## 3 Multimetric Map-Aware Routing Protocol (MMMR)
### Metrics Evaluation
\[u_{1,i}(d_{i})=e^{-\left(\frac{d_{i}}{d_{ref}}\right)^{\alpha}} \tag{3}\]1  
**Available bandwidth**: Multimedia services (e.g., video streaming) require a given amount of network resources to run correctly. To improve the QoS (Quality of Service) provided with our proposal, we included an estimator of the available bandwidth in VANETs based on a previous approach, called the available bandwidth estimator (ABE) developed in [13]. The ABE algorithm estimates the available bandwidth in a link between two general nodes in IEEE 802.11 networks. We previously evaluated ABE for VANETs in [14] and improved its operation further in [15]. Here, we summarize the ABE proposal, while a full explanation can be found in [13]. Each node estimates its percentage of idle time by sensing the common wireless medium. This value is included in its hello messages. The ABE algorithm uses the idle times of the emitter (\(T_{s}\)) and the receiver (\(T_{r}\)) of a link of capacity \(C\). Furthermore, ABE computes the collision probability of the hello messages, named \(p_{hello}\). The packet collision probability of packets of \(m\) bits, named \(p_{m}\), is derived from the collision probability of the hello messages using Equation (20). \[u_{1,i}(d_{i})=e^{-\left(\frac{d_{i}}{d_{ref}}\right)^{\alpha}} \tag{3}\]2  
The function, \(f(m)\), is used in Equation (20) to estimate the packet collision probability that is included in the ABE algorithm. This \(f(m)\) was obtained in [13] by computing the Lagrange interpolating polynomial, taking pairs of values of packet losses (\(p_{m}\)) and losses of hello messages (\(p_{hello}\)) from simulations. The result was \(f(m)=-5.65\cdot 10^{-9}\cdot m^{3}+11.27\cdot 10^{-6}\cdot m^{2}-5.58\cdot 1 0^{-3}\cdot m+2.19\). The additional overhead introduced by the binary exponential backoff mechanism used in IEEE 802.11 networks was computed in [13] using Equation (21). \[u_{1,i}(d_{i})=e^{-\left(\frac{d_{i}}{d_{ref}}\right)^{\alpha}} \tag{3}\]3  
where \(T_{m}\) (in s) is the time separating the emission of two consecutive frames, DIFS (Distributed Inter Frame Space) [16] is a fixed interval and \(\overline{\text{backoff}}\) is the number of backoff slots decremented on average for a single frame. Finally, a node estimates the available bandwidth, \(\text{ABE}_{i}\), on each neighbor's, \(i\)', wireless link using Equation (22) [13]. Notice that for us, \(s\) is the current forwarding node and \(r\) refers to every neighbor, \(i\), with which \(s\) establishes a link. \[u_{1,i}(d_{i})=e^{-\left(\frac{d_{i}}{d_{ref}}\right)^{\alpha}} \tag{3}\]4  
As was done in [13], in this present work, we considered the packet size (\(m\)) as a variable, but also, we took into consideration other variables that are determinant in vehicular scenarios: the nodes'density (\(N\)) and the average speed of the nodes (\(s\)). Our goal was to obtain a new function, \(f(m,N,s)\), to be included in Equation (20) instead of the former \(f(m)\) used in [13]. The routing protocol will be able to make better forwarding decisions to minimize packet losses in VANETs, since \(N\) and \(s\) are determinant configuration parameters. We computed a multiple lineal regression [17] using the software, IBM SPSS 20 [18], with results obtained from simulations, varying the three parameters (\(m\), \(N\) and \(s\)) in a wide range of values of interest in urban scenarios. After the analysis, we obtained the expression for \(f(m,N,s)\) shown in Equation (23). Then, we used Equation (24) to estimate the collision probability of packets. \[u_{1,i}(d_{i})=e^{-\left(\frac{d_{i}}{d_{ref}}\right)^{\alpha}} \tag{3}\]5  
\[u_{1,i}(d_{i})=e^{-\left(\frac{d_{i}}{d_{ref}}\right)^{\alpha}} \tag{3}\]6  
Finally, the value for the available bandwidth of each neighbor, \(i\), is obtained using Equation (22), where \(p_{m}\) is now substituted by the new \(p(m,N,s)\). Then, using Equation (25), the algorithm assigns a value to the available bandwidth metric (\(u_{4,i}\)), which is closer to one when the bandwidth is very high.