# Integrating Autonomous Vehicles (AVs) into Urban Traffic: Simulating Driving and Signal Control
## 3 Methodology
### 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 [PERSON]'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:  
\[D_{i}=\frac{c(1-g_{i})^{2}}{2\cdot(1-y_{i})}+\frac{{(y_{i})}^{2}}{2q_{i}g_{i}( 8-y_{i})}. \tag{7}\]  
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, [PERSON] et al. [37] enhanced it by introducing the following equation:  
\[D_{i}=\frac{cq_{i}(x-y_{i})^{2}}{2x^{2}(1-y_{i})}+\frac{x^{2}}{2(1-x)}, \tag{8}\]  
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]:  
\[minD=\frac{1}{n}{\sum_{i=1}^{n}\frac{D_{i}}{N_{i}}}. \tag{9}\] \begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Parameter’s** & **AV** & **AV** & **AV** & **AV** & **Human** \\  & **Cautious** & **Normal** & **Aggressive** & **Platoon** & **Human** \\ \hline Advanced merging & on & on & on & on & on \\ Cooperative lane change & on & on & on & on & off \\ Safety distance reduction factor & 1.00 & 0.60 & 0.75 & 0.75 & 0.60 \\ Min clearance (front/rear) in (m) & 1.00 & 0.50 & 0.50 & 0.50 & 0.50 \\ Maximum deceleration for cooperative & \(-\)2.50 & \(-\)3.00 & \(-\)6.00 & \(-\)6.00 & \(-\)3.00 \\ braking in (m/s\({}^{2}\)) & \(-\)2.50 & \(-\)3.00 & \(-\)6.00 & \(-\)6.00 & \(-\)3.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Parameters governing lane change behavior in PTV VISSIM [25].