# ESCAPE: Evacuation Strategy through Clustering and Autonomous Operation in Public Safety Systems
## 6 Numerical Results
### Comparative Evaluation
#### First Scenario: Why Minority Games?  
In this scenario, we compare our proposed ESCAPE framework, and specifically the minority-game component, with two different approaches regarding the way that evacuees in the disaster area choose to evacuate or not:  
1. The first alternative method is the following: evacuee \(m\) chooses whether they will evacuate or not through desired evacuation route \(e\) by taking into consideration how far they are from \(e\), i.e., based on distance \(d_{m,e}\). The greater \(d_{m,e}\) is, the lower the probability for the evacuee to evacuate is; conversely, the lower \(d_{m,e}\) is, the greater their probability to evacuate is. That is: \(Pr_{NotEvacuate}=d_{m,e}\) and \(Pr_{Evacuate}=1-d_{m,e}\). In the following, we refer to this strategy as \"Distance\".
2. The second alternative method is the following: evacuee \(m\) chooses whether they will evacuate or not through desired evacuation route \(e\) by taking into consideration the threshold number of evacuees that can physically go through evacuation route \(e\) at time slot \(t\), i.e., \(C_{e}-|M|_{e}(t)\), as discussed in Section 4. In particular, if \(C_{e}>|M|_{e}(t)\) then \(Pr_{NotEvacuate}=\dfrac{1}{C_{e}-|M|_{e}(t)}\) and \(Pr_{Evacuate}=1-\dfrac{1}{C_{e}-|M|_{e}(t)}\), meaning that the more evacuees are already in the evacuation route, the greater the probability of not to evacuate is, as the evacuation route is congested. Now, if \(C_{e}\leq|M|_{e}(t)\) then we consider that \(Pr_{NotEvacuate}=1.0\) and \(Pr_{Evacuate}=0.0\). In the following we refer to this strategy as \"Capacity\".  
In particular, Figure 4(a) shows the average number of evacuees that are already in each evacuation route \(e\), i.e., \(|M|_{e}\), in combination with the corresponding capacities (Cap). It is obvious that our approach demonstrates better performance between all alternatives, as it properly and dynamically distributes evacuees between the available evacuation routes. This is confirmed by the fact that our proposed approach presents the lowest average number of evacuees in all routes, while these numbers being below the corresponding capacities for all routes. This means that, with the ESCAPE service, evacuation routes never become too congested, thus leading evacuees away from the disaster area quickly in a safe way. On the other hand, the two other approaches gather a greater average number of evacuees per evacuation route, which is above the capacity for all the routes, making them very congested and unsafe because of potential evacuation delays. Between the two other approaches, the one with the capacity threshold of evacuees is the worst because the algorithm waits for the number of the evacuees already in the routes to drop below capacity limits, and when this happens many evacuees choose them again in order to evacuate. As a result, the average number of evacuees remains high (and above the capacity threshold). On the other hand, the approach with the distance weights (even if it underperforms compared to our proposed approach), it still outperforms the approach with the capacity criterion. This is due to the fact that the former accomplishes a wider distribution of evacuees in evacuation routes than the latter approach, as the criterion to choose an evacuation route is distance \(d_{m,e},\forall m\in M,\forall e\in E\). Figure 4(b) complies with the aforementioned observations, as the total average reward function of our approach is the greatest one compared to the other two approaches.