## 4 The Up/Down Mechanism of WiFi MAPs
### State Diagram
Let \(P_{\Delta t}\) be the average power consumed by each MAP for an \(\Delta t\) interval in the PWMNS, and \(C_{\Delta t}\) be the power consumption per unit of time. The average power \(P_{\Delta t}\) is calculated by Equation (1) assuming that, for a time interval \(\Delta t\ =\ m\ \times\ t_{DOWN}\ +\ n\ \times\ t_{UP}\), _IFACE_DOWN_s_ state is reached \(m\) times and _MAP_ON_s_ state \(n\) times:  
\[P_{\Delta t}\ =\ \frac{P_{IFACE\_DOWN}\ \times\ m\ \times\ t_{DOWN}\ +\ P_{MAP\_ON}\times\ n\ \times\ t_{UP}}{\Delta t} \tag{1}\]  
while power consumption for the same time interval \(\Delta t\) is calculated by Equation (2):  
\[C_{\Delta t}=\ P_{IFACE\_DOWN}\ \times\ m\ \times\ t_{DOWN}+P_{MAP\_ON}\times n \ \times\ t_{UP} \tag{2}\]  
We have measured the power consumption in one Linksys [45] MAP working with DD-WRT [46] firmware. Below we show the result, for a day (\(\Delta t\ =\ 24\) h) assuming \(m\ =\ 0\) in case 1 and \(n\ =\ 0\) in case 2:  
1. 9.4 Watts in _MAP_ON_s_ (i.e., \(C_{\Delta t}\ =\ 9.4\) Watts \(\times\ 24\) h \(=\ 225.6\) Watt \(-\) hour). 2. 7.6 Watts in _IFACE_DOWN_s_ (i.e., \(C_{\Delta t}\ =\ 7.6\) Watts \(\times\ 24\) h \(=\ 182.4\) Watt \(-\) hour). Usual mode for this MAP is case 1, where power saving does not exist. On the other hand, as can be noted in case 2, a maximum power saving of 44 Watts can be achieved for a day of operation. Thus, our mechanism can generate a power saving in the mid-point of both cases, whenever \(m>0\) and \(n>0\). Power consumption is a kind of human interference in the Environment. According to the Spanish Consumers and Users Organization (OCU) [47], 1 W of power for one year corresponds to 5.7 kg of carbon dioxide emitted to the atmosphere. Making calculations for carbon dioxide savings in the Linksys system, we obtain the following values, respectively:  
1. 53.58 kg of carbon dioxide in _MAP_ON_s_. 2. 43.32 kg of carbon dioxide in _IFACE_DOWN_s_. Figure 4: Power consumption variation related to D(t). We compare these results with other recent MAPs, concretely the WRT160 NL Router/AP Linksys/Cisco [48] equipped with the standard IEEE 802.11n (two wireless interfaces). Table 2 shows the average power consumed in the considered states. As can be noted, depending on the higher used-bandwidth, the average power consumed by the MAP is increased by 0.7 or 1.6 Watts, respectively, from the _IFACE_DOWN_s_ state. Attending to previous results, they make clear that, when the time interval for the wireless interface to be deactivated is maximized, power savings are also maximized. This deactivation time interval will be increased whenever either \(m\) or \(t_{DOWN}\) duration are increased. Factor \(m\) is determined by the number of times that the node returns to _IFACE_DOWN_s_ state (the node is unused). On the other hand, \(t_{DOWN}\) duration impacts the availability of the node in the PWMNS when it is required for any route. We consider \(t_{DOWN}\) duration a variable parameter which depends on power saving and traffic requirements. Similarly, \(t_{UP}\) duration must also be configurable, because it impacts the speed for the node to be inactive in case it is interfered or just unused.