# Reinventing Mobility Paradigms: Flying Car Scenarios and Challenges for Urban Mobility
## 3 The Model
The number and location of transition areas and roads within the city should provide a suitable coverage of the city and, at the same time, assuring safe conditions for entering the ground traffic network. To summarize, the following preliminary conditions have been set to perform the experiment:  
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2. Flying cars are suitably equipped to keep the right distances among them and between them and ground obstacles. 3. Flying mode is allowed over the city at a suitable minimum height, while landing and take-off have been allowed only at some prefixed transition areas and roads, which are connected to the ground network. 4. To move between specific origin/destination pairs, a combination of flying and ground mode can be adopted: flying mode allows moving quickly for the longer leg between transition nodes, while ground mode has to be used to reach the specific trip destination or to start from a given trip origin. Starting from the above conditions, the agent-based model has been specified as follows:  
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2. Each vehicle \(i\) (in flying or ground mode) is associated with an agent \(A_{i}\) (from hereafter the terms agents and vehicle will be used in an interchangeable manner). 3. For each couple (\(A_{i}\), \(A_{j}\)) of agents, the following conditions hold:
4. In ground mode, \(\forall A_{i}\) following \(A_{j}\) along the ground axis \(x\), the minimum distance \(d_{ij}\) between \(A_{i}\) and \(A_{j}\) is \(d_{ij}=t\cdot y_{gi}+s_{ib}\), where \(t\) is the technical time for starting braking, assumed the same for all the \(A_{i}\) (\(t=1\) sec); \(v_{gi}\) is the ground speed of \(A_{i}\); \(s_{ib}\) is the braking distance at a constant deceleration \(a_{i}\), which has been assumed the same for all the \(A_{i}\). 5. In flying mode, \(\forall A_{i}\) flying over \(A_{j}\), the vertical position along the \(z\) axis is \(h_{i}=d_{0}+n\cdot s_{z}\), where \(d_{0}\) is the minimum height allowed to overfly the urban area; \(s_{z}\) is the minimum vertical separation between \(A_{i}\) and \(A_{j}\), which is the same for each couple of agents (\(A_{i}\), \(A_{j}\)); \(n\) is the number of agents under \(A_{i}\) on the \(z\) axis. 6. In flying mode, \(\forall A_{i}\) following \(A_{j}\) along the same horizontal route, the minimum distance between \(A_{i}\) and \(A_{j}\) is constant and equal to \(s_{x}\). 7. \(\forall A_{i}\) passing from ground to flying mode, the climbing occurs at the transition areas based on a booked and confirmed time-slot authorization; this time slot depends on the estimated arrival time at the transition area, which in turn depends on ground traffic conditions. 8. \(\forall A_{i}\) passing from flying to ground mode, the descent occurs at the transition areas based on a booked and confirmed time-slot authorization; this time slot is estimated when leaving from the origin transition area according to the expected flying time between two transition areas. Note that agents can use only one horizontal route, although at different heights, then at a first attempt no separations along \(z\) have been introduced. 1. [leftmargin=*]
2. Each \(A_{i}\) moves between a trip origin/destination (\(O\)/\(D\) from hereafter) pair by following a path that can be made by both ground and aerial links according to the conditions listed below:
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4. \(\forall A_{i}\) moving between an \(O\)/\(D\) pair, if the Euclidean distance between the \(O\)/\(D\) pair is less than \(d_{min}\) the trip will take place on ground mode only, otherwise a combination of ground and aerial links will be used;
5. Each \(A_{i}\) that moves between an \(O\)/\(D\) pair will choose one path according to a minimum cost criterion;
6.