# Outside Dynamic Evacuation Routes to Escape a Wildfire: A Prototype App for Forest Firefighters
## 3 Materials and Methods
### Evacuation Routes Algorithm
### Virtual Sensor Network Coverage

It is necessary to monitor the study area using a sensor network to obtain the fire propagation algorithm's input parameters. To model the network as close to reality as possible, the transmitter device XBee-PRO S2 was chosen, whose characteristics are ideal for this type of environment. The equipment has a transmission power of 10 mW, a data rate of 250,000 bps, and a reception sensitivity of \(-102\) dBm and operates on the ISM frequency of 2.4 GHz. These data are used in the following sections to calculate the sensor network's optimal coverage that ensures a successful connection. #### 3.4.1 Link Calculation

The transmission power values and the necessary link margin for optimal communication can be calculated based on the total system loss prediction. The following expression can define the link calculation:

\[ME(dB)=Pt+Gt-L+Gr-THrx \tag{2}\]

where _ME_ (_dB_) is the link margin, _Pt_ is the transmitted power, _Gt_ is the transmission gain, \(L\) is the propagation losses, _Gr_ is the receiver gain, and _THrx_ is the receiver sensitivity. For the transmitting equipment's data, taking into account a link margin of 10 dB to guarantee communication even if there are additional losses due to rain, mist, or other external factors, a minimum propagation loss (_L_) is obtained as 105 dB. #### 3.4.2 Propagation Model

The analyzed habitat is a deciduous forest, characterized by its dry condition and trees with low leaf density. Three propagation models were studied for this environment: Friis Free Space [36], Weissberger, and ITU Early Vegetation [37]. The equations for the Friis model are given by:

\[L(dB)=-20\log{(\frac{\lambda}{4\pi d})} \tag{3}\]

where \(\lambda\) and \(d\) are measured in meters. The losses were calculated using the data from the Xbee-PRO device. The same device is used for all models. The equations for the Weissberger model are given by:

\[L(dB)= \begin{cases}0.45f^{0.284}d&d<14\text{ m}\\ 1.33f^{0.284}d^{0.588}&d>14\text{ m}\end{cases}  \tag{4}\]

The equations for the ITU Early Vegetation model are given by:

\[L(dB)=1.33f^{0.284}d^{0.588} \tag{5}\]

where \(d\) is the depth of the foliage in meters and \(f\) is the frequency in GHz for both models (Weissberger and ITU Early Vegetation). Table 1 shows the results obtained from the propagation losses to find the optimal distance between the nodes, considering the attenuation result calculated in Equation (2). According to the Friis Free Space model, the coverage is more than 130 m; for the Weissberger model, the coverage is around 100 m; and for the ITU Early Vegetation model, the result is close to 80 m. Remembering that 10 dB of link margin was taken and that it seeks to optimize the network's costs and ensure the communication link, coverage of 100 m is proposed for the sensor network model. Finally, Figure 4 shows the sensor network model with the previously calculated coverage distance; this is used to monitor the entire area and warm about possible inconveniences (wildfires). Each point in the network represents a sensor node that uses the meteorological API to obtain the necessary values to calculate fire spread. Sixty nodes are used to cover the study area; this creates a virtual sensor network (VSN). This network is used for the constant monitoring of an area. It is related to the application proposal in general; e.g., if there is an ignition point within the area, the fire spread process is executed, and, at the same time, possible evacuation routes are calculated (the routes depend on the position of the user). The implementation of this application using Google Maps and the network design are outside the scope of this paper. ## 4 Scenarios and Results Analysis

This section analyzes the behavior of evacuation routes and performance metrics under different simulation scenarios. It is worth mentioning that these metrics may change depending on the equipment's characteristics. The tests were carried out with a computer with Intel CI3-7200U 8 GB/ 1 TB/W10.