## 3 Multimetric Map-Aware Routing Protocol (MMMR)
### Metrics Evaluation  
In this section, we detail each one of the four metrics included in our multimetric algorithm MMMR, which is a geographic routing protocol based on hop-by-hop forwarding decisions. The use of these metrics is a way to improve the choice of the next forwarding node. The four metrics considered are the distance to a destination, the trajectory of the vehicles, the nodes' density and the available bandwidth. They are described below. **Distance**: The typical goal of most geographic routing protocols is to send packets hop-by-hop to their destination, so that the next forwarding hop is the neighbor that is closest to the destination. These kind of protocols are based on the knowledge of geographic information of every node in the scenario. Each vehicle knows its own position and also the position of the destination. Therefore, it is usually assumed that the position of the packet's destination and the positions of the next hop candidates are sufficient to make proper forwarding decisions. We also use the distance (\(d\)) to the destination as a metric to evaluate each neighbor in our proposal. We obtain this information from the fact that senders \begin{table}
\begin{tabular}{c c c} \hline \hline
**Neighbor _i_** & **Reception Time of the Last HM** & **Reception Time of the First HM** & **No. HM** \\ \hline
32 bits & 8 bits & 8 bits & 8 bits \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Extra data per node used in the neighbor list included in the HM. know the destination position (\(x_{D},y_{D}\)) and also each neighbor includes in the hello messages its own position. With the position (\(x_{i},y_{i}\)) of each neighbor, \(i\), we can obtain its Euclidean distance (\(d_{i}\)) to the destination (\(D\)) (see Equation (2)):  
\[d_{i}((x_{i},y_{i}),(x_{D},y_{D}))=\|\vec{x}_{i}-\vec{x}_{D}\|=\sqrt{(x_{i}-x_{D })^{2}+(y_{i}-y_{D})^{2}} \tag{2}\]  
To compute the metric based on this distance, \(u_{1,i}\), we use Expression (3), where \(d_{i}\) is the previous Euclidean distance and \(d_{ref}\) is a reference distance, above which losses start to increase notably faster. This \(d_{ref}\) is obtained from simulations where we evaluated the performance of a fixed node set in different distances from the AP. The results are presented in Figure 1, where we can see that \(d_{ref}\) is around 2,000 m in our urban scenario. Notice that for a transmission range of 250 m, such a path of around 2,000 m would take around eight hops. \(\alpha\) is an attenuation factor that equals 0.77, obtained after a mathematical regression using the results of the simulations mentioned before and shown in Figure 1. This value, represented in Figure 1, measures the utility of the metric of the distance. Consequently, low distances to the destination obtain a high benefit, while long distances to the destination obtain low profits. The main settings used in this evaluation are presented in Table 3. \begin{table}
\begin{tabular}{l c} \hline \hline
**Parameter** & **Value** \\ \hline Simulation area & 1,500 m \(\times\) 1,500 m \\ Number of nodes & 120 vehicles \\ Maximum node speed & 50 km/h \\ Transmission/sensing range & 250/300 m \\ MAC specification & IEEE 802.11p \\ QoS access category & BE (best effort) \\ Bandwidth & 12 Mbps \\ Simulation time & 1,000 s \\ Maximum packet size & 1,000 bytes \\ Traffic profile & CBR (Constant Bit Rate) 4 Kbps \\ Routing protocol & GPSR \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The main simulation setting used in the distance evaluation. Figure 1: The relation between the distance to the destination and packet losses. In this case, the shorter value of the distance, \(d_{i}\), the better that node \(i\) will be classified, because we prefer a neighbor as close as possible to the destination. This way, Equation (3) tends to one when the distance to destination \(d_{i}\) tends to zero. We selected a negative exponential function to penalize drastically those neighbors with bad values in this metric.