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Related Works

Theorem 6. If G is connected, the trees constructed by the MT-EO algorithm must be connected shortest-path trees

4.4.1 Impact of Objects’ Speeds

First, we consider the scenario in which the update cost dominates the overall communication cost. To achieve this, we compare all schemes under various ob-jects’ speeds. Higher the speed is, more events are generated; thus, the update cost will dominate the performance. In Fig. 4.4, sensors are deployed regularly and four sinks are deployed. The query rate is set to be 1 query/second in this ex-periment. Fig. 4.4(a) shows the communication cost (i.e., the number of packets transmitted in the network) of these schemes with the value of object speed varied.

As can be seen in Fig. 4.4(a), the update cost is constant in the QF scheme because no update packet has to be sent. The update costs of all other schemes will grow when the speed becomes higher since more update packets have to be sent. The update cost of the MC scheme grows enormously, because no in-network

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Figure 4.4: Performance study with objects’ speeds varied, where sensors are deployed regularly and four sinks are deployed.

ing technique is applied. Our proposed schemes outperform the QF scheme and the MC scheme when the speed is lower than 10 units/second. Since the sens-ing radius of a sensor is 4 units, 10 units/second is relatively high. We further give an insight into our proposed scheme. Obviously, the broadcast forwarding scheme has lower update cost than the unicast scheme has. However, as can been seen later, the unicast scheme has higher query success rate than the broadcast scheme has. Besides, we can see that the EO scheme outperforms the MT-HW scheme slightly, because more packets are saved due to the overlap of tree edges.

Fig. 4.4(b) shows the query response time of these schemes, where the query response time is defined as the time elapsed between the time at which the query issued and the time at which the query result returned. The MC scheme is the best

because any query only has to be forwarded to the sink. Our proposed schemes are slightly worse than the QF scheme because two phases are required in our schemes. Although the MC scheme has the best performance in terms of query response time, the query result may not be the most up-to-date one. This problem becomes further severe when packet loss happens. A measurement, query error, is defined as the number of hops between the real location of the object and the lo-cation carried by the query reply at the time at which query is returned to the user.

In Fig. 4.4(c), it can be seen that the MC scheme suffers from higher query errors.

Finally, Fig. 4.4(d) shows the query success rates under different schemes. Note that a query may fail due to packet collision, packet loss, buffer overflow and con-taminated Detected Lists. More packets transmitted in the network usually means more collision. Thus, our proposed scheme and the MC scheme perform worse than the QF scheme does eventually, but all schemes have similar performance under reasonable speed. Note that the broadcast forwarding scheme has the worst performance due to the contaminated Detected List problem; however, the unicast forwarding scheme can be used to solve this problem.

Since the number of sinks is an important issue in this chapter, the scenario used in Fig. 4.4 is applied again in Fig. 4.5 except that 256 sinks are deployed now. It is observed that if the number of sinks is large, a considerable amount of update messages will be generated. Thus, when the update cost dominates the communication cost, using less sinks is better. Finally, experiments with the random deployment model is investigated in Fig. 4.6, where the number of sinks is 4. We can see that the success rates under the random deployment model are lower than that under the regular deployment model, because the collision phe-nomenon is very severe in the random deployment model. When a node has many neighbors, this node usually suffers severe collision due to the contention and the hidden terminal problem. Therefore, we further compute the average number of neighbors of a sensor. The average numbers of neighbors of a sensors under the regular deployment model and the random deployment model are 3.875 and 5.666 respectively. Thus, we conjecture that the severe collision phenomenon in the

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Figure 4.5: Performance study with objects’ speeds varied, where sensors are deployed regularly and 256 sinks are deployed.

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Figure 4.6: Performance study with objects’ speeds varied, where sensors are deployed randomly and four sinks are deployed.

dom deployment model is caused by the hidden terminal problem and the higher contention between sensors. We further give an insight into our proposed scheme.

We can find that the performance of the unicast forwarding scheme is very bad due to the buffer overflow problem. The reason can be explained as follows: when an event occurs, there are averagely 5.666 update packets will be injected into the sending buffer and the length of sending buffer is 10 only. Thus, the length of the sending buffer should be designed carefully. Other most observations made under the regular deployment model could be applied to the random deployment model. In the following experiments, we only show the results under the regular deployment model.