#### 3.5. Car Following Models and Lane Change Models

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/s

^{2}).CC8 and CC9: Desired acceleration from a standstill and at 80 km/h. in m/s

^{2}

$${s}_{f}={s}_{0}+{v}_{f}\xb7{T}_{f}+{\displaystyle \frac{{v}_{f}\xb7\u2206{v}_{f}}{2\sqrt{{a}_{b}\xb7b}}}$$

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 $\mathsf{\Delta}{v}_{f}$ 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.

^{2}) $\left({a}_{follower}\right)$ 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].

$${a}_{follower}=a\xb7\left(1-{\left({\displaystyle \frac{{v}_{f}}{{v}_{0}}}\right)}^{\delta}-{\left({\displaystyle \frac{{s}_{f}}{s}}\right)}^{2}\right)$$

In this context, $a$ stands for the maximum acceleration in (m/s^{2}), ${v}_{f}$ refers to the current speed of the following vehicle in (m/s), and ${v}_{0}$ indicates the desired speed in (m/s). The exponent $\delta $, 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).

$${g}_{f}={x}_{lead}-{x}_{i}-{l}_{i},$$

$${g}_{r}={x}_{i}-{x}_{follower}-{l}_{follower,}$$

where ${x}_{lead}$ 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, ${x}_{follower}$ refers to the position of the following vehicle in the target lane in (m), and ${l}_{follower}$ 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 ${(g}_{f,min}$ and ${g}_{r,min})$. The minimum acceptable gap ${g}_{f,min}$ is influenced by safety distance, relative speeds, and deceleration.

$${d}_{i}={\displaystyle \frac{{({v}_{lead}-{v}_{i})}^{2}}{2\xb7({g}_{f}-{s}_{0})}},$$

$${d}_{follower}={\displaystyle \frac{{({v}_{i}-{v}_{follower})}^{2}}{2\xb7({g}_{r}-{s}_{0})}}.$$

^{2}), 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

$${D}_{i}={\displaystyle \frac{c{(1-{g}_{i})}^{2}}{2\xb7(1-{y}_{i})}}+{\displaystyle \frac{{{(y}_{i})}^{2}}{2{q}_{i}{g}_{i}(8-{y}_{i})}}.$$

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 $i$.

$${D}_{i}={\displaystyle \frac{c{q}_{i}{(x-{y}_{i})}^{2}}{2{x}^{2}(1-{y}_{i})}}+{\displaystyle \frac{{x}^{2}}{2(1-x)}},$$

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

$$\mathit{min}D={\displaystyle \frac{1}{n}}{\sum}_{i=1}^{n}{\displaystyle \frac{{D}_{i}}{{N}_{i}}}.$$

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

#### 3.8.1. Average Queue Length Validation

$$AccuracyDifference\left(\mathrm{\%}\right)=\left({\displaystyle \frac{SimulatedAverageQueue-EstimatedAverageQueue}{EstimatedAverageQueue}}\right)\times 100.$$

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

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

$$E={\sum}_{i=1}^{n}\left(a+b\xb7{v}_{i}+c\xb7{{v}_{i}}^{2}+d\xb7{{v}_{i}}^{3}\right)\xb7\u2206t$$

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 $\mathsf{\Delta}t$ (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.

Source link

Ali Almusawi www.mdpi.com