# Priority of Emergency Vehicle Dynamic Right-Of-Way Control Method in Networked Environment
## 2 PDR-EVs Control Method
### Avoidance of EVs Guidance Control Method  
#### 2.3.1 Safe Convergence Gap  
When the \(v\)-th vehicle enters the buffer zone, it must change lanes in time to avoid passing EVs. Regarding safety, it is assumed that the CV to be changed is \(V_{0}\), and the surrounding CVs are \(V_{1}\), \(V_{2}\), \(V_{3}\), and \(V_{4}\), as presented in Figure 5. The minimum safe time headways that should be met when the \(V_{0}\)-th vehicle merges are \(S_{0}(D_{V1},D_{V0})\), \(S_{0}(D_{V2},D_{V0})\) and \(S_{0}(D_{V3},D_{V0})\), where \(S_{0}(D_{V1},D_{V0})\) is the time headway behind the target lane, \(S_{0}(D_{V2},D_{V0})\) is the time distance ahead of the target lane, and \(S_{0}(D_{V3},D_{V0})\) is the time headway in front of the current lane [17]. When the EV's front buffer touches the front \(j\)-th vehicle (as depicted in Figure 4), it is investigated whether \(H_{i+k}(t),\forall k\in\mathrm{K}\) in the interval \(DMS(t)\) meets the requirements for safe entry. Let the minimum safe merging gap function be \(Gap_{min}(t_{s,j},k,j)\). For the \(j\)-th vehicle that is about to change lanes, its minimum safe merging gap can be expressed by:  
\[Gap_{min}(t,k,j)=S_{0}(D_{i+k}(t),D_{j}(t))+S_{0}(D_{i+k+1}(t),D_{j}(t))+l_{j},\forall k\in\mathrm{K},\forall j\in J \tag{4}\]  
where \(Gap_{min}(t,k,j)\) is the minimum convergence gap at \(t\) moments that satisfies the driving state of the \(j\)-th vehicle, the \(i+k\)-th vehicle, and the \(i+k+1\)-th vehicle, and \(l_{j}\) is the body length of the \(j\)-th vehicle. Apparently, the moment to trigger the search procedure is not equal to when the \(j\)-th vehicle is merging, and function \(Gap_{min}(t_{s,j},k,j)\) cannot be utilized as a judgment condition for the \(j\)-th vehicle to merge safely. Therefore, it is not advisable to set the speed of the \(j\)-th vehicle as \(v_{j}(t)\), (\(v_{min}\leq v_{j}(t)\leq v_{max}\)) and the EV's  
Figure 4: Schematic diagram of the dynamic monitoring interval. Figure 5: Schematic diagram of the safe merge gap. speed as \(v_{E}(t)\), \((v_{E}(t)>v_{j}(t))\). The buffer is constantly compressed with time, but, at any moment, it satisfies Equation (5):  
\[\int_{t_{s,j}}^{\theta_{j}}(v_{E}(t)-v_{j}(t))dt=L_{2},\forall j\in\mathbf{J}, \forall\theta_{j}\in\Theta \tag{5}\]  
The magnitude of \(\theta_{j}\) is determined by the difference between \(v_{j}(t)\) and \(v_{E}(t)\). Although the magnitudes of \(v_{j}(t)\) and \(v_{E}(t)\) vary with time, \(\theta_{j}\) must be between the two values, which can be expressed by \(\theta_{j,max}\geq\theta_{j}\geq\theta_{j,min}\). According to the speed correlations of \(S_{0}(D_{i+k}(t),D_{j}(t))\) and \(S_{0}(D_{i+k+1}(t),D_{j}(t))\) with the \(i+k\)-th vehicle, the \(i+k+1\)-th vehicle, and the \(j\)-th vehicle [18], the speed correlation satisfies. \[S_{0}(D_{i+k}(t_{c,j}),D_{j}(t_{c,j}))=\int_{t_{c}}^{t_{c}+\beta_{j}}\int_{t_{c }}^{t_{c}+\tau}\bigl{|}a_{i+k}(\tau)-a_{j}(\tau)\bigl{|}d\delta_{j}d\tau+\bigl{|} v_{i+k}(t_{c,j})-v_{j}(t_{c,j})\bigr{|}*\delta_{j},\forall j\in J,t_{c,j}\in \Omega,\delta_{j}\in\Phi \tag{6}\]  
\[S_{0}(D_{i+k+1}(t_{c,j}),D_{j}(t_{c,j}))=\int_{t_{c}}^{t_{c}+\beta_{j}}\int_{t_{ c}}^{t_{c}+\tau}\bigl{|}a_{i+k+1}(\tau)-a_{j}(\tau)\bigl{|}d\delta_{j}d\tau+ \bigl{|}v_{i+k+1}(t_{c,j})-v_{j}(t_{c,j})\bigr{|}*\delta_{j},\forall j\in J,t_ {c,j}\in\Omega,\delta_{j}\in\Phi \tag{7}\]  
It can be deduced that, subject to \(v_{j}(t_{s,j})=v_{max}\), \(Gap_{min}(t_{c,j},k,j)\) satisfies Equation (8):  
\[Gap_{min}(t_{c,j},k,j)\leq Gap_{min}(t_{s,j},k,j)\bigl{|}v_{j}(t_{s,j})=v_{max },\forall k\in\mathrm{K},\forall j\in J \tag{8}\]  
If the inequality given by Equation (9) is established, the inequality in Equation (10) must be established. That is, the \(j\)-th vehicle can safely merge into the inner lane gap.