**3.4 Lifetime prolongation evaluation**

To evaluate the scheduling scheme in terms of power conservation, we compare the cooperative scheduled scheme with a single-tier network or a tier of a multi-tier architecture consisting of N nodes monitoring without coordination among them as (Rahimi et al., 2005; Kulkarni et al., 2005; Feng et al., 2005), in which, nodes are awakened with a time period of T. We note that the evaluation is over the sensing subsystem and that the radio subsystem (*i.e.*; transmission and reception of packets) is not taken into account.

The energy consumed in the network for object detection by N nodes during a duty-cycle interval of T in the non-collaborative scheduling is:

$$E = \mathcal{N} \cdot \left( T\_{sleep} \cdot P\_{sleep} + E\_{w\\_up} + E\_{cap} + E\_{det\text{left}} \right) \tag{5}$$

where Tsleep and Psleep are the period and power consumption for a node in sleep mode. Ew\_up, Ecap and Edetect respectively are the energies consumed in waking up a node, capturing a picture and performing object detection.

Let us now consider the cooperative scheduling algorithm in a clustered tier/network. Both, the interval between waking up consecutive nodes in the same cluster and the period of waking up a given node are functions of the cluster-size of the cluster which the nodes belong to. In one hand, in clusters with high cluster-size, Tinterval is small and thus cluster duty-cycle frequency is increased. On the other hand, higher number of nodes in the cluster causes longer periods TP for awaking a given node of the cluster and thus yields an enhancement for power conservation in cluster's members. Assuming average cluster-size for all clusters in the tier/network, TP will be:

$$T\_P = \frac{T \cdot \mu\_{\text{C}\_{\text{size}}}}{\mu\_{\text{C}\_{\text{size}}} - \gamma \cdot (\mu\_{\text{C}\_{\text{size}}} - 1)} \tag{6}$$

where T is the base period for waking nodes in the base un-coordinated tier. Figure 8 shows the evolution of Tp normalized by T (*i.e.*; Csize/β) for several node densities and clustering scales, γ. We may observe that the node average duty-cycle frequency is reduced by factors that are, for example, on the order of 0.78 for a 200 node network and a scale factor of γ = 0.6.

Fig. 8. TP/T for several node densities and clustering scales.

Consequently, the total amount of averaged consumed energy by nodes for object detection in the coordinated tier during TP will be:

Power Management in Sensing Subsystem of Wireless Multimedia Sensor Networks 565

$$E\_P = E + N \cdot P\_{sleep} \cdot (T\_P - T) \tag{7}$$

From (6) and (7):

$$E\_P = E + \frac{\boldsymbol{\gamma} \cdot \boldsymbol{T} \cdot (\mu\_{\text{C}\_{\text{size}}} - \mathbf{1})}{\mu\_{\text{C}\_{\text{size}}} - \boldsymbol{\gamma} \cdot (\mu\_{\text{C}\_{\text{size}}} - \mathbf{1})} \cdot \boldsymbol{N} \cdot P\_{\text{sleep}} \tag{8}$$

So:

564 Wireless Communications and Networks – Recent Advances

The energy consumed in the network for object detection by N nodes during a duty-cycle

where Tsleep and Psleep are the period and power consumption for a node in sleep mode. Ew\_up, Ecap and Edetect respectively are the energies consumed in waking up a node, capturing

Let us now consider the cooperative scheduling algorithm in a clustered tier/network. Both, the interval between waking up consecutive nodes in the same cluster and the period of waking up a given node are functions of the cluster-size of the cluster which the nodes belong to. In one hand, in clusters with high cluster-size, Tinterval is small and thus cluster duty-cycle frequency is increased. On the other hand, higher number of nodes in the cluster causes longer periods TP for awaking a given node of the cluster and thus yields an enhancement for power conservation in cluster's members. Assuming average cluster-size

*size*

( 1)

(6)

**300 nodes 250 nodes 200 nodes 150 nodes 100 nodes 50 nodes**

*size size C*

*C C T*

where T is the base period for waking nodes in the base un-coordinated tier. Figure 8 shows the evolution of Tp normalized by T (*i.e.*; Csize/β) for several node densities and clustering scales, γ. We may observe that the node average duty-cycle frequency is reduced by factors that are, for example, on the order of 0.78 for a 200 node network and a scale factor of γ = 0.6.

Consequently, the total amount of averaged consumed energy by nodes for object detection

0.5 0.55 0.6 0.65 0.7

**Clustering Scale**

 

*P*

*T*

Fig. 8. TP/T for several node densities and clustering scales.

in the coordinated tier during TP will be:

1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.5

**TP/T**

*E N (T P E E E ) sleep sleep w\_up cap detect* (5)

interval of T in the non-collaborative scheduling is:

a picture and performing object detection.

for all clusters in the tier/network, TP will be:

$$\frac{E\_P}{T\_P} = \frac{E \cdot (\mu\_{\mathbb{C}\_{\text{size}}} - \gamma \cdot (\mu\_{\mathbb{C}\_{\text{size}}} - 1))}{T \cdot \mu\_{\mathbb{C}\_{\text{size}}}} + \frac{\gamma \cdot (\mu\_{\mathbb{C}\_{\text{size}}} - 1) \cdot N \cdot P\_{\text{sleep}}}{\mu\_{\mathbb{C}\_{\text{size}}}}$$

$$\frac{E\_p}{T\_P} = \left(1 - \frac{\mu\_{\mathbb{C}\_{\text{size}}} - 1}{\mu\_{\mathbb{C}\_{\text{size}}}} \cdot \gamma \right) \cdot \frac{E}{T} + \frac{N \cdot \gamma \cdot (\mu\_{\mathbb{C}\_{\text{size}}} - 1)}{\mu\_{\mathbb{C}\_{\text{size}}}} \cdot P\_{\text{sleep}} \quad \text{where} \ (0 < \gamma < 1) \quad \text{and} \ (\mu\_{\mathbb{C}\_{\text{size}}} > 1)$$

Therefore, the consumed power is:

$$P\_P = \mathcal{X} \cdot P + \sigma \cdot P\_{sleep} \tag{9}$$

where:

$$\begin{aligned} \mathcal{A} &= \left( 1 - \frac{\mu\_{\mathbb{C}\_{\text{size}}} - 1}{\mu\_{\mathbb{C}\_{\text{size}}}} \cdot \mathcal{\mathcal{Y}} \right) \qquad \text{and} \quad 0 < \mathcal{A} < 1 \\\\ \sigma &= \frac{N \cdot \mathcal{Y} \cdot \left( \mu\_{\mathbb{C}\_{\text{size}}} - 1 \right)}{\mu\_{\mathbb{C}\_{\text{size}}}} \qquad \text{and} \quad 0 < \sigma < \mathcal{Y} \cdot N \end{aligned}$$

Parameter P in Equation (9) is the power consumed in the network with the base uncoordinated mechanism. The consumed power in our scheme (PP) is reduced by a factor λ with respect to P. The λ factor depends on the average cluster-size and the clustering scale factor. As can be observed from Equation (9) increasing Csize produces lower values of λ, and thus a saving in energy with respect the uncoordinated system. For example a Csize =1.5 (100 nodes with γ=0.5) produces a λ = 1 – γ/3 = 0.83 while a Csize = 2.15 (200 nodes with γ = 0.5) produces a λ = 1–0.53γ = 0.73. The other term (σPsleep) in Equation (9) is due to the fact of taking nodes to sleep mode in intervals of duration (TP > T) and then nodes sleep Tp–T more time than in the un-clustered scheme.

Figure 9 illustrates the impact of factor λ in Equation (9) in terms of node densities for several clustering scales. From this figure we can see that in high node density tiers, the factor λ is more beneficial since Csize is higher and thus there is more potential of cooperation among nodes.

Figure 10 shows the consumed power (P) in the base un-coordinated tier for object detection in four cases of period of duty-cycle for different node densities. The consumed power has been computed for nodes consisting of Cyclops as camera sensor embedded in the host MICA II, similar to the tier 1 in (Kulkarni et al., 2005).

Fig. 9. Factor λ in cooperative scheduling for several clustering scales.

Fig. 10. Consumed power (P) for a non-cooperative tier/network of nodes consisting of Cyclops.

For instance, in the case without coordination, the power consumed in a tier consisting of 200 nodes that performs monitoring with a duty cycle of T=5 second, is 1.344 watts. In the coordinated network with the same number of nodes and a clustering scale of 0.5, the power consumed by the network would be reduced by a factor λ of 0.737 (see Figure 9) at the cost of increasing 52.60 mW, (σPsleep). This means a tier power consumption of 1.3440.737 + 0.0526 = 1.043 Watts implying a reduction of 22.39%. Thus, in this case, the Prolongation Lifetime Ratio (PLR) would be of 1.344/1.043 = 1.289. Figure 11.a,b shows the prolongation lifetime ratio assuming a clustering scale of 0.5 and 0.6 for different node densities in four cases of duty-cycle (T). Tiers with high number of nodes have higher capability for cooperation and thus their nodes can conserve considerable amount of energy comparing to sparse networks and consequently, have longer prolonged lifetime. The figure indicates the more prolongation lifetime for dense tiers.

Fig. 11. Prolongation Lifetime Ratio (PLR) for different node densities in the clustered tier with a clustering scale equal to (a) 0.5. (b) 0.6, in four states of base awakening period.

### **4. Future work**

566 Wireless Communications and Networks – Recent Advances

**γ=0.7 γ=0.65 γ=0.6 γ=0.55 γ=0.5**

50 100 150 200 250 300

**Node density**

Fig. 9. Factor λ in cooperative scheduling for several clustering scales.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

0.5

1

1.5

**P (watt)**

2

2.5

3

**T= 3s T= 5s T= 10s T= 15s**

3.5

**λ**

Fig. 10. Consumed power (P) for a non-cooperative tier/network of nodes consisting of

For instance, in the case without coordination, the power consumed in a tier consisting of 200 nodes that performs monitoring with a duty cycle of T=5 second, is 1.344 watts. In the coordinated network with the same number of nodes and a clustering scale of 0.5, the power consumed by the network would be reduced by a factor λ of 0.737 (see Figure 9) at the cost of increasing 52.60 mW, (σPsleep). This means a tier power consumption of 1.3440.737 + 0.0526 = 1.043 Watts implying a reduction of 22.39%. Thus, in this case, the Prolongation Lifetime Ratio (PLR) would be of 1.344/1.043 = 1.289. Figure 11.a,b shows the prolongation lifetime ratio assuming a clustering scale of 0.5 and 0.6 for different node densities in four cases of duty-cycle (T). Tiers with high number of nodes have higher capability for cooperation and thus their nodes can conserve considerable amount of energy comparing to

50 100 150 200 250 300

**Node density**

Cyclops.

In the clusters established by the depicted mechanism, each cluster member has a common sensing region with the CH. The clusters do not have any intersection and each cluster monitors its covering domain with only intra-cluster collaboration. Clustering with the capability of intersection and cooperation among clusters can increase the scale of efficiency of monitoring performance and power conservation of cluster members. In a monitoring mechanism utilizing intra and inter cluster cooperation, sensing regions are allocated to intersected clusters thus can be monitored with a higher frequency and/or consuming less amount of energy although the node selection and scheduling procedure will be more complicated. Some initial work has been done in (Alaei & Barcelo, 2010).
