# Agreement Technologies for Coordination in Smart Cities
## 3 Applications
### Evacuation Coordination in Smart Building
#### 3.2.3 Personalised Route Recommendation
An adequate notion of fairness of evacuation route recommendations is important to assure the trustworthiness of the system from the evacuees' viewpoint [33]: the guidance should not only achieve good overall performance of the evacuation process but must also generate evacuation routes for each of the evacuees that each of them perceives as efficient and fair. For example, if there are two close-by evacuees at some building location, they should be offered the same evacuation route or, if not possible, then routes with similar safety conditions and evacuation time. We aim at proposing available safe simple paths with a maximised safety acceptable in terms of duration in free flow for each evacuation origin. By acceptable in terms of duration in free flow, we mean the paths whose traversal time in free flow is within an upper bound in respect to the minimum free flow duration among all the available evacuation paths for that origin. The concept of envy-free paths was introduced in [37]. Basically, it defines a path allocation to be _a-envy-free_ if there is no evacuee at origin \(o^{\prime}\) that envies any other evacuee at origin \(o\) for getting assigned the path with a lower duration than the \(\alpha\)th power of the path duration assigned to the evacuee on \(o^{\prime}\). **Agile routes**. When an unpredicted hazard occurs on a part of the evacuation route, it becomes unsafe and impassable. If, in the computation of an evacuation route, we did not consider this fact and the related possibility to reroute to other efficient evacuation routes on its intermediate nodes, then, in case of contingency, rerouting towards safe areas might be impossible, causing imminent fatalities of evacuees. A similar case may occur if, for example, a high flow of evacuees saturates an evacuation path and causes panic. Therefore, we prefer routes where each intermediate node has a sufficient number of dissimilar efficient evacuation paths towards safe exits, if possible, within the maximum time of evacuation given for a specific emergency case. In that respect, evacuation centrality is defined in [38] as follows. _Evacuation centrality_\(C_{\epsilon}(i)\) of node \(i\) is a parameter that represents the importance of node \(i\) for evacuation. The value of the evacuation centrality of the node is the number of available, sufficiently dissimilar, time-efficient evacuation paths from that node \(i\) towards safe exits. Once we find the evacuation centrality measure for each node of the graph, the objective is to find an evacuation path that maximises the overall value of the intermediate nodes' centrality measures. We call every such path _agile evacuation path_: a path where an evacuee has higher chances to reroute in case of contingency in any of the intermediate nodes or arcs. _Path agility_\(\Delta(k)\) is defined as:  
\[\Delta(k)=\ _{|(i,j)\in k|}\sqrt{\prod_{(i,j)\in k}C_{\epsilon}(j)}\]  
Since we are not concerned about the number of arcs in the path, we take the \(\mid(i,j)\in k\mid\) th root of the Nash product in this formula. We recommend the evacuation paths with the highest agility to evacuees and recompute this value every time the safety and/or congestion conditions change along the recommended path.