## 3 Strategy and Model
### Intersection Signal Coordination Model Based on Time Slice Division
Therefore, the virtual lane-borrowing vehicles are allowed to enter the bus approach of the intersection space slice, where \(T_{\text{allow}}^{p}\) is calculated as follows:  
\[T_{\text{allow}}^{p}=\min\Bigl{\{}T_{\text{basic}}^{p},T_{\text{travel}}^{q}- T_{\text{travel}}^{p}-T_{\text{cycle}}+\text{mod}(T_{\text{travel}}^{p}-T_{ \text{remain}}^{\text{red}},T_{\text{cycle}})-T_{\text{queue}}\Bigr{\}} \tag{8}\]  
If \(T_{\text{travel}}^{q}-T_{\text{travel}}^{p}\leq T_{\text{cycle}}-\text{mod}(T_{ \text{travel}}^{p}-T_{\text{remain}}^{\text{red}},T_{\text{cycle}})+T_{\text{ queue}}\), the virtual lane-borrowing vehicles cannot pass through the intersection before the approaching bus reaches the intersection. Therefore, the virtual lane-borrowing vehicles are forbidden to enter the bus approach of the intersection space slice, i.e., \(T_{\text{allow}}^{p}=0\). When the current signal phase is green (i.e., non-red phase; note that the yellow phase is also classified as green phase here) then  
\[\text{mod}(T_{\text{travel}}^{p}-T_{\text{remain}}^{\text{green}},T_{\text{ cycle}})>T_{\text{red}}? \tag{9}\]  
where \(T_{\text{remain}}^{\text{green}}\) is the remaining time of the current green phase. If mod(\(T_{\text{travel}}^{p}-T_{\text{remain}}^{\text{green}},T_{\text{cycle}})>T_{ \text{red}}\), the signal phase of the intersection is green when the virtual lane-borrowing vehicles reach the intersection. Therefore, the virtual lane-borrowing vehicles are allowed to enter the bus approach of the intersection space slice, where \(T_{\text{allow}}^{p}\) is calculated as follows:  
\[T_{\text{allow}}^{p}=\min\Bigl{\{}T_{\text{basic}}^{p}\,T_{\text{cycle}}-\text{ mod}(T_{\text{travel}}^{p}-T_{\text{remain}}^{\text{green}},T_{\text{ cycle}})\Bigr{\}} \tag{10}\]If \(\text{mod}(T_{\text{travel}}^{p}-T_{\text{remair}}^{\text{green}},T_{\text{cycle}}) \leq T_{\text{red}}\), the signal phase of the intersection is red when the virtual lane-borrowing vehicles reach the intersection. \[T_{\text{travel}}^{q}-T_{\text{travel}}^{p}>T_{\text{red}}-\text{mod}(T_{\text{ travel}}^{p}-T_{\text{remair}}^{\text{green}},T_{\text{cycle}})+T_{\text{queue}}? \tag{11}\]  
If \(T_{\text{travel}}^{q}-T_{\text{travel}}^{p}>T_{\text{red}}-\text{mod}(T_{\text{ travel}}^{p}-T_{\text{remair}}^{\text{green}},T_{\text{cycle}})+T_{\text{queue}}\), the virtual lane-borrowing vehicles can pass through the intersection before the approaching bus reaches the intersection. Therefore, the virtual lane-borrowing vehicles are allowed to enter the bus approach of the intersection space slice, where \(T_{\text{allow}}^{p}\) is calculated as follows:  
\[T_{\text{allow}}^{p}=\min\Bigl{\{}T_{\text{basic}}^{p}T_{\text{travel}}^{q}-T_{ \text{travel}}^{p}-T_{\text{red}}+\text{mod}(T_{\text{travel}}^{p}-T_{\text{ remain}}^{\text{green}},T_{\text{cycle}})-T_{\text{queue}}\Bigr{\}} \tag{12}\]  
If \(T_{\text{travel}}^{q}-T_{\text{travel}}^{p}\leq T_{\text{red}}-\text{mod}(T_{ \text{travel}}^{p}-T_{\text{remair}}^{\text{green}},T_{\text{cycle}})+T_{\text {queue}}\), the virtual lane-borrowing vehicles cannot pass through the intersection before the approaching bus reaches the intersection. Therefore, the virtual lane-borrowing vehicles are forbidden to enter the bus approach of the intersection space slice, i.e., \(T_{\text{allow}}^{p}=0\). After dividing the time slice of the intersection space slice, detect and judge whether the current signal phase ends or whether \(T_{\text{allow}}^{p}\) decreases to 0. If yes, the time slice division of the next cycle is performed. Figure 5 presents the logic control flow of the above time slice division strategy.