one is the trajectory model of the first vehicle, while the other is the Gipps car-following model of the three rear vehicles. The trajectory model of four vehicles affected has been developed above; thus, increased emission factors of the four vehicles can be calculated as follows:(7)EFincreased,trajectory,x=3600⋅∑iERi⋅VSPBini,trajectory,xveffected,x−∑iERi⋅VSPBini,normal,xvnormal,x,x=1,2,3,4,where EFincreased,trajectory,x (g/km) is the increased emission factors of the xth affected vehicle, VSP Bini,trajectory,x is the time fraction in the ith VSP bin of trajectory after violations, and Veffected,x (km/h) is the average speed after violations.


## 2.3.1. The First Affected Vehicle

The trajectory of the first affected vehicle can be described when the following two factors are determined: (1) idling time and (2) acceleration and deceleration data.For the idling time, sixty-six groups of idling time data in violation situations are collected. The average idling time is 2.08 s (standard deviation is 3.03).For the acceleration and deceleration data, a corresponding relationship between vehicle speed and acceleration is developed in the low-speed range based on GPS trajectory data (see Figure6).Figure 6
Speed and corresponding acceleration in the low-speed range (with the first and third quantiles). (a) Speed distribution under low-speed range of queuing. (b) Acceleration distribution under low-speed range of queuing.
(a)
(b)As shown in Figure6, based on the GPS trajectory data of 44 intersections, a total of 18,709 pieces of valid data of the first 10-s deceleration and 10-s acceleration around the idling time are extracted. At low speed, each speed corresponds to a group of accelerations. In other words, the process of acceleration and deceleration in violation conditions can be totally described after knowing the initial speed before violations. The acceleration of the first affected vehicle can be calculated as equations (2)–(3):(2)as,t=randomarangevs,t,when  acceleration or deceleration,(3)a=0,v=0,when idling,where Vs,t are the speeds in the acceleration and deceleration states at time t; the states are acceleration and deceleration when s is a and d, respectively. arange (Vs,t) are the corresponding acceleration range of Va,t and Vd,t. Each corresponding acceleration range has a database in which random values are taken by numerical simulation.


## 2.3.2. The Rear Three Vehicles of the First Four Affected Vehicles

The rear three vehicles decelerate after the sudden stop of the first affected vehicle. At the intersection, acceleration of the rear vehicle is closely related to the speed of the preceding vehicle, the speed of the rear vehicle, and the distance between the two vehicles. The Gipps car-following model can not only fulfill the above requirement but also generate rather realistic VSP distributions among the car-following models [33], which are calculated as equations (4)–(6):(4)vnt+τ=minvnacct+τ,vndect+τ,(5)vnacct+τ=vnt+2.5⋅anτ1−vntvnd0.025+vntvnd,(6)vndect+τ=−τdn+τ2d2+dn2⋅xn−1t−xnt−Sn−1−τvnt+vn−1t2dn−1.where an (m/s2) is the maximum desired acceleration of the following vehicle; dn (m/s2) is the maximum desired deceleration of the following vehicle; d^n−1 (m/s2) is the estimation of the maximum desired deceleration of the leading vehicle; T (s) is the apparent reaction time; Sn−1 is the effective length of a vehicle, which consists of the vehicle length and the minimum distance between the vehicles; θ is the additional delay for braking, which is 0.5; and α, β, and γ are parameters, which are 2.5, 0.025, and 0.5, respectively.


## 2.3.3. Emission Increment at Trajectory Level

At the trajectory level, the study focused on second-by-second activities of the first four affected vehicles. Two different models are developed: one is the trajectory model of the first vehicle, while the other is the Gipps car-following model of the three rear vehicles. The trajectory model of four vehicles affected has been developed above; thus, increased emission factors of the four vehicles can be calculated as follows:(7)EFincreased,trajectory,x=3600⋅∑iERi⋅VSPBini,trajectory,xveffected,x−∑iERi⋅VSPBini,normal,xvnormal,x,x=1,2,3,4,where EFincreased,trajectory,x (g/km) is the increased emission factors of the xth affected vehicle, VSP Bini,trajectory,x is the time fraction in the ith VSP bin of trajectory after violations, and Veffected,x (km/h) is the average speed after violations.


## 2.4. Traffic Flow Level

At the traffic flow level, a linear emission model that can describe the relationship between emission factors and idling time in the one-stop and two-stop scenarios is developed by using GPS-collected data at 44 intersections in Beijing. Increased emissions are calculated by the number of stops and idling time before and after violations based on the linear emission model.


### 2.4.1. Linearly Emission Model

In this section, a linear emission model which can describe the relationship between emission factors and idling time in the one-stop and two-stop scenarios is developed. The emission model is developed based on the emission rate data and 85 VSP distributions, which are constructed based on the number of stops and idling time.(1) VSP Distribution. Based on field measurements from the available research on emissions, there are three typical trajectories for a vehicle passing through an intersection (see Figure 7): (a) No stop, (b) one stop, and (c) multiple stops at the intersection (30, 31). It is hypothesized that each of these speed profiles generates different levels of emissions, with type three generating the highest amount of emission due to longer idling time and more acceleration and deceleration circles.Figure 7
Three types of GPS trajectories at mixed-flow intersection.The equation for calculating VSP is provided by equation (8). VSP values are binned at an interval of 1 kW/ton. This article analyzes the VSP bins of −20 kW/ton to 20 kW/ton. More than 98% of the VSP data are in this range.(8)VSPt=A⋅vt+B⋅vt2+C⋅vt3m+at+g⋅sinθ⋅vt,where at (m/s2) is the acceleration, g (m/s2) is the acceleration due to gravity, which is 9.8 m/s2; and sinθ is the road grade. A  (kw·s/m), B  (kw·s2/m2), and C  (kw·s3/m3) are road load coefficients, representing rolling resistance, rotational resistance, and aerodynamic drag, respectively; the values of A, B, and C are 0.156461, 0.0020002, and 0.000493, respectively. m (ton) is the vehicle weight, and the value is 1.4788 ton.Based on GPS trajectory data, idling time rarely exceeds 150 s for one-stop vehicles, or 275 s for two-stop vehicles. Thus, 85 VSP distributions are developed based on the number of stops, idling time, and division of upstream and downstream (see Table1).Table 1
Information of the eighty-five VSP distributions.
Serial number
Spatial position
Number of stops
Idling time (s)
1
Downstream of intersection
0
0
2
Upstream of intersection
0
0∼2
3
Upstream of intersection
1
2∼5
4
Upstream of intersection
1
5∼10
5
Upstream of intersection
1
10∼15
……
30
Upstream of intersection
1
135∼140
31
Upstream of intersection
1
140∼145
32
Upstream of intersection
1
145∼150
33
Upstream of intersection
2
10∼15
34
Upstream of intersection
2
15∼20
35
Upstream of intersection
2
20∼25
……
83
Upstream of intersection
2
260∼265
84
Upstream of intersection
2
265∼270
85
Upstream of intersection
2
270∼275(2) Emission Rates. Vehicle emission rate data were derived from the local emission rate model for light-duty gasoline vehicles (see Figure 8), and the type of gasoline emission standard is China IV.Figure 8
Mean emission rates in each VSP bin.(3) Emission Factors. Idling time and number of stops are the most important changes under the violation. Therefore, the eimssion factors have two key parameters: number of stops and the idling time based on GPS data (see Figure 8). The downstream emission factor is constant, as there is no stop. The emission factors are calculated as follows:(9)EFv=3600⋅∑iERiVSPBiniv,where EFv (g/km) is the emission factor at the average speed of v (km/h). ERi (g/s) is the mean emission rate of the ith VSP Bin. VSPBini is the fraction in the ith VSP Bin.The emission factors increase linearly with the increase in idling time, as shown in Figure9. The difference in emission factors between one-stop and two-stop vehicles is small under the same idling time. It is because the two-stop vehicle keeps a low speed and low acceleration, while the corresponding VSP value is concentrated around zero, and the corresponding emission rate is also small. But the range of the idling time of one-stop and two-stop vehicles is obviously different. The emission factor model is shown as follows:(10)EFc,i=ac,i⋅tidling+bc,i,c=1,2,i=1,2,3,4,where EFi, EFj (g/km) are emissions of types i and j. When i = 1, 2, 3, 4, EFi is the emission factor of CO2, CO, NOX, and HC of one-stop vehicles, respectively. When c = 1, 2, EFj is the emission factor of one-stop and two-stop vehicles, respectively. tidling is the idling time of the vehicle. ai and bi are parameters.Figure 9
Emission factor model based on the number of stops and idling time.
(a)
(b)


### 2.4.2. Variations of Vehicles Operating at Traffic Flow Level

At the traffic flow level, the study focused on the number of stops and idling time for the subsequent vehicles after the first four vehicles, which is divided into two scenarios (see Figure10).(1)
Unsaturated condition of the vehicle fleet after being disturbed by violations;(2)
Saturated condition of the vehicle fleet after being disturbed by violations.Figure 10
Characteristics of subsequent vehicles after violations.As shown in Figure10, the total lost time of the first four affected vehicles is 4 s in the unsaturated condition. The idling time of subsequent vehicles increases by 4 s, and the number of stops is still one. Under the saturated condition, two vehicles will transform from one stop to two stops due to the increased idling time. And the idling time of two-stop vehicles increases by 4 s. Suppose that the maximum number of stops for all vehicles is two. Subsequent vehicles are divided into three types: (type A) one-stop vehicle, the increase in idling time is equal to the total lost time, (type B) transformation from one-stop vehicle to two-stop vehicle, and (type C) two-stop vehicle, the increase in idling time is equal to the total lost time of cycles.Under the unsaturated condition, the subsequent vehicles are all type A. Under the saturated condition, vehicles that passing through the intersection are types A, B, and C at the beginning. As cycles pass, type A vehicles will disappear first, followed by type B vehicles. After all vehicles transform to two-stop vehicles, vehicles passing through the intersection are all type C.As shown in Figure11, VSP distributions of vehicles with and without violations are divided into three conditions, which corresponds to types A, B, and C (see Figure 11). For types A and C, the number of stops of affected vehicles is constant. Thus, the difference in VSP distributions of vehicles with and without violations is small. For type B, the number of stops transforms from one to two, and the idling time increment is the sum of the lost time and the red-light time. The frequency of VSP distributed above 0 kW/ton will be much highly affected by violations.Figure 11
VSP distributions of vehicles with and without violations. (a) One-stop vehicle (type A). (b) The vehicle transforms from one stop to two stops (type B). (c) Two-stop vehicle (type C).
(a)
(b)
(c)Take equation (10) as a reference. The emission model has been developed based on the number of stops and idling time. The operation change of subsequent vehicles, which are after the first four affected vehicles, is reflected in the number of stops and idling time. Therefore, increased emissions of the subsequent vehicles can be obtained by the emission model above. Based on equation (11), the numerical simulation method is used to calculate the emissions under violation conditions.(11)EFincreased,flow,y=acAfter,i⋅tafter+bcAfter,i−acBefore,i⋅tbefore+bcBefore,i,where EFincreased,flow,y (g/km) is the increased emission factors of subsequent vehicles. y is the yth vehicle of vehicles going through the intersection in the cycle. tafter is the idling time after violations, and tbefore (s) is the idling time without violations. cAfter and cBefore are stopping numbers before and after violations, respectively.


## 2.4.1. Linearly Emission Model

In this section, a linear emission model which can describe the relationship between emission factors and idling time in the one-stop and two-stop scenarios is developed. The emission model is developed based on the emission rate data and 85 VSP distributions, which are constructed based on the number of stops and idling time.(1) VSP Distribution. Based on field measurements from the available research on emissions, there are three typical trajectories for a vehicle passing through an intersection (see Figure 7): (a) No stop, (b) one stop, and (c) multiple stops at the intersection (30, 31). It is hypothesized that each of these speed profiles generates different levels of emissions, with type three generating the highest amount of emission due to longer idling time and more acceleration and deceleration circles.Figure 7
Three types of GPS trajectories at mixed-flow intersection.The equation for calculating VSP is provided by equation (8). VSP values are binned at an interval of 1 kW/ton. This article analyzes the VSP bins of −20 kW/ton to 20 kW/ton. More than 98% of the VSP data are in this range.(8)VSPt=A⋅vt+B⋅vt2+C⋅vt3m+at+g⋅sinθ⋅vt,where at (m/s2) is the acceleration, g (m/s2) is the acceleration due to gravity, which is 9.8 m/s2; and sinθ is the road grade. A  (kw·s/m), B  (kw·s2/m2), and C  (kw·s3/m3) are road load coefficients, representing rolling resistance, rotational resistance, and aerodynamic drag, respectively; the values of A, B, and C are 0.156461, 0.0020002, and 0.000493, respectively. m (ton) is the vehicle weight, and the value is 1.4788 ton.Based on GPS trajectory data, idling time rarely exceeds 150 s for one-stop vehicles, or 275 s for two-stop vehicles. Thus, 85 VSP distributions are developed based on the number of stops, idling time, and division of upstream and downstream (see Table1).Table 1
Information of the eighty-five VSP distributions.
Serial number
Spatial position
Number of stops
Idling time (s)
1
Downstream of intersection
0
0
2
Upstream of intersection
0
0∼2
3
Upstream of intersection
1
2∼5
4
Upstream of intersection
1
5∼10
5
Upstream of intersection
1
10∼15
……
30
Upstream of intersection
1
135∼140
31
Upstream of intersection
1
140∼145
32
Upstream of intersection
1
145∼150
33
Upstream of intersection
2
10∼15
34
Upstream of intersection
2
15∼20
35
Upstream of intersection
2
20∼25
……
83
Upstream of intersection
2
260∼265
84
Upstream of intersection
2
265∼270
85
Upstream of intersection
2
270∼275(2) Emission Rates. Vehicle emission rate data were derived from the local emission rate model for light-duty gasoline vehicles (see Figure 8), and the type of gasoline emission standard is China IV.Figure 8
Mean emission rates in each VSP bin.(3) Emission Factors. Idling time and number of stops are the most important changes under the violation. Therefore, the eimssion factors have two key parameters: number of stops and the idling time based on GPS data (see Figure 8). The downstream emission factor is constant, as there is no stop. The emission factors are calculated as follows:(9)EFv=3600⋅∑iERiVSPBiniv,where EFv (g/km) is the emission factor at the average speed of v (km/h). ERi (g/s) is the mean emission rate of the ith VSP Bin. VSPBini is the fraction in the ith VSP Bin.The emission factors increase linearly with the increase in idling time, as shown in Figure9. The difference in emission factors between one-stop and two-stop vehicles is small under the same idling time. It is because the two-stop vehicle keeps a low speed and low acceleration, while the corresponding VSP value is concentrated around zero, and the corresponding emission rate is also small. But the range of the idling time of one-stop and two-stop vehicles is obviously different. The emission factor model is shown as follows:(10)EFc,i=ac,i⋅tidling+bc,i,c=1,2,i=1,2,3,4,where EFi, EFj (g/km) are emissions of types i and j. When i = 1, 2, 3, 4, EFi is the emission factor of CO2, CO, NOX, and HC of one-stop vehicles, respectively. When c = 1, 2, EFj is the emission factor of one-stop and two-stop vehicles, respectively. tidling is the idling time of the vehicle. ai and bi are parameters.Figure 9
Emission factor model based on the number of stops and idling time.
(a)
(b)


## 2.4.2. Variations of Vehicles Operating at Traffic Flow Level

At the traffic flow level, the study focused on the number of stops and idling time for the subsequent vehicles after the first four vehicles, which is divided into two scenarios (see Figure10).(1)
Unsaturated condition of the vehicle fleet after being disturbed by violations;(2)
Saturated condition of the vehicle fleet after being disturbed by violations.Figure 10
Characteristics of subsequent vehicles after violations.As shown in Figure10, the total lost time of the first four affected vehicles is 4 s in the unsaturated condition. The idling time of subsequent vehicles increases by 4 s, and the number of stops is still one. Under the saturated condition, two vehicles will transform from one stop to two stops due to the increased idling time. And the idling time of two-stop vehicles increases by 4 s. Suppose that the maximum number of stops for all vehicles is two. Subsequent vehicles are divided into three types: (type A) one-stop vehicle, the increase in idling time is equal to the total lost time, (type B) transformation from one-stop vehicle to two-stop vehicle, and (type C) two-stop vehicle, the increase in idling time is equal to the total lost time of cycles.Under the unsaturated condition, the subsequent vehicles are all type A. Under the saturated condition, vehicles that passing through the intersection are types A, B, and C at the beginning. As cycles pass, type A vehicles will disappear first, followed by type B vehicles. After all vehicles transform to two-stop vehicles, vehicles passing through the intersection are all type C.As shown in Figure11, VSP distributions of vehicles with and without violations are divided into three conditions, which corresponds to types A, B, and C (see Figure 11). For types A and C, the number of stops of affected vehicles is constant. Thus, the difference in VSP distributions of vehicles with and without violations is small. For type B, the number of stops transforms from one to two, and the idling time increment is the sum of the lost time and the red-light time. The frequency of VSP distributed above 0 kW/ton will be much highly affected by violations.Figure 11
VSP distributions of vehicles with and without violations. (a) One-stop vehicle (type A). (b) The vehicle transforms from one stop to two stops (type B). (c) Two-stop vehicle (type C).
(a)
(b)
(c)Take equation (10) as a reference. The emission model has been developed based on the number of stops and idling time. The operation change of subsequent vehicles, which are after the first four affected vehicles, is reflected in the number of stops and idling time. Therefore, increased emissions of the subsequent vehicles can be obtained by the emission model above. Based on equation (11), the numerical simulation method is used to calculate the emissions under violation conditions.(11)EFincreased,flow,y=acAfter,i⋅tafter+bcAfter,i−acBefore,i⋅tbefore+bcBefore,i,where EFincreased,flow,y (g/km) is the increased emission factors of subsequent vehicles. y is the yth vehicle of vehicles going through the intersection in the cycle. tafter is the idling time after violations, and tbefore (s) is the idling time without violations. cAfter and cBefore are stopping numbers before and after violations, respectively.


## 2.5. Increased Emissions Affected by Violations

The analysis of emissions affected by violations includes two levels. At the trajectory level, the study focused on second-by-second activities of the first four affected vehicles. At the traffic flow level, the study focused on the aggregated parameters (number of stops and idling) for the subsequent vehicles after the first four vehicles, and the conditions are divided into two categories: unsaturated and saturated conditions of the vehicle fleet disturbed by violations.The sum of the increased emissions on these two levels is the total emission at intersections affected by violations, which can be calculated as follows:(12)AE=∑x=ee+3EFincreased,trajectory,x+∑x=e+4nEFincreased,flow,x∑i=1nEFi+EFdownstream·D,where AE (%) is the increased emission increment of the cycle. e is the eth vehicle, which is the location of the first affected vehicle. n is the vehicle number of the cycle. EFincreased,trajectory,x (g/km) is the increased emission factors of the first four affected vehicles. EFincreased,flow,y (g/km) is the increased emission factors of the subsequent vehicles after the first four affected vehicles. EFi (g/km) is the normal emission factors of vehicles. EFdownstream (g/km) is the emission factors downstream of the intersection. D (km) is the distance of the study range, which is 200 meters.


## 3. Case Study

Numerical simulations are designed in the case. The impact of violations on intersection emissions can be quantified based on the model built at the trajectory and traffic flow levels. The numerical simulation object of the case is the arterial (north-south) direction of the intersection. The seven simulation conditions are listed as follows:(1)
The average lost time is 5.52 s according to the violation data.(2)
Traffic flow arrival distribution conforms to Poisson distribution.(3)
The research scope is in 200 meters of the intersection.(4)
The maximum number of stops is two.(5)
The average speed of the normal vehicle at the intersection is 16.74 km/h according to the 1666 trajectories.(6)
The frequency of violations is 1 time/cycle/lane based on the actual statistics.(7)
The two objects to be compared are (1) vehicle emissions in this cycle before the violation and (2) the same vehicles after violations. The number of vehicles is the same.


### 3.1. Case Intersection

A typical intersection in Beijing (Anli and Huizhong North) is chosen as a reference for the case intersection, which is the arterial and collector protected intersection. The simulation object is the arterial (north-south) direction of the intersection. The signal information and channelization information are shown in Table2.Table 2
Signal and channelization information of case intersection.
Signal information (s)
Channelization information
Phase
Green
Yellow
All red
Direction
Lane number
North-south straight
74
3
2
Straight
Left
Right
North-south turn left
42
3
2
North
3
1
1
East phase
34
3
2
South
3
1
Straight-right
West phase
28
3
2
East
0
1
Straight-right
Cycle time
198
West
1
1
Straight-right


### 3.2. Results and Discussion

When the volume is 38 veh/lane/cycle, for example, emission increment under violations in the case study is as shown in Figure12 The x-axis indicates the cycle number, and the y-axis indicates the emission increment under the impact of violations. VSN means “the number of stops of vehicles is increasing after violations.” Figure 12 explains the impact of violations on emissions at intersections under the volume from the following four aspects.(1)
The cycle number is less than 13: emission increment increases as VSN until the proportion of two-stop vehicles after violation reaches 100%.(saturated flow/(volume - saturated flow after violations) = 13).(2)
The cycle number is equal to 13: all vehicles have to stop twice after violations.(3)
The cycle number is between 13 and 26: the stopping number is two and the stopping time is increasing, the growth rate of emission after violations has a slower trend, and is even smaller than the growth rate of emission before violations.(4)
The cycle number is over 26: the three-stop vehicle will appear after violations.Figure 12
Emission increment after violations such as cycle passing (volume = 38 veh/lane/cycle).Based on the analysis above, emission increment under violations in the case study is shown in Figure13 The x-axis indicates the vehicle volume, and the y-axis indicates the emission increment under the influence of violations. And different volumes will have different simulation cycles to avoid three-stop vehicles. Taking CO2 as an example, the increment of CO2 emissions can be divided into unsaturated and saturated states.(1)
Under the unsaturated condition, the emission increment is constant, and when the volume is 35 veh/lane/cycle, the emissions have barely increased (1.08%) because the stopping number is constant and the idling time only increases by 5.52 s.(2)
Under the saturated condition, the emission increment increases sharply as the one-stop vehicle gradually transforms to the two-stop vehicle because of violations. As the proportion of two-stop vehicles after violations reaches 100%, and as the proportion before violations keeps increasing, the increment of emissions will decrease steadily. At the ninth cycle (half an hour), the emission increment is changed from 45% to 33% as the volume is changed from 36 to 42 veh/lane/cycle.(3)
As the cycle passes, the increment emissions of violations will have another increasing-decreasing process when three-stop vehicles appear. And a more increasing-decreasing process will appear when multiple-stop vehicles appear.Figure 13
Emission increment after violations for saturated/unsaturated conditions as cycle passing.


## 3.1. Case Intersection

A typical intersection in Beijing (Anli and Huizhong North) is chosen as a reference for the case intersection, which is the arterial and collector protected intersection. The simulation object is the arterial (north-south) direction of the intersection. The signal information and channelization information are shown in Table2.Table 2
Signal and channelization information of case intersection.
Signal information (s)
Channelization information
Phase
Green
Yellow
All red
Direction
Lane number
North-south straight
74
3
2
Straight
Left
Right
North-south turn left
42
3
2
North
3
1
1
East phase
34
3
2
South
3
1
Straight-right
West phase
28
3
2
East
0
1
Straight-right
Cycle time
198
West
1
1
Straight-right


## 3.2. Results and Discussion

When the volume is 38 veh/lane/cycle, for example, emission increment under violations in the case study is as shown in Figure12 The x-axis indicates the cycle number, and the y-axis indicates the emission increment under the impact of violations. VSN means “the number of stops of vehicles is increasing after violations.” Figure 12 explains the impact of violations on emissions at intersections under the volume from the following four aspects.(1)
The cycle number is less than 13: emission increment increases as VSN until the proportion of two-stop vehicles after violation reaches 100%.(saturated flow/(volume - saturated flow after violations) = 13).(2)
The cycle number is equal to 13: all vehicles have to stop twice after violations.(3)
The cycle number is between 13 and 26: the stopping number is two and the stopping time is increasing, the growth rate of emission after violations has a slower trend, and is even smaller than the growth rate of emission before violations.(4)
The cycle number is over 26: the three-stop vehicle will appear after violations.Figure 12
Emission increment after violations such as cycle passing (volume = 38 veh/lane/cycle).Based on the analysis above, emission increment under violations in the case study is shown in Figure13 The x-axis indicates the vehicle volume, and the y-axis indicates the emission increment under the influence of violations. And different volumes will have different simulation cycles to avoid three-stop vehicles. Taking CO2 as an example, the increment of CO2 emissions can be divided into unsaturated and saturated states.(1)
Under the unsaturated condition, the emission increment is constant, and when the volume is 35 veh/lane/cycle, the emissions have barely increased (1.08%) because the stopping number is constant and the idling time only increases by 5.52 s.(2)
Under the saturated condition, the emission increment increases sharply as the one-stop vehicle gradually transforms to the two-stop vehicle because of violations. As the proportion of two-stop vehicles after violations reaches 100%, and as the proportion before violations keeps increasing, the increment of emissions will decrease steadily. At the ninth cycle (half an hour), the emission increment is changed from 45% to 33% as the volume is changed from 36 to 42 veh/lane/cycle.(3)
As the cycle passes, the increment emissions of violations will have another increasing-decreasing process when three-stop vehicles appear. And a more increasing-decreasing process will appear when multiple-stop vehicles appear.Figure 13
Emission increment after violations for saturated/unsaturated conditions as cycle passing.


## 4. Conclusions

This paper studies the impact of violations on emissions at intersections based on the real-world driving trajectory data. First, the characteristics of vehicle operating affected by violations are analyzed. Second, a violation emission model is developed to evaluate emission increment under trajectory and traffic flow levels. Finally, a numerical simulation is conducted to assess the impact of violations on emissions based on the existing study. The main findings from the research can be summarized as follows.The headway stabilized by the fourth affected vehicle, and the average total lost time caused by violations is 5.52 s. The effect of violations can be divided into trajectory and traffic flow levels.The proposed emission model under trajectory and traffic flow levels can be used for estimating the impact of violations. The trajectory is modeled by the Gipps car-following model, and the proposed linear emission model based on the number of stops and idling time is used for the traffic flow level. At the trajectory level, the first four vehicles have obvious trajectory characteristics. The operating mode of the first affected vehicle is deceleration-idling-acceleration. The other three vehicles are modeled by the Gipps car-following model. At the traffic flow level, the proposed linear emission model based on the number of stops and idling time is used for estimating the emission of subsequent vehicles.The emission increment is constant under the unsaturated condition and is 1.08% when the volume approaches saturated flow. The emission increment increases sharply as the one-stop vehicle gradually transforms to the two-stop vehicle because of violations under the saturated condition, and the maximum emission increment reaches 45% in half an hour in the case. The increment of emissions decreases steadily as the proportion of two-stop vehicles after violations reaches 100%, and the proportion before violations keeps increasing.More emission numerical simulations for different types and frequencies of violations are recommended for further studies. In addition, three-stops and above should be considered in high-frequency violation scenarios.



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*Source: 7539829-2020-03-21.xml*