The results so far have shown that the routing tree generated by the DECOR algorithm is significantly more balanced than the one produced by MHS which would result in greater lifetime. The cost is that the nodes in the tree are on average up to 10% further from the sink than in the tree produced by MHS. In this section another cost is examined, namely the number of control packets required to generate the tree. These costs are likely to be negligible compared to the network’s energy usage because they are a one-off initial setup cost; nevertheless it is still useful to take them into consideration.
Fig. 7.17 shows the average number of control packets transmitted by each node.
Under the MHS algorithm each node broadcasts an initial advert and then broad-casts an adoption confirmation packet for each child it adopts plus it must also transmit a packet requesting adoption. Although it appears that the average num-ber of transmitted packets under MHS remains constant, it does in fact increase logarithmically with radius (r = 0.976, p = 0.00083) and density (r = 0.939,
7.4. CONTROL OVERHEAD 173
Figure 7.16: After the second phase of DECOR the amount of extra latency is greatly reduced and is at most 9.21% though it grows with radius.
p = 0.0055), approaching three.
The variation in the number of packets transmitted under MHS cannot derive from imbalance because, regardless of the balance, each node can have only one parent and therefore precisely one confirmation packet is broadcast per node regardless of the number of children that parent already has. Instead, the small variation must derive from a small number of nodes being unable to connect to the routing tree at all because of voids in the network space. The increase in the number of broadcast packets with density is the result of fewer voids and therefore fewer nodes that bring down the average. The increase with radius, on the other hand, is probably because the number of nodes caught in voids becomes an even smaller proportion of the total as the number of nodes in the network increases. This also explains why the correlation is logarithmic because the maximum number of transmissions on average under MHS is three.
In contrast to MHS, under DECOR the number of packets transmitted per node falls slightly with density (r = −0.968, p = 0.00155) but increases with radius (r = 0.999, p = 3.48 × 10−8). The fall with density is probably because the child nodes are more likely to be adopted by their first choice parent which reduces the number of packets that need to be transmitted. On the other hand, previous results already showed that the balance of the network falls as the radius increases because more nodes are unable to fill their quotas. The knock-on effect of that is that the child nodes find it harder to get adopted and must transmit more
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Control Packets Sent Per Node
10 Neighbours per Node
Control Packets Sent Per Node
10 Neighbours per Node
Figure 7.17: The number of packets sent by each node is higher under DECOR and increases with radius whereas under MHS a node never sends more than three packets.
requests.
Despite DECOR requiring more packets per node, the cost is very small, no more than four extra packets per node in the worst case. Compared to the number of data packets that will be transmitted by each node over the course of the network’s lifetime these extra packets are negligible.
The results for the average number of control packets received by each node are very different, as shown in Fig. 7.18. Again the number under MHS increases logarithmically, but barely, with radius (r = 0.992, p = 0.00011) but clearly increases with density (r = 0.999, p = 2.21 × 10−10). With DECOR there is an increase in the number of packets received with both radius (r = 0.999, p = 5.87 × 10−7) and density.
It is not obvious whether the results for ten neighbours per node are erroneous or whether the relationship is logarithmic. Ignoring that data point shows a very strong linear correlation (r = 0.999, p = 2.31 × 10−8) whereas the correlation, assuming a logarithmic relationship, is weaker but still significant (r = 0.905, p = 0.013).
As a result of the invariance with radius of received packets under MHS and the increase under DECOR, the difference between the two grows as radius increases.
However, at the lowest radius value, the nodes using DECOR actually receive up
7.5. CHAPTER SUMMARY AND CONCLUSIONS 175
Control Packets Received Per Node
10 Neighbours per Node
Control Packets Received Per Node
10 Neighbours per Node
Figure 7.18: The average number of control packets received per node increases with density and, in the case of DECOR, with radius as well. However, because DECOR can aggregate many adoption confirmations into a single packet and MHS cannot, the difference in the number of packets received is not as great as the difference in the number transmitted.
to 34.78% (±4.55%) fewer packets on average than with MHS, though at the largest radius the DECOR algorithms results in up to 43.11% (±1.66%)more packets per node.
Interestingly, despite nodes transmitting more than double the number of control packets each under DECOR when the radius is 100m, the number they receive is less than 1.5 times as many. This is because under DECOR many adoption confirmations can be aggregated into a single packet whereas under MHS nodes select parents sequentially so that every adoption has its own confirmation packet which is received by all neighbours.
7.5 Chapter Summary and Conclusions
This chapter builds on the previous chapter by showing that the distributed con-struction of a static routing tree which aims at maximising inner-corona balance is an effective method for maximising network lifetime. This approach to lifetime maximisation is new and the results in this chapter show that, compared to the next best distributed protocol MHS, significant improvements can be made.
The DECOR algorithm works by imposing a limit on the number of children
than nodes may adopt during the tree construction phase. The limits are carefully chosen based on the predicted number of nodes in each level of the routing tree. A second phase was included to allow for complete connectivity and greatly reduce the added latency.
The simulation results in this chapter confirm that DECOR can achieve full connectivity while providing significant increases to balance which correspond to a lifetime increase of up to 85% compared to MHS. The major trade-off to achieve this is latency which increases by between 5% and 10% which is a small price to pay for such a large improvement in network lifetime.
To the best of my knowledge the two protocols proposed in the last two chapters are the only fully distributed protocols that aim to maximise inner-corona bal-ance. The DECOR protocol proposed in this chapter has been shown to provide a very large increase in network lifetime with only a small trade-off. However, the simulated network conditions in this chapter are somewhat idealised. In the next chapter the DECOR algorithm is tested in scenarios that move beyond the sim-plified corona model to show that even under those conditions it still outperforms the next best protocol, MHS.
Much of the work presented in this chapter was published in [KF12c].
Chapter 8
DECOR Beyond the Corona Model
In the previous chapter the DECOR algorithm was proposed and analysed and the results showed that it could provide significant improvements to inner-corona balance for a small latency trade-off. All the preceding analysis has been based on the corona model which offers a mathematically convenient model for a sensor network but makes some simplifications and imposes constraints in order to do so.
In this chapter, the DECOR algorithm is analysed in scenarios that are somewhat different from the simple corona model.
First, the unit disk graph (UDG) model is dropped and a more accurate packet reception rate model is used which is then used throughout the rest of this chapter.
Second, in Section 8.2, the effect of moving the sink away from the centre of the network is considered. Although it is obvious that this will increase the latency of the network, the question is what effect it will have on DECOR’s ability to produce a balanced tree. Finally, in Section 8.3, the method of deployment is changed to a Gaussian distribution and the DECOR algorithm is modified to account for a different distribution type.
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8.1 Packet Reception Rate
The corona model, with its fixed width coronas, is based on the UDG model which states that every node has the same, fixed transmission range. The UDG model can be thought of as predicting the packet reception rate (PRR) and predicting it to be 100% if the distance between transmitted and receiver is below some threshold and 0% if the distance is greater than that value. Although this simplification was strongly justified in Section 3.3, it remains an inaccurate model of the PRR.
In this section the more accurate packet reception rate (PRR) model derived by Zuniga and Krishnamachari is used [ZK04]. The model, shown in equation (8.1), relates the PRR to distance based on the log-normal shadowing model (see Chapter 3 for more details and Table 3.1 for the values of the variables).
Following the results in that chapter, the absolute reception-based blacklisting (ARB) strategy is used by the nodes to determine the optimal relay nodes. The results using this more accurate model are in line with those found using the unit disk graph model.
Fig. 8.1 shows the balance achieved by DECOR with ARB compared to MHS.
It is clear that the balance achieved by DECOR is very high, ranging between 0.87 (±0.03) and 0.98 (±0.007) and is significantly higher than under MHS. An interesting result is that while the balance under MHS falls with radius, the balance achieved by DECOR shows no statistically significant variation with ra-dius (p = 0.135). However, balance does increase logarithmically with density (r = 0.978, p = 0.00069). The improvement of DECOR over MHS increases with both radius (r = 0.999, p = 1.63 × 10−6) and density (r = 0.983, p = 0.00042), ranging between 22.19% (±3.96%)and 106.77% (±20.51%).
These results are reflected in the max/mean ratio shown in Fig. 8.2 which again demonstrates that the results for DECOR are significantly better than for MHS, ranging between 68.30% (±16.04%) and 300.39% (±47.06%) lower. Similarly to balance, the improvement of DECOR increases with both radius (r = 0.991,
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Balance 10 Neighbours per Node
12 Neighbours per Node
Figure 8.1: Balance is remarkably high under DECOR with a realistic PRR model, increasing logarithmically with density but not falling with radius. Over-all, DECOR provides between 20% and 100% more balance than MHS.
p = 0.00013) and density (r = 0.991, p = 0.00013). Overall, the corresponding lifetime increase is up to 250%.
The reason for the significantly higher balance of DECOR with this model com-pared to the earlier results is that under ARB the average link is longer which raises the effective density of the network. All the results have shown that bal-ance increases with density under the DECOR algorithm and therefore it is not surprising that the DECOR algorithm performs better under ARB than under UDG.
The connectivity in all configurations is 100% under both DECOR and MHS and the trade-off for latency remains, as with the unit disk graph model. Fig. 8.3 shows that the latency under DECOR is higher than under MHS. As with the earlier results, the extra latency is relatively small, between 7.35% (±0.91%) and 13.49% (±0.76%), but increases slowly with radius (r = 0.987, p = 0.00025) and density (r = 0.988, p = 0.00019).
The results for the average number of control packets sent per node are shown in Fig. 8.4. As with the results using the UDG model in the previous chapter, the number of packets sent under MHS increases logarithmically with radius (r = 0.984, p = 0.000396) but is invariant with density (p = 0.923). With DECOR, the number increases with both radius (r = 0.992, p = 8.72 × 10−5) and density (r = 0.932, p = 0.0067).
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Figure 8.2: The max/mean ratio under DECOR is significantly lower than under MHS, showing an increased lifetime of up to 250%.
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Figure 8.3: The trade-off for the improved balance is extra latency but these results accord with the earlier ones in showing a small increase, this time up to 13.49%.