## 4 Analysis of Energy Consumption  
In this section we analyze the energy consumption in Adaptive TrimTree and compare it with energy usage in Fat-Tree topology Minimum Spanning Tree (MST) of ElasticTree [11]. For the analysis purposes we have used the topologies shown in Figure 3a-c to represent full connected fat-tree DCN with all active switches, MST ElasticTree, and Adaptive TrimTree respectively. For \(n\)-port fat-tree DCN topology, the number of servers, switches in the edge layer, aggregation layer and core layer and links are given in Table 1.  
In our analysis we use 48-port topologies with different number of pods. We have used PRONTO 3240 as commodity switches in DCN at all layers. Power specification for a PRONTO 3240 switch [10] is given in Table 2.  
[PERSON] et al. [10] developed a formula for empirical power consumption model of the entire network in their testbed comprising of 10 virtual switches on a single physical switch. Since each individual virtual switch cannot be shut down separately, they measure the power consumption of the entire physical switch with no ports turned on which is 66.7 W leading to 6.67 for each virtual switch as its chassis power consumption. To calculate the power consumption in fat-tree DCN topology we generalize the formula by [PERSON] et al. for ports operating at different data rates, in Equation (1):  
\[Power\;consumed\;by\;DCN=6.67\times N_{s}+\sum_{i=1}^{d}P_{i}\cdot J_{i} \tag{1}\]  
where 6.67 W is the chassis power consumption of each virtual switch, \(N_{s}\) = number of active virtual switches, \(P_{i}\) is the active power of a single port at the data rate level \(i\), and \(J_{i}\) is the corresponding number of active ports at that data rate level and \(d\) is the total number of data rates at which ports can \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Number of Points**} & **Number of** & **Number of** & **Number of Switches in Core** & **Number of Aggregation** & **Number of Switches in Edge** & **Number of** \\  & **Serves [n\({}^{3}\)/4]** & **Layer [(n/2)\({}^{2}\)]** & **Layer [n\({}^{2}\)]** & **Layer [5/4 (n)\({}^{2}\)]** & **Links [3/4 (n)\({}^{2}\)]** \\ \hline
48 & 27,648 & 576 & 2304 & 2880 & 82,944 \\
24 & 3456 & 144 & 576 & 720 & 10,368 \\
16 & 1024 & 64 & 256 & 320 & 3072 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Number of servers, switches and links in DCN fat-tree topology. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**PRONTO 3240**} & \multicolumn{4}{c}{**Port Data Rate (Mbps)**} \\ \cline{2-5}  & **None Active** & **10** & **100** & **1000** \\ \hline Power (W) & 66.7 & 70.7 & 80.2 & 111.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Power specifications of the PRONTO 3240 switch [10]. operate. Power consumption in Fat-Tree, ElasticTree and Adaptive TrimTree are computed and the results given in Table 3. Note that in our example, we assume only two data rates for ports: 1 Gbps and 100 Mbps therefore \(d=2\). The power consumed by an active port at maximum data rate (1 Gbps) is 1 W and power consumed by active ports at 100 Mbps 0.3 W. We assume that in Adaptive TrimTree 25% of ports are operating at 100 Mbps which is both reasonable and realistic keeping in view that it is a MST for meeting the current traffic demand, although this percentage can exceed. Also some ports can operate at 10 Mbps consuming 0.15 W of power.