Sensitivity Analysis

In this subsection, we experiment the impact of different parameters by varying the value of one parameter while keeping other parameters unchanged. In each experiment we let the sensors operates for 1000 time-units. We repeat each experiment 10 times and present the average values.

In the first experiment, the communication range of each sensor is set to be 40. The error threshold is set to 0.5^◦C. We varied k, the number of hops for each sensor to exchange its readings in algorithm DClocal, from 1 to 6. In Figure 4.4, the total remaining energy of

0 50000 100000 150000

1 2 3 4 5 6

k

Total Remaining Energy

DCglobal DClocal

Figure 4.4: The impact of the value of k on the total remaining energy.

0 5 10 15 20 25 30 35 40

1 2 3 4 5 6

k

Number of Representatives

DCglobal DClocal

Figure 4.5: The impact of the value of k on the number of r-nodes.

0 50000 100000 150000

10 20 30 40 50

Stan dard Error

Total Remaining Energy

DCglobal DClocal Naive

Figure 4.6: The impact of the standard error on the total remaining energy.

DCglobal and DClocal at the end of the simulation is plotted.

As can be seen in Figure 4.5, due to the property of DCglobal, the number of r-nodes selected by DCglobal is not affected by k and the available energy is almost constant. On the other hand, when the value of k is less than 3, the available energy of DCglobal is higher than that of DClocal. This is because that, for smaller k, more r-nodes are selected by DClocal.

Therefore, the energy consumed in answering queries is higher. In Figure 4.5, when the value of k increases, the number of r-nodes selected by DClocal decreases. Since the number of r-nodes for answering queries decreases, the available energy of DClocal increases. As shown in Figure 4.4, the available energy of DClocal is higher than that of DCglobal when k is equivalent to 3 or 4.

However, the energy consumption in exchanging readings also increases as the value of k increases. As mentioned before, if the cost of increasing the value of k is higher than the benefit of increasing, the available energy decreases, as can be seen in Figure 4.4 when the value of k is larger than 4. Therefore, from the observation we can concluded that in this example the optimal value of k is 3 or 4.

0 2 4 6 8 10 12 14 16 18

10 20 30 40 50

Stand ard Error

Number of Representatives

DCglobal DClocal

Figure 4.7: The impact of the standard error on the number of r-nodes.

In the second experiment, we varied the standard error of the readings of the events in our network simulator. The standard error controls the volatility of the reading of sensors since the readings of sensors are the weighted average of the events in the network. The total remaining energy of different situation at the end of the simulation is shown in Figure 4.6.

In this experiment, we set the value of k is 3, thus the available energy of DClocal is always higher than that of DCglobal for different values of standard error. In Figure 4.6, for both DCglobal and DClocal, the available energy decreases as the standard error increases. This is because that for more volatile environment, more r-nodes are selected to fully data-cover the whole network. The number of r-nodes selected by DCglobal and DClocal can be seen in Figure 4.7. Therefore the energy consumption of the network in more volatile environment is larger. Since no r-nodes are selected in Naïve scheme, the available energy of Naïve is always the smallest one.

In the third experiment, we varied the values of the error threshold. The available energy of DClocal with different value of k and DCglobal is shown in Figure 4.8. As can be seen in the figure, the available energy of each algorithm is inversely proportional to the error threshold.

0 50000 100000 150000

0.1 0.3 0.5 0.8 1

Error Threshold

Total Remaining Energy

DCglobal DClocal with k = 1 DClocal with k = 3 DClocal with k = 5

Figure 4.8: The impact of the error threshold on the total remaining energy.

This is because that, for larger value of the error threshold, the number of r-nodes needed to fully data-cover the whole network is less. The number of r-nodes selected by DClocal with different value of k and DCglobal can be seen in Figure 4.9. In addition, the available energy of DClocal with k = 3 is the highest among all the cases, which is consistent with the discussion of Figure 4.4. The available energy of DClocal with k = 1 is the lowest, since the number of r-nodes in this case is the most.

In addition, for the value of error threshold larger than 0.8, the available energy of the 4 cases tends to be constant. This is because that the r-nodes almost cover all their neighbors within k-hops distance when the value of the error threshold is 0.8.

0 10 20 30 40 50 60

0.1 0.3 0.5 0.8 1

Error Thresho ld

Number of Representatives

DCglobal DClocal with k = 1 DClocal with k = 3 DClocal with k = 5

Figure 4.9: The impact of the error threshold on the number of r-nodes.

Chapter 5

Conclusions

In this paper we focused on approximate query processing in sensor networks. Since the readings of nearby sensors are usually correlated, it is power-efficient to group these sensors together and let only one of them respond to queries. We proposed a innovative concept called data-coverage to address the problem. We proved that the data-covering problem which selects minimal number of sensors as r-nodes with the union of their data-coverages data-cover all the sensors in the network is an NP-complete problem by reducing the set-covering problem to the data-covering problem. We then devised two heuristic algorithms DCglobal and DClocal to solve the data-covering problem. Algorithm DCglobal is a centralized algorithm executed at sink. The ratio between the number of selected r-nodes selected by DCglobal and that of the optimal solution is bounded. Since the message cost of selecting r-nodes in executing DCglobal is very high, we devised another distributed algorithm DClocal. Each sensor discovers its data-coverage by exchanging readings with only nearby neighbors. The sensors exchange their data-coverage size with nearby sensors to select sensors with locally largest coverage size as r-nodes. Through the experimental study, it can be seen the performance of DClocal is almost as good as DCglobal with energy consumption less than the energy consumption of DCglobal. The selected r-nodes answer queries within the pre-specified error threshold and the network lifetime is prolonged.

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