14 15 16 17 18
0 20 40 60 80 100
Power Consumption [kW]
Traffic Threshold [%]
Samlpe 1 Samlpe 2 Samlpe 3
14.6 14.8 15 15.2 15.4
58 60 62 64
Figure 4.3: Examples of the results obtained during simulation analysis using E(X) = 60 % and σ= 0.1. c2019 IEEE
Fig. 4.3 shows three results from the 100 random samples which is generated based on E(X) = 60 % and σ = 0.1. Unlike the numerical analysis, each result in Fig. 4.3 exhibits a different traffic threshold that minimizes the total power consumption of the network. However, the traffic thresholds that minimize the total power consumption of the network are close to 61.85 %, which is the result of numerical analysis. Thus, we calculate the minimum, average, and maximum value of the traffic thresholds that minimize the power consumption, and compare those values with the numerically calculated optimal threshold. Moreover, we also need to evaluate the amount of reduction of power consumption by applying our proposed optimal traffic threshold to random samples. Consequently, we analyze these aspects and show the results in Fig. 4.4, Fig. 4.5, and Table 4.2.
60 65 70 75 80 85 90 95 100
60 65 70 75 80
Traffic Threshold [%]
E( X ) [%]
Simulation Result Theoretical Optimal Threshold
(a)σ= 0.05
Figure 4.4: Numerically calculated Topt (dashed line at the x-shaped point) and simulation results (normal line at the circular point) of TTh that minimize the power consumption. Each panel exhibits differentσ values. Circular points show the average values of 100 samples in each case, and range bars show the maximum and minimum values. c2019 IEEE
60 65 70 75 80 85 90 95 100
60 65 70 75 80
Traffic Threshold [%]
E( X ) [%]
Simulation Result Theoretical Optimal Threshold
(b)σ= 0.1
Figure 4.4: Numerically calculated Topt (dashed line at the x-shaped point) and simulation results (normal line at the circular point) of TTh that minimize the power consumption. Each panel exhibits differentσ values. Circular points show the average values of 100 samples in each case, and range bars show the maximum and minimum values. c2019 IEEE
60 65 70 75 80 85 90 95 100
60 65 70 75 80
Traffic Threshold [%]
E( X ) [%]
Simulation Result Theoretical Optimal Threshold
(c)σ= 0.15
Figure 4.4: Numerically calculated Topt (dashed line at the x-shaped point) and simulation results (normal line at the circular point) of TTh that minimize the power consumption. Each panel exhibits differentσ values. Circular points show the average values of 100 samples in each case, and range bars show the maximum and minimum values. c2019 IEEE
60 65 70 75 80 85 90 95 100
60 65 70 75 80
Traffic Threshold [%]
E( X ) [%]
Simulation Result Theoretical Optimal Threshold
(d)σ= 0.2
Figure 4.4: Numerically calculated Topt (dashed line at the x-shaped point) and simulation results (normal line at the circular point) of TTh that minimize the power consumption. Each panel exhibits differentσ values. Circular points show the average values of 100 samples in each case, and range bars show the maximum and minimum values. c2019 IEEE
thresholds that minimize the power consumption. Panel (a), (b), (c), and (d) of Fig. 4.4 show the results in the case of σ= 0.05, 0.1, 0.15, and 0.2, respec-tively. In all cases, our calculated optimal traffic thresholds fall within the range of the simulation results. In addition, our proposed optimal traffic threshold ap-proaches the average value of the simulation results. For anyσ, increasing E(X) increases the optimal traffic threshold. Increasing the σ of the distribution in-creases the variety of the traffic loads and consequently elongates the range bars of the simulation results. Because the increased variety of the traffic loads may lead to flexible BBU aggregation, the deviation between our proposal optimal traffic threshold and the average value of the simulation results increases. There-fore, from the result of Fig. 4.4, our proposed scheme appropriately matches the simulation result when σ is small, but even at large values of σ, the calculated results veer toward the average value of the simulation result.
14 15 16 17 18 19 20 21 22 23
60 65 70 75 80
Power Consumption [kW]
E( X ) [%]
TTh = 0%
TTh = Topt TTh = 100%
(a)σ= 0.05
Figure 4.5: Total power consumption of the network, simulated for different mean traffic loads. Range bars present the maximum, average and minimum values of 100 samples. c2019 IEEE
14 15 16 17 18 19 20 21 22 23
60 65 70 75 80
Power Consumption [kW]
E( X ) [%]
TTh = 0%
TTh = Topt TTh = 100%
(b)σ= 0.1
Figure 4.5: Total power consumption of the network, simulated for different mean traffic loads. Range bars present the maximum, average and minimum values of 100 samples. c2019 IEEE
14 15 16 17 18 19 20 21 22 23
60 65 70 75 80
Power Consumption [kW]
E( X ) [%]
TTh = 0%
TTh = Topt TTh = 100%
(c)σ= 0.15
Figure 4.5: Total power consumption of the network, simulated for different mean traffic loads. Range bars present the maximum, average and minimum values of 100 samples. c2019 IEEE
14 15 16 17 18 19 20 21 22 23
60 65 70 75 80
Power Consumption [kW]
E( X ) [%]
TTh = 0%
TTh = Topt TTh = 100%
(d)σ= 0.2
Figure 4.5: Total power consumption of the network, simulated for different mean traffic loads. Range bars present the maximum, average and minimum values of 100 samples. c2019 IEEE
TTh = 0 %, Topt, and 100 %. Panel (a), (b), (c), and (d) of Fig. 4.5 show the results in the case of σ = 0.05, 0.1, 0.15, and 0.2, respectively. Here, TTh = 0 % means that all subareas operate in SC mode, and TTh = 100 % means that sub-areas are recommended to operate in LC mode if the traffic load of a subarea does not exceed the BBU capacity. Regardless of traffic load distribution, our proposed optimal traffic threshold conserves the total power in the network. In the results of all distributions when TTh = 0 %, the total power consumption in-creases linearly with the mean traffic load. Because the SC mode RRHs can be packed into BBUs very flexibly, the number of active BBUs linearly increases with the total traffic load; hence, the total power consumption increases linearly with E(X). Asσ increases, the power consumption atTTh = 100 % decreases and reaches close to power consumption at TTh =Topt because multiple traffic loads transported by LC mode RRHs can be compacted into one BBU. Consequently, the packing becomes more flexible, and the number of active BBUs after aggre-gation decreases. WhenTTh = 100 % andσ = 0.05, the total power consumption increases linearly, but its slope is smaller than the slope when TTh = 0 %. This occurs because one RRH has a large traffic load and many BBUs are already ac-tive; this small slope is only affected by the dynamic power consumption of BBUs, not the static power consumption of BBUs. Although TTh = 100 % implies that the subareas are recommended to operate in LC mode to save energy, our results show that it leads to increased power consumption of BBUs, thus the total power consumption of the network increased. Therefore, only considering power saving on RRHs may increase the total power consumption of the network because of the BBUs, and our proposed approach can reduce power consumption of RRHs while optimizing BBU aggregation to reduce power consumption of BBUs.
Table 4.2: Power Saving Percentage c2019 IEEE σ E(X) [ %] From TTh = 0 % From TTh = 100 %
0.05
60 10.82 % 17.32 %
65 11.39 % 14.86 %
70 11.50 % 11.77 %
75 11.37 % 8.78 %
80 11.76 % 6.49 %
0.1
60 11.14 % 16.02 %
65 10.80 % 14.23 %
70 11.18 % 11.80 %
75 11.51 % 9.07 %
80 11.51 % 5.83 %
0.15
60 12.37 % 12.75 %
65 11.30 % 12.73 %
70 11.16 % 10.89 %
75 11.16 % 7.97 %
80 11.52 % 4.23 %
0.2
60 13.23 % 9.21 %
65 11.93 % 10.02 %
70 11.64 % 8.62 %
75 11.19 % 5.39 %
80 11.15 % 1.14 %
opt
sumption atTTh = 0 % andTTh = 100 % at different traffic load distributions. We compared the average power consumption of 100 samples whenTTh = 0 %, 100 %, and Topt. Our proposed approach conserves at most 17.32 % of the total power consumption at σ = 0.05 and E(X) = 60 %. We can also infer from Table 4.2 that the power saving from TTh = 0 % is around the same value (about 11 %) for traffic distributions havingσ from 0.05 to 0.2 and E(X) in the range of 60 % to 80 %. However, the power saving from TTh = 100 % varies between 1.14 % to 17.32 %. As mentioned above, all subareas operate in SC mode at TTh = 0 %, so the RRHs can be aggregated with a minimum number of active BBUs. Our proposed approach also provides a minimum number of active BBUs for RRHs, but the number of active RRHs at Topt is less than the number of active RRHs atTTh = 0 %, which keeps the power saving around the same value. Conversely, TTh = 100 % implies that subareas should operate in LC mode if the traffic load of a subarea does not exceed the BBU capacity. The increase ofσ and E(X) can raise the probability of traffic load in a subarea that exceeds the BBU capacity, followed by more active SC mode RRHs which can be packed in BBUs flexibly.
As a result, the power saving at Topt decreases with an increase in σ and E(X).
Therefore, our proposedToptis most effective when E(X) is around 60 % for small values of σ.