## 7 Simulation Results
### Performance Evaluation in a VANET Scenario  
In this subsection we introduce a brief performance evaluation of our proposal in a VANET scenario, where we proved the MMDSR protocol plus the multi-user game-theoretical approach described in Section 4. Video flows are transmitted from two vehicles to two access points AP1 and AP2 (see Figure 18), respectively. AP1 is the Ana Torres Institute (a surgery clinic) and AP2 is the Hospital Clinic of Barcelona, which represent two emergency units where vehicles will send their multimedia warning messages upon the event of a traffic accident. Each vehicle will send its multimedia warning message to the closest AP. We carried out ten simulations per point using the NS2 [35]. Figure 19 shows  
Figure 16: Behaviour of \(p_{i}^{*}\) as the fraction of packet losses (\(FPL\)) through the medium-quality path (\(FPL_{m}\)) increases. Here the FPL through the best path remains constant. Figure 17: Behaviour of \(p_{i}^{*}\) as the fraction of packet losses (\(FPL\)) through the best path (\(FPL_{b}\)) increases. Here the FPL through the medium-quality path remains constant. the results with confidence intervals (CI) of 90 percent. In the simulations, we used a real city area obtained from the example district of Barcelona, Spain (see Figure 18). In order to simulate a realistic scenario, the CityMob for Roadmaps (C4R) [38] simulator was used to obtain the mobility model. C4R is a mobility generator that uses the Simulation of Urban MObility (SUMO) engine [39]. Besides, C4R imports maps directly from OpenStreetMap [40] and generates NS2 compatible files to specify the mobility model for the vehicles through the city along the whole simulation. The simulation settings of the VANET scenario are shown in Table 6.  
Figure 19a shows the average percentage of packet losses for \(N\) = 2 users when using the game-theoretical scheme against the case of non using it (_Non game_ option). We can see how including the game-theoretical routing scheme, the average video packet losses are reduced from 26% to 11%. This decrement of the average packet losses is due to the optimal selection of paths based on a probability value (_i.e._, \(p^{*}\)) that optimally balances the load among the two paths at stake (_i.e._, the best and the medium-quality paths) depending on the quality of the paths. Figure 19b depicts the average end-to-end packet delay. We can see that the case including the _Game_ scheme improves the delay compared to the _Non Game_ case. It is reduced from 0.09 s to 0.04 s. Figure 19c depicts the average jitter delay suffered by the packets. Here, we observe that the jitter using the game-theoretical scheme shows slightly better result compared to the _Non Game_ case for 2 players. This has been a first performance evaluation of our game-theoretical routing approach applied in vehicular ad hoc networks. Results show clear benefits after including our game-theoretical approach in a multipath location-based routing protocol over VANETs. Based on these incipient results, in a next work we will further develop a multi-hop geographical routing protocol for VANETs based on a game-theoretical approach to send video warning messages in a smart city following a similar work strategy made in this paper. Our previous experience with VANET routing protocols [41, 42] will be a good starting point since in our design we will consider the special inherent features of VANETs. The main difference with this current work will be the design of the game-theoretical routing algorithm based on a hop-by-hop forwarding strategy instead of on an end-to-end forwarding path strategy as we did in this present work. We foresee enhanced results for VANETs after including this modification. Figure 18: Simulation scenario of Barcelona, Spain (N = 2 users). It includes two emergency units: AP1 (Ana Torres surgery clinic) and AP2 (Hospital Clinic of Barcelona). Figure 19: Simulation results for \(N\) = 2 users.