Performance Result and Analysis

The performance of HCR was evaluated with different network parameters, including S/D types and node densities. We run the simulation for one hundred times with each network parameter set and plot the average value. The simulation result indicates that HCR is better than other methods in all respects.

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Fig. 27. Full-Corner 4: Node density VS. number of transmission

0 50 100 150 200 250 300

5 7 9 11 13 15

Node Density

No. of Transmission

BF FCMN HCR

Fig. 28. Full-Corner 8: Node density VS. number of transmission

0 50 100 150 200 250 300 350

5 7 9 11 13 15

Node Density

No. of Transmission

BF FCMN HCR

Fig. 29. Full-Corner 16: Node density VS. number of transmission

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Fig. 30. Block 4: Node density VS. number of transmission

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Fig. 31. Corner 4: Node density VS. number of transmission

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Fig. 32. Line 4: Node density VS. number of transmission

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Fig. 33. Line 8: Node density VS. number of transmission

0 50 100 150 200 250 300 350

5 7 9 11 13 15

Node Density

No. of Transmission

BF FCMN HCR

Fig. 34. Line 16: Node density VS. number of transmission

0 50 100 150 200 250

5 7 9 11 13 15

Node Density

No. of Transmission

BF FCMN HCR

Fig. 35. Cycle 4: Node density VS. number of transmission

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Fig. 36. Cycle 8: Node density VS. number of transmission

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Fig. 37. Cycle 16: Node density VS. number of transmission

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Fig. 38. Cycle 32: Node density VS. number of transmission

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Fig. 39. Energy cost using LG-HCR

Figures-27, Fig. 28 and Fig. 29 presents the variation in the number of transmissions with node density when HCR, BF and FCMN are adopted separately.

These results show that the energy cost of FCMN grows as the node density increases, since the choices of possible paths also increases, and the redundant paths are not adequately pruned. The energy cost of BF grows as the number of sinks increases, because BF transmits the packet to each sink along many paths, and does not perform the path aggregation. However, the energy cost of BF decreases as the node density increases, since the choice of possible paths also increases. The method therefore

always has a good chance of choosing a better next hop. The figures, which are from Fig. 30 to Fig. 38, indicate the same argument with variety of network topology.

Further, these figures show that the topology with agglomerate sinks is more benefit from path aggregation than the topology with circumfluent sinks. In the worst case, like Fig. 35 shows, the HCR method has similar number of transmission with the brute force method, and therefore aggregating the path almost produces no benefit.

Figure-39 shows that the energy consumption using LG-HCR is slightly higher than that using the original HCR due to more relay nodes needed to transfer data within groups. Overall, the energy cost of HCR is more stable and less than other methods.

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Fig. 40. Robustness of HCR and LG-HCR

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Fig. 41. Flooding scope of HCR and LG-HCR

Fig. 42. Improvement in robustness using LG-HCR over HCR

Figure-40 presents that LG-HCR has better robustness in term of number of NTR.

We also observe that the higher node density has fewer number of NTR, in other words topology with higher node density is more robust. Therefore, the robustness of a network topology becomes weak robust as time goes by. In this simulation, we evenly distribute the 400 nodes within topology which sizes vary from 3400x3400 to 2200x2200. In HCR algorithm, about 15% of nodes out of 400 (i.e. 60 nodes) are NTR. However, in LG-HCR algorithm, only about 7% of nodes out of 400 (i.e. 28 nodes) are NTR. Figure-41 displays the average flooding scope of the two methods under different node density. Both methods have a similar number of nodes with HCVs which need to be corrected. Under those NTR cases, in average only about 5% of 400 nodes (i.e. 20 nodes) are needed to be updated with the correct HCVs for each case Restricted flooding can save more energy compared with full-scale flooding because the flooding scope is relative tiny. Figure-42 shows that LG-HCR produces a 60% improvement over HCR in the total number of CNs, indicating that LG-HCR is much more robust than HCR. This result can be easily expounded. For a Node-X, and its neighbor Node-Y, their HCVs of the two nodes are (X1,X2,X3,...,Xn) and (Y1,Y2,Y3,...,Yn) respectively. It has a property as |Xk-Yk||≤ 1, for any k in the range [1, n]. It implies that there are only three kinds of node-X’s neighbors where the difference of hop count value between node-X and its neighbor are 1, 0, and -1. If node-Y was failed, it makes kth component of HCV of node-X inacurate only when Yk<Xk and node-Y is the only neighbor of node-X that the kth component of node-Y

is smaller than node-X. Since nodes in sensor networks usually are deployed with high density. Consequently, the sensor nodes’ average number of neighbors is much larger. Even through NTR happens some time, usually the node has few chances to conform to the above two conditions especially under higher node density. The flooding scope is very small due to analogous reasons described above.

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Fig. 43. Node density VS. transmission delay

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Fig. 44. Comprehensive comparison between HCR and LG-HCR

Figure-43 indicates the extra delay cost by LG. This is because LG has to relay

packets through group leaders. However, the original HCR has the same delay with BF, because HCR combines the shortest paths from one source to each sinks. Finally, Figure-44 comprehensively compares HCR and LG-HCR in terms of delay, robustness and energy consumption, and indicates that LG-HCR is significantly more robust than HCR, but also has a longer delay and slightly higher energy cost.