# Analysis and Design of Functional Device for Vehicular Cloud Computing
## 6 Simulation Results  
In this section, we use a rigorous mathematical analysis to discuss the performance of vehicular networks. The experimental results evaluate the performance of vehicular networks for an outage probability based on the designed relay-assisted selection scheme by using MATLAB tools. As directing the transmission between \(S\) and \(D\) is a simply wireless communication link from Section 4.1 and has many experimental results, we cannot do the experiments again in this work. The simulation scenario mainly considers a two-hop relay vehicular network where a vehicle can transmit messages to other vehicles via a relay vehicle. According to Section 5.1, vehicles could collect SNR information which is embedded in the packet header from the upper vehicles in the device. To verify the performance of the system, a Monte Carlo simulation (1000 times) is adopted via MATLAB toolboxes. Subsequently, the PDF in Equation (15) is illustrated in Figure 3. The analytical results are an excellent match to the simulation results for the cases where \(\gamma_{1}=\gamma_{2}\), \(2\gamma_{2}\), and \(3\gamma_{2}\). With the growth of \(\gamma\), the outage probability of \(p_{\tau}(\gamma)\) gradually decreases until it reaches 0. Before \(\gamma=0.5\), the outage probability of \(p_{\tau}(\gamma)\) gradually increases from the bottom (diamond line) to the top (star line). After \(\gamma=0.5\), we get opposite results from before \(\gamma=0.5\). Based on the analysis of Section 3, we know the instantaneous SNR \(\gamma_{AF}\) depends on the gain \(A\). When the gain \(A\) is \(\sqrt{P_{s}/(P_{s}h_{1}^{2}+N_{0})}\), the instantaneous SNR \(\gamma_{AF}\) is equivalent to Equation (9). Hereafter, we get the approximated instantaneous SNR Equation (10). In this situation, the gain \(A\) is \(1/h_{1}\). The various SNRs have some effects on the outage probability of vehicular networks. In vehicular networks, a vehicle-assisted network adopts the AF protocol. The gain's influence on the relay system is shown in Figure 4.  
Equation (7) helps us get a tight lower bound for an AF system instead of being an exact formula for the choice of relay gain in Equation (11). From the analysis of Section 3, we know the instantaneous SNR \(\gamma_{AF}\) is dependent on the gain \(A\). The different SNRs have some effects on the outage probability of vehicular networks. Figure 4 plots the types of relay gain effects on relay systems. We can see from the figure that the two curves are essentially indistinguishable for all practical purposes with the growth of SNR. Thus, the outage probability is essentially indistinguishable according to the two curves, especially at higher SNRs. The variation of the outage probability with \(\gamma\) at different AF relay \(A\) gains has been studied for setting an outage threshold \(\gamma_{th}\). The results of the outage probability versus outage threshold \(\gamma_{th}\) are shown in Figure 5 for different values of \(\gamma\). We can see that the higher SNR \(\gamma\) reduces the outage probability in all AF relay gain cases. Moreover, it is clear that, for the same \(\gamma\) case, the two curves are essentially indistinguishable. Figure 4: A Monte Carlo simulation for the different types of Amplify-and-Forward (AF) relay gain \(A\). Figure 3: A comparison between the analytical results for the Probability Density Function (PDF) of a full link and the simulation results in different signal-to-noise ratio (SNR) cases. During the process of deriving the final outage probability, we obtained some intermediate results, such as Equations (22) and (23). These results can help us better evaluate the performance of vehicular networks. Figure 6 compares the performance of AF relay-assisted vehicles for the cases where \(\gamma_{1}=\gamma_{2}\), \(2\gamma_{2}\), and \(3\gamma_{2}\) in terms of Equation (22). With the growth of SNR \(\gamma\), the outage probability \(P_{out}\) gradually decreases to 0.