# Priority of Emergency Vehicle Dynamic Right-Of-Way Control Method in Networked Environment
## 2 PDR-EVs Control Method
### Dynamic Monitoring Intervals  
On actual city roads, EVs are generally faster than CVs. When the front buffer interval of the EV touches the CV's tail, the search procedure is triggered to search the inside lane for gaps where the CV can merge into. This is demonstrated in Figure 4, which assumes that the moment when the rear of the \(j\)-th vehicle touches the buffer interval at the front of the EVs is \(t_{s,j}\) and defines the dynamic monitoring interval as the dividing line between EV's non-intrusive interval and the buffer interval as the starting point of the interval. The rear of the \(j\)-th vehicle's front is the the \(j+1\)-th vehicle as the end of the interval. The dynamic monitoring interval at time \(t\) is given by:  
\[DMS(t)=X_{D}(t)-X_{S}(t) \tag{1}\]  
where \(X_{S}(t)\) represents the spatial position of the buffer start at time \(t\), and \(X_{D}(t)\) denotes the spatial position of the end of the buffer at time \(t\).  
At the same time, the vehicle infrastructure cooperation system obtains the CV's real-time dynamic position and speed. The distance of the \(i+k\)-th vehicle from the starting point of the dynamic monitoring interval at time \(t\) is represented by \(S_{i+k}(t)\), and the headway of the \(i+k\)-th vehicle at moment \(t\) is presented by Equation (2):  
\[H_{i+k}(t)=S_{i+k+1}(t)-S_{i+k}(t),\forall k\in\mathrm{K} \tag{2}\]  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Meaning** \\ \hline K & the CV set of the inner lane into the dynamic monitoring interval \\ \hline \(J\) & collection of CVs in the outer lane into the buffer zone \\ \hline \(G\) & headway between the adjacent front and rear CVs in the inner lane within the dynamic monitoring interval \\ \hline \(\Psi\) & collection of instantaneous moments when CVs in the outer lane enter the buffer zone \\ \hline \(\Omega\) & collection of moments at the start of the merge before lane change in the outside lane \\ \hline \(\Theta\) & set of times from the receipt of the guidance signal to the start of the merge by the CV in the outside lane \\ \hline \(\Phi\) & outside lane CV avoidance EV lane change time collection \\ \hline A & solution set of the acceleration of vehicle \(j\), \(\mathrm{A_{+}}\) denotes a positive solution set, and \(\mathrm{A_{-}}\) signifies a negative solution set such that \(\forall j,j\in J,\mathrm{A_{+}}\cup\mathrm{A_{-}}=\mathrm{A},\mathrm{A_{+}} \cap\mathrm{A_{-}}=0\) \\ \hline \(t\) & moment when the CV is currently running \\ \hline \(j\) & outer lane CV number, \(\forall t,\forall j,j\in J\) \\ \hline \(i\) & inside lane CV number \\ \hline \(i+k\) & the CV number of the inner lane currently in the dynamic monitoring interval, \(\forall t,\forall k,i+k\in\mathrm{K}\) \\ \hline \(\tau\) & maximum communication delay time of vehicle infrastructure cooperation system \\ \hline \(t_{s,j}\) & instantaneous moment when vehicle \(j\) enters the buffer interval, \(\forall j,t_{s,j}\in\Psi\) \\ \hline \(t_{c,j}\) & starting moment of the merging before vehicle \(j\) changes lanes, \(\forall j,t_{c,j}\in\Omega\) \\ \hline \(\theta_{j}\) & time between the vehicle j receiving the guidance signal and the start of the merge, \(\forall j,\theta_{j}\in\Theta\) \\ \hline \(\delta_{j}\) & time for vehicle \(j\) to avoid EV lane change and enter the inner lane, \(\forall j,\delta_{j}\in\Phi\) \\ \hline \(v_{min}\) & minimum speed for CV operation \\ \hline \(v_{max}\) & maximum speed for CV operation \\ \hline \(a_{max}\) & maximum operating speed change of CV \\ \hline \hline \end{tabular}
\end{table}
Table 2: Parameter definition.  
Let function \(D_{id}(t)\) represent the speed of the \(i\)-th vehicle at moment \(t\), and the speed rate of change is:  
\[D_{id}(t)=D_{id}(v_{id}(t),a_{id}(t)) \tag{3}\]  
where \(v_{id}(t)\) denotes the longitudinal velocity of the \(id\)-th vehicle at moment \(t\), \(a_{id}(t)\) is the longitudinal acceleration of the \(id\)-th vehicle at moment \(t\), and \(id\) is the number of CVs.