## 5 Performance Evaluation Results and Discussion
### Effects of Misbehaving REPs and Mitigation of the Effects by S-REPs  
Figure 19 shows the number of different successful bids between cases with and without misbehaving mobile hosts for both the pedestrian and vehicle simulation cases. We chose 5% and 30% as the ratio of misbehaving hosts to evaluate how bid results are affected by the ratio of misbehaving hosts and how S-REPs can mitigate the effect of misbehaving hosts for low and high ratios. In all cases, the number of different successful bids is smaller with one S-REP per P-REP compared to the case with no S-REPs for both the pedestrian and vehicle cases. In addition, the evaluation scores of successful bids in cases with some misbehaving mobile hosts were lower than the evaluation scores of successful bids without misbehaving hosts when the evaluation scores were different. These results confirmed that S-REPs can mitigate the effects of misbehaving REPs that fail to fulfill the role of REP.  
We illustrate the reason why the number of different successful bids with 500 mobile hosts is smaller than that with 250 mobile hosts in Figure 19. According to the method by which P-REPs volunteer, as described in Section 4.4.1, one mobile host can be a one-hop neighbor of multiple P-REPs. If a mobile host becomes a one-hop neighbor of multiple P-REPs, the mobile host can receive D2D Bid Invitations messages, including the same bid invitation from multiple P-REPs. Therefore, the mobile host can receive the same bid invitation from multiple P-REPs. This has the same effect as having additional S-REPs. As the number of mobile hosts increases, each mobile host is more likely to be a one-hop neighbor of multiple P-REPs, and the number of different successful bids becomes smaller. We note two additional points. (i) The number of different successful bids between cases with and without misbehaving mobile hosts is larger in the vehicle case than in the pedestrian case. (ii) The reduction rate in the number of different successful bids between cases with and without misbehaving mobile hosts is smaller in the vehicle case than in the pedestrian case. We consider the reason for (i) as follows. The number of D2D messages for \(T_{b}=1\) shown in Figure 20 is the result for 500 mobile hosts with no misbehaving mobile hosts. The ratios of the average number of D2D RevAuc message receptions to the average number of D2D RevAuc message transmissions in Figure 20 are 20.98 for the pedestrian  
Figure 19: Number of different successful bids in cases with misbehaving hosts. and 21.16 for the vehicle with \(T_{b}=1\). This implies that the average number of mobile hosts participating in a D2D RevAuc with a P-REP is larger in the vehicle case than in the pedestrian case. Therefore, more mobile hosts participate in RevAuc through misbehaving P-REPs in the vehicle case than in the pedestrian case. Regarding the reason for (ii), we think that the faster movement of vehicle hosts causes the one-hop neighbors of a P-REP to be unreachable through two-hop D2D communication by S-REPs more often than for pedestrian hosts, and the effectiveness of S-REPs is reduced. In the proposed method, S-REPs send and receive the same amount of data as P-REPs for Bid Invitations Query messages and Bid Invitations messages. The amount of data for Bids messages of S-REPs is the same as the amount of data for Bids messages of P-REPs in many cases even though the set of mobile hosts that P-REPs communicate with can be different from the set of mobile hosts that S-REPs communicate with. Therefore, the cellular traffic with \(m\) S-REPs per P-REP becomes almost \((m+1)\) times as large as the cellular traffic with no S-REP per P-REP.