# MUXER--A New Equipment for Energy Saving in Ethernet
## 4 Results

Table 2: Parameters are used in the models (Calculated with Cisco Power Calculator [18]). Each MUXER has some components which consume the powers: IC Chip, ports, switching fabric. They are as denoted in Table 2 as \(\text{P}_{\text{ic-chip}}\), \(\text{P}_{\text{m-fixed}}\). Because each port of the switch has only one \(\text{K}_{\text{buffer}}\) to store and to process ordered MAC Frames, this paper uses the M/M/1/K*FCFS queue ([PERSON]'s notation for queuing models) to model the rate of MAC Frame generated and came to the ports of switches or MUXERs. In this model, the request arrives according to a Poisson process with arrival rate \(\lambda\) and number of services with rate \(\mu\). The request will be blocked if the switch's buffer has been reached to \(\text{K}_{\text{buffer}}\). In this paper, we assume each port of switch has the same buffer capacity \(\text{K}_{\text{buffer}}\) (bytes), each MAC frame that comes to its switch has the same size \(\text{S}_{\text{frame}}\) (bytes). With the M/M/1/K*FCFS [36], the probability when there are m MAC frames in the queue of each port is denoted as:  
\[Pr[N=m]=\frac{(1-\rho)\rho^{m}}{1-\rho^{\frac{k}{5}+1}} \tag{1}\]  
where, \(K=\text{K}_{\text{buffer}}\), \(S=\text{S}_{\text{frame}}\), \(m\in[0,\,\ldots,\,K/S]\), \(\rho=\lambda/\mu\). Figure 11: Power consumption results of network devices. (**a**) Switch of DASAN; (**b**) Switch of Cisco; (**c**) Router of Cisco. The probability of overload buffer is happened when \(N=K/S\). We have:  
\[Pr[N=\frac{K}{S}]=\frac{(1-\rho)\rho^{\frac{K}{S}}}{1-\rho^{\frac{K}{S}+1}} \tag{2}\]  
This paper analyzes two models in case of night time, which has low load traffic. In this case, MUXERs turn on IC Chips, and they act as the controllers to receive and to delivery MAC frame to the switches on which they are controlling. In these two cases, this paper brings a comparison between two models about the power consumption, where each model consumes in a time range \(t\). In other side, this paper uses some parameter values to run simulations to compare the difference between two models, with \(K=512\) KB, \(S=850\) bytes, each switch has 8 Fast Ethernet ports (100 Mbps). Therefore, we have \(\frac{K}{S}=602\) frames and \(\mu=15,420\) frames/s. In each switch, there are three power model types: power consumption of active ports \(\text{P}_{\text{port-active-s}}\), power consumption of idle ports \(\text{P}_{\text{port-idle}}\), and power consumption of switch utilization \(\text{P}_{\text{fixed-s}}\). They are calculated as:  
\[\text{P}_{\text{port-active-s}}=\text{P}_{\text{port}}+\text{P}_{\text{port- transition}} \tag{3}\]  
\[\text{P}_{\text{fixed-s}}=\text{P}_{\text{s-fixed}}+\text{P}_{\text{line- card}}+\text{P}_{\text{fabric}} \tag{4}\]  
In each MUXER, there are also three power model types: power consumption of active ports \(\text{P}_{\text{port-active-m}}\), power consumption of idle ports \(\text{P}_{\text{port-idle}}\), and power consumption of MUXER utilization \(\text{P}_{\text{fixed-m}}\). We have:  
\[\text{P}_{\text{port-active-m}}=\text{P}_{\text{in-port}}+\text{P}_{\text{eg- port}}+\text{P}_{\text{port-transition}}=2\text{P}_{\text{port}}+\text{P}_{\text{ port-transition}} \tag{5}\]  
\[\text{P}_{\text{fixed-m}}=\text{P}_{\text{m-fixed}}+\text{P}_{\text{lc-chip}} \tag{6}\]  
Equations (4) and (6) gives us the Total power consumption due to utilization of SWITCH (\(\text{P}_{\text{fixed-s}}\)) and Total power consumption due to utilization of MUXER (\(\text{P}_{\text{fixed-m}}\)) respectively, on the other hand Total power consumption of active port of SWITCH (\(\text{P}_{\text{port-active-s}}\)) and Total power consumption of active port of MUXER (\(\text{P}_{\text{port-active-m}}\)) is in Equations (3) and (5) respectively. The cumulative values of these are given in the next paragraph.