## 3 Design of a General Relay-Node Selection on Intersection
### Description of a General Intersection  
A general intersection with \(N_{\text{b}}\) branches is shown in Figure 2. A message comes from one branch and is expected to be delivered to other \(N_{\text{b}}-1\) branches. Extend the branch so that the message comes from the direction of the message dissemination and build a coordinate system with the origin point at \begin{table}
\begin{tabular}{l l} \hline \hline
**Notations** & **Descriptions** \\ \hline \(\upsilon\) & message dissemination speed \\ \(\hat{t}_{\text{d}}\) & delay in the whole procedure \\ \(\beta\) & average one-hop message progress \\ \(R_{\text{max}}\) & maximal distance of message dissemination along the road in the whole procedure \\ \(PDR\) & packet delivery ratio \\ \(\hat{\lambda}\) & equivalent node density \\ \(p^{i,i}_{\text{seg\_sel}}\) & probability of the selection of the \(i\)-th segment in the \(j\)-th iteration \\ \(h^{j,i}_{\text{seg\_bro}}\) & average vehicle numbers in other segments in the message dissemination direction when the \\ \(i\)-th segment is selected in the \(j\)-th iteration \\ \(\mu^{i,i}_{\text{seg}}\) & the average vehicle numbers in the \(i\)-th segment of the \(j\)-th iteration \\ \(N_{\text{P\_slot}}\) & number of time slots spent when a segment is selected \\ \(T_{\text{slot}}\) & duration of a time slot \\ \(N_{\text{seg}}(j)\) & number of segments in the \(j\)-th iteration \\ \(p^{i,c}_{\text{sec\_con}}\) & single probability of the success case in the \(c\)-th contention of the \(i\)-th final segment \\ \(p_{c,\text{con}}\) & single probability of the collision case in the \(c\)-th contention of the \(i\)-th final segment \\ \(p_{c}\) & probability of the selection of a back-off timer in the \(c\)-th contention \\ \(C_{\text{w}}(c)\) & maximal number of back-off timers in the \(c\)-th contention \\ \(p^{i,c}_{\text{suc}}\) & whole success probability after \(c\) contentions in the \(i\)-th final segment \\ \(T_{\text{con\_seg}}\) & contention latency of the \(i\)-th segment \\ \(T_{\text{con\_si}}(c)\) & durations spent in the collision case in the \(c\)-th contention \\ \(T_{\text{suc\_si}}(c)\) & durations spent in the success case in the \(c\)-th contention \\ \(N_{\text{recon}}\) & number of the contention re-attempt \\ \(T_{\text{part\_I}}\) & partition latency in Intersection Phase \\ \(T_{\text{con\_I}}\) & contention latency in Intersection Phase \\ \(\hat{p_{\text{I}}}\) & message progress in Intersection Phase \\ \(PDR_{\text{I}}\) & PDR in Intersection Phase \\ \(R^{u,i,m}_{\text{P\_B}}\) & partition range on the \(n\)-th branch in Branch Phase when \(\text{Raley}_{\text{I}}\) is in the \(i\)-th final segment on the \(m\)-th branch \\ \(T^{u,i,m}_{\text{part\_B}}\) & partition latency on the \(n\)-th branch in Branch Phase when \(\text{Raley}_{\text{I}}\) is in the \(i\)-th final segment on the \(m\)-th branch \\ \(T^{u,i,m}_{\text{con\_B}}\) & contention latency on the \(n\)-th branch in Branch Phase when \(\text{Raley}_{\text{I}}\) is in the \(i\)-th final segment on the \(m\)-th branch \\ \(\hat{\rho}^{u,i,m}_{\text{B}}\) & message progress on the \(n\)-th branch when \(\text{Raley}_{\text{I}}\) is in the \(i_{\text{I}}\)-th final segment on the \(m\)-th branch \\ \(PDR^{u,i,m}_{\text{P\_B}}\) & PDR on the \(n\)-th branch when \(\text{Raley}_{\text{I}}\) is in the \(i_{\text{I}}\)-th final segment on the \(m\)-th branch \\ \(T_{\text{part\_B}}\) & partition latency in Branch Phase \\ \(T_{\text{con\_B}}\) & contention latency in Branch Phase \\ \(\hat{\rho}_{\text{B}}\) & message progress in Branch Phase \\ \(PDR_{\text{B}}\) & PDR in Branch Phase \\ \(v_{\text{max}}\) & maximum speed of vehicles \\ \(d_{\text{inter\_veh}}\) & average inter-vehicle distance \\ \(v_{\text{max\_rule}}\) & limit speed in a specific road scenario \\ \hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._C (the center of the intersection).