## 5 Simulation Results
### Random Networks  
Finally we study the performance of the proposed protocol under four networks with random topology. For the random networks, 64, 81, 100, and 121 nodes are randomly deployed in a square network area, respectively (see the example in 7(c)). Multi-hop CBR traffic flows are randomly generated with randomly chosen source and destination nodes. A half of the transmitters generate CBR session with 1,000-byte frames, and the rest of them generate CBR sessions with 700-byte frames. All the other configurations of nodes are the same as those in the chain networks. Figure 10: Simulation results for grid networks when \(\sigma_{dB}=4\) dB. (a) Throughput. (b) Delay. Figure 9: Simulation results for grid networks when \(\sigma_{dB}=0.01\) dB. (a) Throughput. (b) Delay. Figure 11 presents the throughput and delay curves when \(\beta=4\) and \(\sigma_{dB}=0.01\) dB, and 12 presents the throughput and delay results when \(\beta=4\) and \(\sigma_{dB}=4\) dB. From the two figures, we observe the end-to-end throughput improvement ratios of 10.22%, 12.10%, 12.09%, and 14.72% respectively for the four networks when \(\sigma_{dB}\) = 0.01 dB, and throughput improvement ratios of 11.18%, 12.18%, 32.93%, and 28.70% for the case when \(\sigma_{dB}^{2}\) = 4 dB. The proposed scheme also achieves end-to-end delay ratios of 87.96%, 92.56%, 91.25%, and 87.02% when \(\sigma_{dB}\) = 0.01 dB and 64.30%, 74.34%, 82.32%, and 83.21% when \(\sigma_{dB}\) = 4 dB. We also examined the impact of shadowing standard deviation \(\sigma_{dB}\) on the performance of the proposed scheme. For a 64-node network with a random topology (as shown in 7(c)), we keep all the other parameters intact while increase the standard deviation value from 0.01 dB to 12 dB. Since different network environments have different standard deviation values. Such simulations will help answer the question that under what kind of environments the proposed scheme is effective. Figure 12: Simulation results for random networks when \(\sigma_{dB}=4\) dB. (a) Throughput. (b) Delay. Figure 11: Simulation results for random networks when \(\sigma_{dB}=0.01\) dB. (a) Throughput. (b) Delay. The throughput results are shown in 14(a) and the delay results are shown in 14(b). We find that the normalized throughput improvement ratio ranges from 10.2% to 25.2% when the standard deviation is increased from 0.01 dB to 12 dB. The net improvement, however, is more constant and ranges from 1.6 MB to 2.1 MB. We also observe that the standard deviation has very similar impact on both MAC schemes, as the two curves are roughly parallel to each other. When \(\sigma_{dB}\) gets larger, the throughputs of both schemes decreases. This is because when the channels become more dynamic, more packets will be lost due to transmission errors, leading to goodput degradation. From 14(b), it can be seen that generally about 0.5 s delay reduction is achieved by the proposed scheme over IEEE 802.11 MAC, except for very large standard deviation values. When standard deviation is 10 and 12 dB, both schemes achieve very small delays. We conjecture that because of the large variation of shadowing channels (and thus the transmission ranges), many packets traverse paths with smaller hop-counts, leading to smaller end-to-end delays for both schemes. Overall the proposed scheme outperforms IEEE 802.11 MAC for all the cases considered in this simulation. As illustrated in Figure 1, the effect of log-normal fading is two-sided: (i) some nodes (e.g., Node B) that are within the transmission range, are not neighbor anymore; and (ii) some nodes (e.g., Node C) that are not a neighbor but now are neighbors (and thus exposed nodes). For the chain network considered in the simulations, Type (i) effect is more likely to happen, resulting in broken links and lost packets. Therefore the performance improvement when \(\sigma_{dB}\) = 4 dB is smaller than that when \(\sigma_{dB}\) = 0.01 dB.