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1614 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 covered by those active nodes at some time. As shown in Figure 6, the network coverage is reducing with the network running using both the two algorithms. The higher the network coverage required, the shorter survival time of the network. During the initial operation, the two algorithms have maintained a higher coverage rate. But with the operation of network, more and more nodes exhausted their energy, the network coverage also decreased. Furthermore, the coverage rate of ECBS is always higher than LDAS at the same round during the whole running time. 100 80 (a) LDAS the number of active nodes 160 140 120 100 80 60 40 θ=90%,LDAS θ=85%,LDAS θ=90%,ECBS θ=85%,ECBS 60 20 network coverage 1 0.95 0.9 0.85 0.8 0.75 0.7 0.65 40 20 0 -20 0 20 40 60 80 100 120 (b) ECBS Figure 5 The coverage condition on No.100 round 0.6 θ=90%,LDAS θ=85%,LDAS 0.55 θ=90%,ECBS θ=85%,ECBS 0.5 0 200 400 600 800 1000 1200 1400 1600 1800 running rounds Figure 6 Comparisons of network coverage ratio The network coverage (η) is the ratio of the area covered by those active nodes to the whole monitoring area during the nodes scheduling scheme running process. Aactive ∩ A η () t = (5) A A is the whole monitoring area, and A active is the area 0 0 200 400 600 800 1000 1200 1400 1600 1800 running round Figure 7 Comparisons of active nodes Figure 7 shows the number of active nodes during the network running. As can be seen from Figure 7 and Figure 6, the number of active nodes by ECBS is always less than the number that used by LDAS when the coverage ratio meeting the requirement. Because there are more active nodes in the early operation by LDAS, too much energy were consumed. The active nodes decreased with more and more nodes run out of their energy. And the coverage percentage dropped from 98% to 50% quickly. But the number of active nodes used by ECBS algorithm is kept stability in the whole running process. Using the less active nodes to meet a high coverage, thus the energy has been saved and the lifetime has been prolonged. B. Network Lifetime According to the definition 4 in this paper, network lifetime is the running time of the network meeting the required coverage. As illustrated in Figure 8, the network lifetime is only 70 rounds with no scheduling scheme. Set θ≥90%, using LDAS scheduling scheme the lifetime is 850 rounds and the first dead node occurred on No.104 round. But by ECBS scheduling scheme, the lifetime extends to 1520 rounds and the first dead node occurred on No.382 round. Set θ≥85%, the lifetime is 1020 rounds and the first dead node occurred on No.117 round by LDAS. But by ECBS algorithm, the lifetime extends to 1750 rounds and the first dead node occurred on No.402 round. ECBS algorithm can prolong the network lifetime efficiently. And the lower required coverage, the longer the network lifetime. © 2013 ACADEMY PUBLISHER
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1615 ∑ N Ei () t i= 1 mE () t = N (6) The energy variance function is: = D () t = E ∑ N i E i 1 [ E () t − m () t ] 2 N (7) C. Energy Efficiency Figure 8 Comparison of network lifetime The average energy 0.05 0.045 0.04 0.035 0.03 0.025 0.02 0.015 0.01 θ=90%,LDAS θ=85%,LDAS θ=90%,ECBS θ=85%,ECBS 0.005 0 0 200 400 600 800 1000 1200 1400 1600 1800 running round Figure 10 comparison of the average residual energy ×10 -5 Figure 11 comparison of the energy Variance 30 25 θ=90%,LDAS θ=85%,LDAS θ=90%,ECBS θ=85%,ECBS Figure 9 Comparison of sleep ratio As mentioned above, the sleep ratio is an important parameter to describe the situation of saving energy during the operation. When meeting the coverage requirement, the higher the sleep ratio, the better the energy can be saved. Figure 9 shows that the sleep ratios of ECBS are always higher than that of LDAS algorithm and maintain stability in the whole running time. Moreover with different coverage requirement, the sleep ratios of LDAS are also much different. The higher the network coverage requires the lower sleep ratio. But the sleep ratios of our algorithm have a little change. Figure10 shows the average residual energy of network during operation. It confirms that the residual energy of ECBS is always higher than that of LDAS on the same round. Sleep ratio can only demonstrate the total condition of energy consumed, but not measure the balance of energy consumed. In this paper, the average residual energy and the energy variance function are used to measure that the energy consumed is balanced or not at some time [25]. Considering the two values, the larger the average residual energy and the smaller the energy variance, the better balance of the energy consumed in the network. The average residual energy function is: Energy variance 20 15 10 5 0 0 200 400 600 800 1000 1200 1400 1600 1800 running round From Figure 10 and Figure 11, it can be seen that the ECBS algorithm has a better balance of energy consumed. By LDAS algorithm, the m E (t) decreased more rapidly and the D E (t) were larger. The experiment data shows that using LDAS algorithm some nodes still remained more than 90% energy even when the network died. But using ECBS algorithm, the maximal ratio of the residual energy to the initial energy was about 40% when the network died. It also indicates that LDAS algorithm exits the problem that energy consumes uneven. Thus it will lead to some nodes run out their energy earlier. And then energy hole are formed so as to make the network dying prematurely. Ideally each node in a network running out its energy at the same time will obtain the optimal energy efficiency. © 2013 ACADEMY PUBLISHER
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Page 261: Call for Papers and Special Issues
Page 264: (Contents Continued from Back Cover
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