## 4 Proposal
### Proposed Algorithm
#### 4.2.2 Modified Dijkstra Algorithm (MD)
In the case of efficiency these two behave alike. The results correspond to the obtained value for fairness and congestion in a state k of the simulation. As the number N vehicles evaluated is not the same (10 to 100), the simulation could have more or less states, so it shows the results for all evaluated N vehicles presented in different graphs for each implementation. Figure 22 shows the behavior of Fairness for each implementation, and Figure 23 shows the behavior of average congestion for each implementation for each N-vehicles passed. The main conclusions of this simulation with respect to the behavior of fairness and congestion are:

Figure 19:0 Obtained Fairness in a state k for each N-vehicle set with each implementation. (**a**) Fairness obtained for each N-vehicles with Natural behavior algorithm; (**b**) Fairness obtained for each N-vehicles with Local congestion algorithm; (**c**) Fairness obtained for each N-vehicles with Global Congestion algorithm; (**d**) Fairness obtained for each N-vehicles with Modified Dijkstra algorithm. * Fairness behavior and congestion behavior are very similar: as the maximum capacity of the streets is reached, the streets get saturated which result in a high congestion level implying that the use percentage of the streets is very similar. * GC and LC implementations obtain the highest values in fairness when the congestion level is not high, that means the streets are being used better in those cases. Also, those implementations obtained the best values in efficiency, showing that exists a relation between the trip efficiency for each vehicle, and the use balance in the streets. #### 6.2.2 F Vehicles

In this scenario, a constant number F of vehicles were incorporated to vehicular network in each simulation (k state). Vehicles enter an empty network and simulation stops when a number N of vehicles arrive at the destination node. This means that in contrast with the N-vehicle simulation scenario, there will be vehicles in the network after the final simulation step. Best value comparison for distance was not taken into account in the presented results. Figure 19:1 Obtained Average Congestion in a state k for each N-vehicle set with each implementation. **(a)** Avg. Congestion obtained for each N-vehicles with Natural behavior algorithm; **(b)** Avg. Congestion for each N-vehicles with Local congestion algorithm; **(c)** Avg. Congestion for each N-vehicles with Global Congestion algorithm; **(d)** Avg. Congestion for each N-vehicles with Modified Dijkstra algorithm. (a) Efficiency and Distance

The results correspond to the average value for each group of 5 vehicles, in a sample of 100 vehicles of the total N vehicles passed during the simulation. Also, each metric is presented independently and contains the results for each selected \(F\). Figure 24 represents the obtained efficiency and Figure 25 the obtained trip distance. Figure 26 represents the best-value comparison for efficiency. Figure 19:2 Behavior for route efficiency in the F-vehicles scenario. **(a)** Mean efficiency value for each 5-vehicles set when F is 10; **(b)** Mean efficiency value for each 5-vehicles set when F is 20; **(c)** Mean efficiency value for each 5-vehicles set when F is 30; **(d)** Mean efficiency value for each 5-vehicles set when F is 40. Figure 19:3 Behavior for trip distance in the F-vehicles scenario. (**a**) Mean trip distance value for each 5-vehicles set when F is 10; (**b**) Mean trip distance value for each 5-vehicles set when F is 20; (**c**) Mean trip distance value for each 5-vehicles set when F is 10; (**d**) Mean trip distance value for each 5-vehicles set when F is 20. Figure 19:4 Cont.