## 4 D2D Group Communication Scheme with Bidirectional and InCrentental A-Star (BICA*) Routing
### Path Selection Algorithm
The satisfaction rate is defined as the ratio of packets successfully delivered within its delay budget. Figure 19 shows the satisfaction rates of different content types. It is evident that video has the lowest satisfaction rate compared to the other two content types due to its low delay budget. Nevertheless, the proposed approach can still achieve a satisfaction rate of 98%. Figure 20 gives the satisfaction rate of the video when UEs are on the move. It is more demanding as the moving speed increases. However, our approach can still maintain a satisfaction rate as high as 90%. Figure 17: Delay’s utility value vs. UE’s moving speed. Figure 18: Throughput’s utility value vs. UE’s moving speed. The time it takes in path planning is presented in Figure 21. We can see that the superior performance of our approach and A* comes with a higher computational cost. The simulation is conducted on a personal computer with Intel Xeon E3-1230 V2 and 8 GB RAM. Greedy is the simplest one with the least computational cost. The TSRS comes next. There is a clear tradeoff between path quality and computational cost. The A* has the highest computational cost. It is discernible that the BICA* adopted in the proposed approach can effectively lower the calculation time. We can conclude that in comparison with A*, the proposed approach can achieve better performance with less computational cost. Figure 11:0 Satisfaction rates of different content types. Figure 11:1 Satisfaction rates vs. UE’s moving speed. Figure 22 demonstrates the execution time of A* and the proposed approach when UEs remain stationary and when UEs are on the move. The movement of UEs results in a significant topological change. A* needs to recalculate the path, which leads to a considerable increase in computational cost. Due to the incremental nature of BICA*, the proposed approach can respond to topological change more quickly. Consequently, its computational cost is far less than that of A*. We now consider the effect of both moving speed and group size at the same time. We can see from Figure 23 that the increase in delay is limited if group size increases while UEs remain stationary. On the other hand, the increase in delay is more portentous if the group size is the same while UEs are moving faster. Nevertheless, even when the group's radius is as large as 125 m and moving at a speed of 6 km/hr, the proposed approach can still maintain a delay below 98 ms, which is less than the requirements of most contents. Figure 11:2 Execution time vs. number of UEs. Figure 11:3 Execution time when UEs are on the move. For group mobility, we use the RPGM model in our simulation. For all approaches, as the group moving speed increases, the delay increases accordingly. The results, as shown in Figure 24, resemble the results for UE mobility. The proposed approach outperforms all others and achieves a delay as low as 88 ms when the group speed reaches 9 km/hr. Figure 25 shows the change in satisfaction rate for the different group moving speeds. As expected, the satisfaction rate decreases as the group moving speed increases. In all cases, the proposed approach performs better than others. Figure 11:4 Delay vs. group size and UE’s moving speed. Figure 11:5 Delay vs. group’s moving speed. ## 6 Conclusions

Communication technology keeps evolving, from legend wired networks to today's wireless mobile networking. D2D group communication has received considerable attention for its potential for better resource utilization, less interference, facilitating group communication, and so on. Individuals sharing the same interest in digital content form a group and move as one. Members of a group can share digital content via D2D group communication. Previous routing schemes for D2D group communication consider only geographic information without taking into account the channel conditions. Such an approach may result in a longer delay or even delivery failure. This study counts for channel conditions and defines a utility function considering both delay and throughput.