## 4 The Up/Down Mechanism of WiFi MAPs
### State Diagram  
In Table 1, we define the different states we will consider on any MAP from the power consumption point of view. Under the _MAP_OFF_s state, the MAP does not have any consumption; but will also not be able to autonomously reactive itself to participate in any PWMNS route again. In an _IFACE_DOWN_s_ state, the MAP is saving the power required to communicate through its wireless interface; but will be able to set its wireless interface up at any time. Finally, under _MAP_ON_s  
Figure 2: MAP5 is being interfered generating service disruptions due to traffic from building B.  
state, the MAP is consuming both the power required for its autonomous operation and its wireless interface to transmit and receive. In compliance with both our power saving and interference redressing targets, MAPs in _MAP_ON_s_ state (under certain conditions) will change their state to _IFACE_DOWN_s_. However, MAPs cannot be in this state for a long time, because they can be necessary as alternative routes in the PWMNS and, furthermore, the interferences' effects could have disappeared. We propose that there should be a compromise between node availability and consumption. Regarding the power savings involved in this process, they depend on that amount of time spent in _IFACE_DOWN_s_ state. Hence, in addition to only considering the wireless interface deactivation when interferences appear, we also suggest applying our proposal in [25]; in order for the intermediate nodes (neither source nor sink) to repeatedly change from _MAP_ON_s to _IFACE_DOWN_s_ states. Thus the power savings will be greater than if only applied when those nodes are interfered. After a node enters an _IFACE_DOWN_s_ state it must return to the _MAP_ON_s_ state, so that the node can check if it is required in any route. Hereinafter, we will refer this node as an inactive node; in contrast to any other node maintaining _MAP_ON_s_ state, which we will refer as active node. Those modes of operation are illustrated in the state diagram of Figure 3. It shows two states corresponding to the 2 nd and 3 rd entries in Table 1. It is also indicated the conditions and exit values for every transition in the form condition/variable = exit_value. We must highlight the Boolean downability conditioning-variable D(t), which indicates whether the node will become inactive at instant \(t_{o}\) + \(t_{UP}\) or not. Hence, it is possible to transition from _IFACE_DOWN_s_ state to _MAP_ON_s_ state when \(t_{DOWN}\) seconds have elapsed since reference instant \(t_{o}\); and then \(t_{o}\) will be updated to the current instant. From the _MAP_ON_s_ state both possible transitions require \(t_{UP}\) seconds to have elapsed since the \(t_{o}\) reference instant (and then \(t_{o}\) will be updated to the current instant), but if the node is downable, i.e., D(t) = true, it must transition to the _IFACE_DOWN_s_ state; and otherwise, i.e., D(t) = _false_, the node is to be used in any route and so it will remain in its _MAP_ON_s_ state. \begin{table}
\begin{tabular}{c c c} \hline \hline
**State Name** & **MAP Wireless Interface Is** & **Full MAP System Is** \\ \hline _MAP_OFF_s_ & down & off (it does consume no power) \\ _IFACE_DOWN_s_ & down & on and its wireless interface is down \\ _MAP_ON_s_ & up & on and its wireless interface is up \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Different MAP states from the power consumption point of view. Figure 3: State diagram for our proposal. In Figure 4 we illustrate an example of the time evolution of the average power P(t) consumed by some node, related to the time evolution of the downability variable D(t) corresponding to the same node, according to the state diagram of Figure 3. Thus while D(t) remains true, its P(t) changes repeatedly between P\({}_{\text{MAP\_ON}}\) Watts for \(t_{UP}\) seconds and P\({}_{\text{IFACE\_DOWN}}\) Watts for \(t_{DOWN}\) seconds. When D(t) changes to false (after \(t_{4}\) instant) P(t) will remain at P\({}_{\text{MAP\_ON}}\) Watts level, and this value will be repeated while D(t) remains false.