2.5 Numerical results
2.5.2 Comparative performance analysis
To evaluate the efficiency of the proposed CMS algorithm, I focus on comparing the system cost and running time of the two algorithms CMS and RS, respectively. I simulated the proposed algorithms under the number of packets needed to be sent isX = 25 by usingM
= 20 sub-carriers and the required system reliability is 0.99 *γ = 0.1. The two important performance indicators used to measure the efficiency of the algorithms are the system cost and the elapsed time. They are described in Figure 2.5 and 2.6, respectively.
In Figure 2.5, we can see that the maximum system cost of my algorithm is less than 0.8 (cost units) while the minimum system cost of the RS algorithm is higher than 0.9 (cost units). The average of system cost by the RS algorithm is always higher from 2 to 10 times more than that of the CMS algorithm. It means that my algorithm can save at least 50% of energy thus it prolongs the network lifetime.
Figure 2.6 shows the elapsed time of two algorithms with the same initial parameters. In Figure 2.6a, one can observe that the CMS algorithm gives the results faster than the RS
0 1000 2000 3000 4000 5000 6000 7000 8000 9000
Experiment Index
0 0.5 1 1.5 2 2.5 3
The system cost
RS Algorithm CMS Algorithm
Figure 2.5: The comparison of system cost
algorithm. The histogram of the elapsed time of both algorithms are described in Figure 2.6b. With the higher frequency in the range of small elapsed time, the CMS algorithm spent not much time to find the optimal scheduling meanwhile the RS algorithm need to increase the value of parameter(Nsimparam) to big enough in order to get the optimal scheduling so the RS algorithm runs more slowly than the CMS algorithm.
0<t<1 1<=t<2 2<=t<5 5<=t<1010<=t<50 50<=t b). Elapsed time (time units)
0 1000 2000 3000
Frequency
CMS Algorithm RS Algorithm
0 2000 4000 6000 8000
a). Experiment Index 0
200 400 600
Elapsed time (time units)
RS Algorithm CMS Algorithm
Figure 2.6: The elapsed time of algorithms
The comparison of the system cost under the system reliability constraint:
In order to measure the improvement in system cost of two algorithms, I use the percentage improvement in the price paid for sending data as given in Equation (2.23).
Pimprove= (
1−Cos tCM S Cos tRS
)
x100. (2.23)
where CostCMS and CostRS are the system cost of the CMS algorithm and the RS algo-rithm, respectively. At the first scenario, the model withX= 25packets needed to be sent from number of sub-carriers is M = 10, 15, and 20 while the system reliability required is 0.99. The results of these scenarios are given in Table 2.4, 2.5, 2.6, and described in Figures 2.7a, 2.7b and 2.7c, respectively.
Table 2.4: The improvement in system cost withM = 10
# of System The system cost Pimprove packets sent reliability RS CMS (%)
25 0.62 0.214 0.195 8.88
0.65 1.049 0.976 6.96
0.66 1.292 1. 181 8.59
30 0.64 0.317 0.298 5.99
0.84 1.302 1.204 7.53
0.96 1.866 1.736 6.97
35 0.64 0.742 0.678 8.63
0.84 2.208 1.996 9.6
0.99 2.812 2.663 5.3
The improvement in system cost: 7.6 % Table 2.5: The improvement in system cost withM = 15
# of System The system cost Pimprove
packets sent reliability RS CMS (%)
25 0.66 0.487 0.452 7.19
0.68 0.931 0.598 35.77
0.69 0.946 0.9 4.86
30 0.66 0.549 0.543 1.09
0.84 0.935 0.854 8.66
0.98 1.179 1.108 6.02
35 0.66 0.65 0.63 3.08
0.84 0.954 0.85 10.90
0.99 1.391 1.243 10.64 The improvement in system cost: 9.8 %
In order to improve the quality of data transmission, in the next scenarios, I evaluate the performance of the proposed algorithm when increasing the number of packets needs to be sent isX = 100, the number of sub-carriers in source node is M = 50and M = 100. The improvements in the system cost are given in Table 2.7 and 2.8. The detailed comparison of the system cost between the RS algorithm and the CMS algorithm are described in Figure 2.7d and 2.7e, respectively.
The system reliability required
0 0.5 1 1.5 2 2.5 3
The system cost 1.204 1.736 1.996 2.663
0.214 0.195 1.049 0.976 1.292 1.181 0.317 0.298 1.302 1.866 0.742 0.678 2.208 2.812
L = 10; Y = 25 L = 10; Y = 30 L = 10; Y = 35 RS Algorithm
CMS Algorithm
(a)The improvement in system cost withM= 10
The system reliability required
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
The system cost 0.487 0.452 0.931 0.598 0.946 0.9 0.549 0.543 0.935 0.854 1.179 1.108 0.65 0.63 0.954 0.85 1.391 1.243
L = 15; Y = 25 L = 15; Y = 30 L = 15; Y = 35 RS Algorithm
CMS Algorithm
(b) The improvement in system cost withM = 15
The system reliability required
0 0.5 1 1.5 2 2.5 3
The system cost 0.369 0.489 0.589 0.741 1.357 0.775 1.244 2.384
0.25 0.23 0.41 0.516 0.634 0.826 1.56 0.89 1.469 2.626
L = 20; Y = 25 L = 20; Y = 30 L = 20; Y = 35 RS Algorithm
CMS Algorithm
(c) The improvement in system cost withM = 20
The system reliability required
0 1 2 3 4 5 6
The system cost 3.27 2.15 3.65 2.68 3.82 3.42 3.7 2.75 4.21 3.84 4.98 4.56 3.86 2.85 4.94 4.5 5.8 5.18
L = 50; Y = 100 L = 50; Y = 103 L = 50; Y = 105 RS Algorithm
CMS Algorithm
(d) The improvement in system cost withM = 50
The system reliability required
0 1 2 3 4 5 6 7 8 9
The system cost
L = 100; Y = 100 L = 100; Y = 102 L = 100; Y = 103
8.61
5.21 4.31 6.38 4.5 6.5 5.42 5.84 4.62 6.49 4.85 6.92 5.62 5.96 4.76 7.32 5.82 6.82
RS Algorithm CMS Algorithm
(e)The improvement in system cost withM = 100
Figure 2.7: The improvement in system cost
Table 2.6: The improvement in system cost withM = 20
# of System The system cost Pimprove packets sent reliability RS CMS (%)
25 0.63 0.25 0.23 8.00
0.64 0.41 0.369 10.00
0.65 0.516 0.489 5.23
30 0.66 0.634 0.589 7.10
0.84 0.826 0.741 10.29
0.98 1.56 1.357 13.01
35 0.66 0.89 0.775 12.92
0.84 1.469 1.244 15.32
0.99 2.626 2.384 9.22
The improvement in system cost: 10.12 % Table 2.7: The improvement in system cost withM = 50
# of System The system cost Pimprove
packets sent reliability RS CMS (%)
100 0.72 3.27 2.15 34.25
0.75 3.65 2.68 26.58
0.78 3.82 3.42 10.47
103 0.75 3.7 2.75 25.68
0.86 4.21 3.84 8.79
0.98 4.98 4.56 8.43
105 0.75 3.86 2.85 26.17
0.88 4.94 4.5 8.91
0.99 5.8 5.18 10.69
The improvement in system cost: 17.78 % Table 2.8: The improvement in system cost withM = 100
# of System The system cost Pimprove packets sent reliability RS CMS (%)
100 0.81 5.21 4.31 17.27
0.92 6.38 4.5 29.47
0.96 6.5 5.42 16.62
102 0.85 5.84 4.62 20.89
0.95 6.49 4.85 25.27
0.98 6.92 5.62 18.79
103 0.86 5.96 4.76 20.13
0.98 7.32 5.82 20.49
0.99 8.61 6.82 20.79
The improvement in system cost: 21.08 %
As we can observe from Tables 2.4, 2.5, 2.6, 2.7 and Table 2.8 of 5 scenarios when we increase the number of sub-carrier from M = 10 toM = 100, the system costs decreased down to 7.6%, 9.8%, 10.12%, 17.18% and 21.08% respectively among the CMS algorithm and the RS algorithm. Hence, the proposed algorithm decreases the system cost of data transmission with the same expected system reliability.
Improving the reliability of the data transmission:
In order to reach the reliable data transfer, each sensor node has to send the number of packets Yk being bigger than the original data size Xk. The algorithm must obtain a given level of reliability with as less data redundancy as possible. In this section, with the system (X, M) = (25,10), we will compare the number of packets which node in the RS algorithm and the CMS algorithm sent for the same expected transmission system reliability (0.999). The results are described in Figure 2.8. It can be seen that the node
25 26 27 28 29 30 31 32 33 34 35
Number of packets sent
0.650.7 0.75 0.8 0.85 0.9 0.95 1
The system Reliability
RS Algorithm CMS Algorithm
Figure 2.8: Improving the reliability of data transmission with (X, M)= (25, 10)
in the RS algorithm need to send much more data packets than the CMS algorithm does in order to reach the system reliability(0.999).
The comparison of the data rate versus the number of nodes:
Figure 2.9 depicts the performance in data rate between my proposal and some typical algorithms. It is shown that with a higher number of nodes, the total data rates will increase. The reason for this problem is in the multiuser diversity if the number of nodes in the system increases, the probability of sharing the same resources becomes lower. In Figure (2.9), it is shown that the sum of the nodes data rates achieved by a static TDMA system, in which each node is allocated with the equal transmission power, remained flat for all 8 nodes, while in other algorithms, they grew together with the number of nodes.
Although the node data rates of the CMS algorithm are slightly lower than that of the algorithm in [70], they still are better performances than algorithms in [61,118] and static TDMA.
2 3 4 5 6 7 8 Number of nodes
4 4.5 5 5.5 6 6.5 7 7.5 8 8.5
Sum of the data rates (bits/s/Hz)
Kim et al. algorithm Vasileios et al. algorithm Jang et al. algorithm TDMA algorithm CMS algorithm
Figure 2.9: The comparison of data rate in data communication The comparison of the fairness pointer versus the number of nodes:
In this section, my proposed CMS algorithm is compared with the algorithms proposed in [61, 70, 118] under fairness criterion. The fairness criterion is introduced in [139] and given in Equation (2.24).
F = (∑K
k=1
Rk )2
K
∑K k=1
(Rk)2
(2.24)
The Fairness pointer (F) is a measurement parameter of the equal data rates among nodes in the system, and its values range from 0 to 1. It is better for any resource allocation algorithm if it has a higher value of the fairness pointer. It can be seen in Figure 2.10 that the algorithms in [61, 70] have significant unequal among the nodes in the system.
The fairness pointers of these algorithms are low level and decrease with increasing the number of nodes. While the static TDMA scheme supports a better fairness pointer but it is still much lower than my achieved results and the outcome of the algorithm in [118].
Thus my algorithm can improve the fairness among the nodes in the system.
2 3 4 5 6 7 8 Number of nodes
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Fairness pointer
Kim et al. algorithm Vasileios et al. algorithm Jang et al. algorithm TDMA algorithm CMS algorithm
Figure 2.10: Fairness pointer vs number of nodes