# Queue Spillover Management in a Connected Vehicle Environment
## 3 Intersection Signal Control Modeling
### Signal Optimization Method  
When there is an overflow trend in the queue, the traffic signal needs to be optimized to make the current phase green time of the queue vehicle with overflow trend, to satisfy the queuing requirement as much as possible without overflow. This is related to the current phase of the largest green time \(t_{\text{max}}\), and the current queuing vehicles through the intersection of timing \(t_{0}^{\prime}\). The calculation of \(t_{\text{max}}\) is given below.  
Current Phase Maximum Green Time Calculation  
The maximum green time of the current phase depends on the current phase green time and the maximum allowable green time of other phases, that is:  
\[t_{\text{max}}=t_{1}+t_{2}+t_{g} \tag{13}\]  
where, \(t_{1}\) is the phase free time for all other straight lanes at an intersection, and \(t_{2}\) is the phase free time for all other left lanes at an intersection.  
Time \(t_{2}\) is the difference between the current phase green light time and the minimum green light time of the left phase. The minimum green time is denoted by \(G_{\text{mins}}\) and its value can be determined by the time of the left queue vehicle passing the intersection. It is calculated according to the queue length detected and the Formula (6), and the calculation formula of \(t_{2}\) is as follows.  
\[t_{2}=t_{g2}-G_{\text{mins}} \tag{14}\]  
where, \(t_{g2}\) is the current green time to left phase.  
Time \(t_{1}\) is the difference between the current phase green time of the direct line and the corresponding minimum green time. The minimum green time of the direct lane can be determined according to the time of the pedestrian crossing at the intersection, which is represented as \(G_{\text{min}P}\).  
The calculation of \(G_{\text{min}P}\) involves the width of the lane, which may vary from region to region. According to the \"Code for Urban Road Engineering Design\" [37], the length of a single motor lane is shown in the Table 2.  
The width of a single lane can be obtained from Table 2, and the product of the number of lanes is the width of the pavement, which represent as \(l_{w}\). It is related to the gender and age of pedestrians in the pedestrian crossing. According to the literature [38], the walking speed of the old man was  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \(t_{1}\) & \(t_{2}\) & \(t_{3}\) & \(t_{i}\) \\ \hline \(L_{r1}-L_{c}\) & \(L_{r2}-L_{c}\) & \(L_{r3}-L_{c}\) & \(\cdots\) & \(L_{ri}-L_{c}\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Differential records.  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Model and Lane Type**} & \multicolumn{2}{c}{**Design Speed (km/h)**} \\ \cline{2-3}  & **\textgreater{}60** & \(\leq\)**60** \\ \hline Oversize vehicle or mixed lane (m) & 3.75 & 3.50 \\ Passenger car lane (m) & 3.50 & 3.25 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Lane length.  
selected, i.e., 1.292 m/s to calculate the time at the intersection namely, the minimum green time, and the calculation formula is as follows:  
\[G_{\text{min}P}=\frac{l_{\text{in}}}{1.292} \tag{15}\]  
The formula for calculating \(t_{1}\) is as follows:  
\[t_{1}=t_{g1}-G_{\text{min}P} \tag{16}\]  
If Equations (14) and (16) are taken into Equation (13), \(t_{\text{max}}\) can be obtained.