Simulating Driving and Signal Control

3.5. Car Following Models and Lane Change Models

In the Wiedemann model, human driving behavior is recognized as naturally varying, considering that each driver possesses unique abilities in terms of perception, reaction, and assessing traffic flow [20,25]. The model delineates four driving states: free flow, approaching, following, and critical situation, as illustrated in Figure 6. These states are defined by specific thresholds: ABX and SDX (absolute braking threshold and safe distance threshold in meters) represent the minimum and maximum gap distances during following, respectively; CLDV (closing distance in meters per second) indicates the point at which the driver becomes aware of the narrowing gap; and SDV (sensitive distance in meters) is the critical point when the driver recognizes their proximity to the vehicle ahead. OPDV (opening distance in meters per second) marks the point when the driver realizes they are traveling slower than the vehicle in front.

PTV VISSIM incorporates two versions of the Wiedemann car-following model: Wiedemann 1999 and Wiedemann 1974 [22,27,28]. The main distinction between these versions lies in their level of customization, with Wiedemann 1999 offering a greater number of adjustable parameters, making it more suitable for urban and congested traffic scenarios. In contrast, Wiedemann 1974, which was originally designed for freeway conditions, utilizes more rigid, hard-coded parameters [29]. As this study aims to assess the impact of aggressive autonomous vehicles (AVs) at urban signalized intersections, the Wiedemann 1999 car-following model is utilized. The driving behavior parameters (CC) in Wiedemann 1999 are calibrated using threshold values corresponding to different driving regimes. The PTV Group (2018) outlines the definitions and default values of these CC parameters for human-driven vehicles in Table 4. Users have the flexibility to adjust these parameters based on observed vehicle behaviors, including variables such as look-ahead distance, average standstill distance, and desired safety distance components [30].

The Wiedemann 1999 model is designed for capture and includes more parameters of driving behaviors:

CC0: Standstill distance (the desired gap between two stationary vehicles in meters).
CC1: Following distance (the time-based component of the desired safety distance, dependent on speed in seconds).
CC2: Longitudinal oscillation (the distance a driver allows before closing in on the vehicle ahead in meters).
CC3: Perception threshold for following (the point at which the driver initiates deceleration in seconds).
CC4 and CC5: Negative and positive speed differences (sensitivity to the acceleration or deceleration of the vehicle in front in meters per second).
CC6: Speed influence on oscillation (how distance affects speed fluctuations during following in 10⁻⁴ rad/s).
CC7: Oscillation acceleration (the minimum acceleration or deceleration applied when following another vehicle in m/s²).
CC8 and CC9: Desired acceleration from a standstill and at 80 km/h. in m/s²

The Wiedemann 1999 model determines the acceleration of the following vehicle

(a_{f})

by considering its speed relative to and the distance from the leading vehicle. This model functions across various driving regimes: free driving, where the vehicle accelerates to reach its desired speed when it is far from the vehicle ahead; approaching, where it modifies its speed to prevent a collision; following, where it keeps a safe distance; and braking, where it slows down to avoid a crash. A central aspect of the model is the desired safety distance

(s_{f})

, which is defined by Equation (1).

$s_{f} = s_{0} + v_{f} \cdot T_{f} + \frac{v_{f} \cdot ∆ v_{f}}{2 \sqrt{a_{b} \cdot b}}$

(1)

Here, $s_{0}$ denotes the minimum standstill distance (CC0), $v_{f}$ represents the speed of the following vehicle, and $T_{f}$ indicates the safe time headway (CC1). The term $Δ v_{f}$ refers to the difference in speed between the following and leading vehicles, $a_{b}$ is the maximum acceleration capability of the following vehicle, and $b$ represents the comfortable deceleration rate.

Equation (2) outlines how the acceleration of the following vehicle in (m/s²)

(a_{f o l l o w e r})

is determined by evaluating the current gap between vehicles relative to the desired safety distance, as well as the speed difference between the vehicles [31].

$a_{f o l l o w e r} = a \cdot (1 - {(\frac{v_{f}}{v_{0}})}^{δ} - {(\frac{s_{f}}{s})}^{2})$

(2)

In this context, $a$ stands for the maximum acceleration in (m/s²), $v_{f}$ refers to the current speed of the following vehicle in (m/s), and $v_{0}$ indicates the desired speed in (m/s). The exponent $δ$ , usually set to 4 (unitless), is applied in the calculation. The desired safety distance is denoted by $s_{f}$ in (m), while $s$ represents the current gap to the vehicle ahead (m).

Table 4 outlines the parameters related to car following model’s parameters used in the PTV VISSIM model.

The decision to execute a lane change is determined by the gap acceptance criterion, where a vehicle

i

assesses the available space

g

in the target lane to determine if it is adequate for a safe maneuver. This evaluation includes checking the front gap,

g_{f}

in (m) (Equation (3)), and the rear gap,

g_{r}

in (m) (Equation (4)):

$g_{f} = x_{l e a d} - x_{i} - l_{i},$

(3)

$g_{r} = x_{i} - x_{f o l l o w e r} - l_{f o l l o w e r,}$

(4)

where $x_{l e a d}$ represents the position of the leading vehicle in the target lane in (m), while $x_{i}$ denotes the position of the subject vehicle in (m). The length of the subject vehicle is indicated by $l_{i}$ in (m). Additionally, $x_{f o l l o w e r}$ refers to the position of the following vehicle in the target lane in (m), and $l_{f o l l o w e r}$ is the length of the following vehicle in (m). A vehicle will change lanes if both the front gap ( $g_{f}$ ) and the rear gap ( $g_{r}$ ) are greater than the respective minimum acceptable gaps ${(g}_{f, m i n}$ and $g_{r, m i n})$ . The minimum acceptable gap $g_{f, m i n}$ is influenced by safety distance, relative speeds, and deceleration.

During the lane change, the deceleration

d

accepted by the subject vehicle and the trailing vehicle in the target lane can be expressed in Equation (5):

$d_{i} = \frac{{(v_{l e a d} - v_{i})}^{2}}{2 \cdot (g_{f} - s_{0})},$

(5)

$d_{f o l l o w e r} = \frac{{(v_{i} - v_{f o l l o w e r})}^{2}}{2 \cdot (g_{r} - s_{0})} .$

(6)

In this context,

v_{l e a d}

refers to the speed of the leading vehicle in the target lane in (m/s), while

v_{f o l l o w e r}

is the speed of the following vehicle in the target lane in (m/s). A lane change is carried out if both

d_{i}

and

d_{f o l l o w e r}

fall within acceptable limits in (m/s²), indicating the vehicles’ willingness to decelerate. Table 5 provides an overview of the lane change parameters utilized in the PTV VISSIM model.

3.6. Signal Control Optimization

To enhance the performance of the studied intersection, a signal control optimization was conducted using the PTV VISSIM traffic simulation model. The primary goal of this optimization was to evaluate the impact of different cycle times (60, 80, 100, 120, 140, 160, 180, and 204 s) on intersection performance, as shown in Figure 7a–g. This approach aimed to improve the efficiency of traffic flow by adjusting the signal timings and phasing plans to achieve a more balanced and effective distribution of green times across all approaches. Signal control optimization plays a crucial role in managing traffic flow at intersections by adjusting signal timings and phase sequences. This process aims to reduce delays, minimize congestion, and improve the overall efficiency and safety of urban traffic networks [32,33,34]. The optimization was performed using VISSIM’s stage-based signal controller along with priority rules [35]. Additionally, manual signal timing calculations were conducted using Webster’s method to identify suitable traffic signal timings. The study initially considered the original signal timings and subsequently investigated the effects of the optimized signal control for each cycle time to assess its impact on intersection performance. The results from the manual calculations were compared with those obtained through the optimization conducted in VISSIM, illustrating the comparative outcomes of these optimizations.

Gathering the required input data for the timing model involves both detection and prediction processes. These data are subsequently fed into the VISSIM simulation software, which is managed using Python. Throughout the optimization process, VISSIM provides critical evaluation metrics, such as delay time and queue length, to the model [36].

In traffic signal control, time delay is a critical element that impacts the evaluation of current traffic flow and is frequently used as a key metric for assessing traffic efficiency. The widely recognized Webster signal cross delay formula, illustrated below, is commonly used to calculate this delay:

$D_{i} = \frac{c {(1 - g_{i})}^{2}}{2 \cdot (1 - y_{i})} + \frac{{{(y}_{i})}^{2}}{2 q_{i} g_{i} (8 - y_{i})} .$

(7)

In this formula, c represents the cycle time in (sec), $g_{i}$ denotes the green signal ratio (unitless), $q_{i}$ is the traffic flow rate for phase in (veh/s), $i$ and $y_{i}$ (unitless) indicates the saturation level for phase $i$ .

However, because the previous equation is only applicable when saturation is low, Cheng et al. [37] enhanced it by introducing the following equation:

$D_{i} = \frac{c q_{i} {(x - y_{i})}^{2}}{2 x^{2} (1 - y_{i})} + \frac{x^{2}}{2 (1 - x)},$

(8)

where $x$ represents the saturation level of the intersection (unitless).

To create an appropriate criterion for the timing scheme, the average vehicle delay time for the cycle is utilized as the primary evaluation metric for optimizing signal timing. The goal of the optimization process is to minimize the following formula [36]:

$\min D = \frac{1}{n} \sum_{i = 1}^{n} \frac{D_{i}}{N_{i}} .$

(9)

In this formula, $n$ represents the number of lanes, $D_{i}$ denotes the cycle delay time in (sec) for the $i$ th lane, $N_{i}$ indicates the cycle flow for each lane, and $D$ is the average vehicle delay time for the entire cycle.

3.8. Model Calibrations and Validation

During the calibration of the intersection links, modifications were required for the east- and west-bound directions due to high traffic volumes. Although the original design included two lanes for each direction, observations indicated that vehicles were queuing as though there were three lanes per link in both the east and west-bound directions, as shown in Figure 8.

Since VISSIM allows for only one vehicle per lane, a decision was made to configure both the east- and west-bound directions as having three lanes for each link illustrated in Figure 9. This modification aligns the simulation model more accurately with the observed traffic behavior, ensuring a realistic representation of the flow dynamics at the intersection.

Additionally, another calibration point was identified, indicating that lane changes should not occur except at exit links. Therefore, it was decided to design each lane as a separate link for each direction, as shown in Figure 10. This decision was influenced by the observation that drivers were selecting their destination lanes early, resulting in no lane changes due to the substantial traffic volume.

3.8.1. Average Queue Length Validation

To validate the accuracy of the simulated average queue in this study, real-world data were collected during the red signal phase at different cycle times. Queue measurements were taken simultaneously across all lanes for each direction. The average queue length was calculated by summing the total number of vehicles across the three lanes, multiplying by the standard vehicle length of 4.481 m, and dividing by 3 to account for the three lanes, as presented in Table 7, Table 8, Table 9 and Table 10.

The calculated estimated average queue length was then compared with the simulated average queue from the PTV VISSIM microsimulation platform, as shown in Figure 11. This validation process ensured that the simulation accurately represented real-world conditions, enhancing the reliability of the study’s findings and the subsequent analysis of the impact of AVs on traffic dynamics at the signalized intersection. The accuracy difference was calculated using the following formula:

$A c c u r a c y D i f f e r e n c e (%) = (\frac{S i m u l a t e d A v e r a g e Q u e u e - E s t i m a t e d A v e r a g e Q u e u e}{E s t i m a t e d A v e r a g e Q u e u e}) \times 100 .$

(10)

The accuracy difference for the north-bound direction was around 6.30%. For the east-bound direction, the simulated average queue had an accuracy difference of 10.24%. In the south-bound direction, the accuracy difference was about 3.60%, while the west-bound direction showed an accuracy difference of 3.54%.

3.8.2. Average Travel Time Validation

To validate the accuracy of simulated travel times, a sample of 20 vehicles was randomly selected for each direction, considering different signal phases. Unlike the queue validation, these vehicles were chosen randomly during various signal times to capture a more diverse set of traffic scenarios. The travel time for each vehicle was estimated using a stopwatch between two fixed points spaced 150 m apart. The comparison between the estimated and simulated travel times is presented in Table 11 and illustrated in Figure 12.

The north- and west-bound directions exhibited accuracy differences of approximately 3.87% and 2.84%, respectively, indicating a relatively close alignment between the estimated and simulated travel times. Similarly, the east- and south-bound directions displayed accuracy differences of approximately 4.96% and 4.86%, respectively, as shown in Figure 12. These findings signify the effectiveness of the simulation in replicating real-world travel time dynamics, demonstrating its capability to provide accurate representations of traffic behavior under varying signal conditions.

The contradiction between longer queues and shorter travel times can be explained by differences between real-world human driving and the simulated model. In the simulation, longer queues may form due to conservative driving behaviors, with larger gaps or slower reactions at intersections. However, once vehicles start moving, they tend to accelerate more efficiently in the simulation, leading to smoother traffic flow and shorter travel times. This explains why, despite longer queues, vehicles clear the intersection faster in the model compared to real-world conditions.

3.9. Emission Modeling in VISSIM

In assessing the environmental impact of autonomous vehicles (AVs) at urban intersections, accurately quantifying emissions across different traffic conditions is essential. This study employs the emission modeling features of PTV VISSIM, utilizing the Handbook Emission Factors for Road Transport (HBEFA) to simulate and evaluate pollutant emissions such as CO, NOx, and particulate matter (PM). VISSIM calculates emissions using a polynomial function that takes vehicle speed into account, allowing for detailed analysis of the pollutants generated under varying driving behaviors and traffic scenarios.

$E = \sum_{i = 1}^{n} (a + b \cdot v_{i} + c \cdot {v_{i}}^{2} + d \cdot {v_{i}}^{3}) \cdot ∆ t$

(11)

The total emissions (E) of a specific pollutant (in grams) are calculated using a polynomial function, where $v_{i}$ represents the speed of vehicle $i$ (in kilometers per hour), and $a, b, c,$ and $d$ are empirical coefficients (unitless) specific to vehicle types and driving conditions. The simulation time step $Δ t$ (in seconds) is used to account for emissions generated over time during the simulation. This allows for an accurate estimation of emissions based on real-time vehicle behavior within the VISSIM model.

The coefficients $a, b, c,$ and $d$ are derived from the HBEFA model and are specifically tailored to represent the emission characteristics of different vehicle categories, including both autonomous and human-driven vehicles. These coefficients play a crucial role in modeling the effects of various driving behaviors and traffic conditions on emission levels. They differ based on vehicle type, engine properties, and driving patterns, enabling a realistic evaluation of emissions across different traffic scenarios. The following is a breakdown of these coefficients.

Coefficient $a$ represents the baseline emissions produced when vehicles are idling or moving at low speeds. It tends to be lower for efficient or less aggressive driving behaviors, such as AV platooning, which minimizes idle time and low-speed operations. Coefficient $b$ establishes a linear relationship between speed and emissions, with higher values typically associated with more aggressive driving styles, like AV aggressive, where emissions increase at higher speeds. Coefficients $c$ and $d$ account for the nonlinear effects of speed on emissions, highlighting the significant impact of rapid speed fluctuations, such as during aggressive acceleration or deceleration. These coefficients reflect how dynamic driving behaviors influence overall emissions output.

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Ali Almusawi www.mdpi.com

Greenberg News

Simulating Driving and Signal Control

3.5. Car Following Models and Lane Change Models

3.6. Signal Control Optimization

3.8. Model Calibrations and Validation

3.8.1. Average Queue Length Validation

3.8.2. Average Travel Time Validation

3.9. Emission Modeling in VISSIM

Greenberg

3.5. Car Following Models and Lane Change Models

3.6. Signal Control Optimization

3.8. Model Calibrations and Validation

3.8.1. Average Queue Length Validation

3.8.2. Average Travel Time Validation

3.9. Emission Modeling in VISSIM

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