Safe Region

In the past, many in-network studies investigate how to effectively set up the routing tree and form the clusters for economizing the energy attrition. Unfortunately, seldom of these works center on maintaining the robustness of the clusters so that the sensors can further save power by avoiding re-establishing the clusters frequently. The longer a cluster lives, the more energy conserve for all the members in cluster. In this section, we discuss how to intensify the structure and prolong the lifetime of a cluster.

Since we focus our work on environmental monitoring, sensor nodes report the current data periodically to the clusterheads and clusterheads can do some aggregation and reduction of data. At the same time, sensing attributes such as temperature varies based on terrains or circumstances. That means the reading of a sensor node also changes over time. It brings an inevitable problem that some member nodes which had critical readings may break the ambit of cluster. These nodes are forced to leave the original cluster and try to join other available clusters. Furthermore, if a clusterhead changes the reading caused by environment, it cannot guarantee be the representative node in the future anymore. This is because the rule of electing clusterhead is choosing the node whose reading is the nearest to the mean among the members.

Regardless of clusterhead or member nodes, it wastes power consumption on adjusting clusters, especially on clusterhead.

In view of this, we proposed a concept of safe region, which allots each node(even clusterhead or normal member node) a floating range. If the variance of a node drifts within the floating range, the node will be kept in the cluster with the result that enhances the persistence of the cluster. Now we discuss how to generate the floating region. As mention in clustering phase, we first find out the Temporary Clusterhead(TCH) and average the readings of all the cluster members. The movement of digging out the mean not only decided the New Clusterhead(NCH) but shifted the value of clusterhead to middle of whole cluster members. Therefore, it will move

a Figure 3.6: Example of safe region with user-tolerable threshold ² = 1

out a margin of range to realize the concept of safe region. Fig. 3.6 explained this idea. Fig. 3.6b transforms Fig. 3.6a into a temperature-like chart with pointing out the corresponding nodes.

We can discover that if TCH(node a) is decided to be the clusterhead, we have no safe region at all. Since it exists a critical node(node d) whose reading is fell on the boundary of TCH, which is [9,11]. After re-voting for NCH, the reading of NCH was shifted to [9.5,11.5] result in switching the critical node to node e whose reading is 9.8. Eventually, it generates a safe region, bounded in 0.3 in this example, for the cluster.

Different clusters generate distinct safe regions because the generation of a safe region is depended on NCH and critical node. The closer readings between NCH and critical node, the larger safe region sharing for a cluster. We now further divide the safe region into two sub-regions, called clusterhead floating range and membership floating range, respectively. The clusterhead floating region is allocated to clusterhead, so the membership floating range is to the members of clusters. We prefer to allow clusterheads wider floating range since the changes of the clusterheads may result in extremely energy cost, such as cluster recovering. Member nodes, however, got narrower membership floating range because they will not destroy the completeness of the clusters. In Fig. 3.6b, we got a safe region with 0.3 degrees, we might allocate NCH(node b) a clusterhead floating range with 0.2 and members a membership floating range with 0.1

degrees, respectively. This phase diminishes the possibilities of a node to switch between the clusters, thus retrenches the energy consumption.

Chapter 4

Performance Evaluation

4.1 Simulation Model

We developed a network simulator based on JSIM [13] to generate the queries and the sensors associated with their readings. Our experiments are conducted on network sizes ranging with 600 sensor nodes in a 500m × 500m two-dimensional sensing field. The field is divided into 20m × 20m grid cells. Users request the queries from the sink at point (0,0). The transmission range of each sensor node is set to 30m. The simulation time is 600 seconds and sensors report data every 10 seconds. Sensing reading of each node is generated with a uniform probability distribution from 16 to 24. Packets are divided into two categories, which are data packets and broadcast packets. The energy consumption model refers to [11]. Table 4.1 summarizes the system parameters and setting. Be convenient to narrate, we name our scheme as EDG (Energy-efficient Data Gathering) for the rest experiments.

4.2 Impact of Simulation Time

In Fig. 4.1, we compare the number of bytes of CAG and EDG approaches. The total numbers of sensor nodes are 600. Nodes report the readings in the sensing range every 10 seconds periodically.

For CAG and EDG approaches, the user-tolerable threshold is set to be 0.1 with respect to corresponding clusterheads. CAG proposes an algorithm to build up the message-forwarding tree and generate the clusters in the same time. It decreases the number of bytes because only

Parameter Setting

Sensing field size 500 m × 500 m Number of nodes 600

Report rate 10 sec

Transmission range 30 m Sensing Reading range 16 - 24 Threshold distance (d₀) 75 m

Eelec 50 nJ

ε_{f s} 10 pJ/bit/m²

ε_amp 0.0013 pJ/bit/m⁴

Data packet size 100 bytes Broadcast packet size 25 bytes Packet header size 25 bytes

Initial energy 2 J

Figure 4.1: Number of bytes vs simulation time

0

Figure 4.2: Number of alive sensors vs simulation time

clusterheads have to report the information. However, EDG not only does what CAG has done but also improves the CAG algorithm by reducing the number of clusterheads and offering the sensors the structure of safe region, so EDG has less total messages than CAG. However in 30 to 45 seconds, EDG has the overheads for waiting the regrouping messages and broadcasts adjusting messages from the sink to all the sensors for new network topology. Fig. 4.2 shows the details of total messages. We separate messages into control messages and report messages. Control messages are responsible for establishing forwarding tree and clusters, regrouping clusters in EDG approach. Periodical data reports are included by report messages. At 30 seconds, EDG has more control messages than CAG because EDG needs to exchange messages between local clusters and sink. And EDG has the same report messages due to sink not broadcast clusters combinations yet. When time increased, the number of EDG’s report messages decrease caused by regrouping, and the number of control messages are the same. So in long-term viewpoint, EDG still outperforms CAG by 11 percent of the number of bytes.

We now compare the number of alive sensors with time series of different approaches. We deploy 600 sensors in sensing field. In the Naive approach, all nodes in sensing field report their readings to the sink periodically. As shown in Fig.4.3, the number of alive sensors in

0

100 200 300 400 500 600

Time

Figure 4.3: Number of alive sensors vs simulation time

Naive approach died rapidly especially from 200 seconds to 400 seconds since every sensor has to report the reading. In both CAG and EDG, they are cluster-based approaches so that the member sensors in a cluster are representative of exactly one clusterhead. Thus, the number of alive sensors diminishes slightly since only clusterheads report the readings. Moreover, EDG reduces the number of clusterheads than CAG, so sensors on the path to the sink of these reducing clusterheads have no longer to forward the messages. In the end we can see that the number of alive sensors in EDG is more than the number of alive sensors in CAG.

4.3 Impact of Sensor Number

To measure the scalability between CAG and EDG, we change the number of sensor nodes in the simulated network from 100, 200, 300, 400, 500 to 600. We vary the size of the simulated area according to keep a fixed node density. Fig. 4.4 depicts the relation between the number of clusterheads and the network size. We see the superior performance of our EDG approach.

This is because EDG merged the clusters at the regrouping procedure. In CAG, some neighbor clusters which have the similar readings cannot integrate with each other since they have critical

0

100 200 300 400 500 600

Number of nodes

Figure 4.4: Number of clusterheads vs sensor nodes

0

100 200 300 400 500 600

Number of nodes

Figure 4.5: Number of messages vs sensor nodes

point between them. However, EDG solve the situation by exchanging some messages between sink and clusters to reduce the number of clusters.

Fig. 4.5 shows the number of bytes count for different number of nodes. EDG outperforms CAG in all cases. We also can discover as the network size enlarged, the number of messages of CAG raised heavily where EDG raised lightly. There are two reasons to explain this situation. One is that EDG has fewer number of clusterheads so less messages are send. The other reason is when the network size enlarged, the average distance from a sensor to sink increased. It leads more cost to transmit messages. If a clusterhead is far from sink and is merged by EDG approach, it can save a great deal of messages than CAG. This is why the message overheads of CAG is outstandingly higher than EDG.

4.4 Impact of User-tolerable Threshold

The following experiments investigate the variations of user-tolerable threshold. We deployed sensors in the sensing field and report rate is set to be 10 seconds in 200 seconds total simulation time. Fig. 4.6 and Fig. 4.7 display the number of clusterheads and messages of EDG normalized by that of CAG under the different thresholds, respectively. As shown in Fig. 4.6, when threshold is set to 0, that means users do not permit any errors for reporting answers. Every sensor is identical to a clusterhead to report exactly what it sensed. In this case, CAG and EDG are retrograded as same as Naive approach. With increasing the value of threshold, EDG reduces 15 percent of the number of clusterheads as the threshold is 0.15. In this best case, EDG diminishes 49 clusterheads than CAG. An interesting result is that the number of clusterheads of EDG is closing to CAG again when threshold is increasing. This is because the condition to form a cluster became loosed, a cluster can include more members thus the number of clusters get lessened. Considering an extreme case, all the sensors are included in one cluster because the threshold is too big, then EDG is hard to merge clusters anymore.

0.75 0.8 0.85 0.9 0.95 1 1.05

0 0.05 0.1 0.15 0.2 0.3 0.4

Threshold Nor

mal ized num ber o f clu ster head s

CAG EDG

Figure 4.6: Normalized number of clusterheads vs user-tolerable threshold

4.5 Impact of Changed Events

Monitoring phenomena usually vary their features accompanied with time series so that sensors detect different sensing readings. We then evaluate the impact of the number of changed events.

In Fig. 4.8, we examine the overheads for different ratios of changed events over total 600 sensors.

A changed event means that a sensor node varies its sensing reading. The readings are changed by uniform distribution between a half of user-tolerable threshold with respect to the corresponding clusterheads. The number of bytes count of EDG is less than CAG all the time. By increasing the ratio of changed events, the benefit of safe region in EDG approach appears obviously. This is because EDG allows each sensor a floating range to avoid rebuilding the clusters where CAG does not have. It shows that EDG is more suitable for dynamic sensing environments.

0.86

0.05 0.075 0.1 0.125 0.15 0.175 0.2

Threshold

Figure 4.7: Normalized number of messages vs user-tolerable threshold

0

Ratio of changed events (%) Num

Figure 4.8: Impact of changed events

Chapter 5 Conclusion

In this thesis, we considered the problem of approximate query processing over spatial clustering in sensor networks. We formed sensors into clusters which were bounded by an user-tolerable threshold. We further merged clusters and found an innovative issue called infer-graph set problem. We then designed an heuristic algorithm to devise near-optimal solution. Moreover, the safe region robusts the persistence of clusters without losing the precision. Our experiments showed that EDG outperforms CAG 11 percent of bytes count and 15 percent of clusterheads and EDG was suited in dynamic sensing environments. We concluded that our scheme effected better energy usage of sensors and prolonged the lifetime of sensor networks.

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