## 4 Proposal
### Proposed Algorithm
#### 4.2.2 Modified Dijkstra Algorithm (MD)
The main conclusions of this simulation with respect to the behavior of efficiency are:

* As the number \(F\) of vehicles increases, simulation results for efficiency in the previous simulation are replicated: the route efficiency in all implementations decreases as the set of vehicles in the network reaches the saturation value, in fact, for \(F=30\) and \(F=40\) there is not a great difference between efficiency values in the implementations. * In addition, even when the efficiency values are similar GC have better results. In contrast, this implementation have one of the worst trip distance value. * Trip distance is again related with the efficiency showing a similar increasing/decreasing behavior compared with the efficiency behavior. (b) Fairness and Congestion

The results for fairness and congestion correspond to a sample of the total states in the vehicular network and are presented in different graphics for each \(F\). Obtained results are shown below:

The results correspond to the obtained value for fairness and congestion in a state k of a sample of states in the simulation. Figures 27 and 28 show the behavior of Fairness and Congestion, that is, the value obtained for the state k, where k is one of 10 intermediate states of the simulation selected, for each \(F\). Those 10 states where selected randomly with a uniform distribution to try to represent the initial, intermediate and final state of the vehicular network. Figure 19:5 Best value comparison for efficiency in the F-vehicles scenario. (**a**) Percentage comparison against the best value obtained for efficiency for each 5-vehicles set when F is 10; (**b**) Percentage comparison against the best value obtained for efficiency for each 5-vehicles set when F is 20; (**c**) Percentage comparison against the best value obtained for efficiency for each 5-vehicles set when F is 30; (**d**) Percentage comparison against the best value obtained for efficiency for each 5-vehicles set when F is 40. Figure 19:6 Cont. Figure 19:7 Obtained Fairness in a state k for each F-vehicle value. (**a**) Fairness obtained in a state k when F is 10; (**b**) Fairness obtained in a state k when F is 20; (**c**) Fairness obtained in a state k when F is 30; (**d**) Fairness obtained in a state k when F is 40. The main conclusions of this simulation with respect to the behavior of fairness and congestion are:

* As the previous simulation, the GC and LC fairness is much better than _Normal_ and SMD in low congestion levels of the network, while in high levels of congestion the fairness is pretty much the same. In addition, a relation between fairness and route efficiency exists. ### Reference Scenario Results

In this simulation, a random number F of vehicles were incorporated to vehicular network in each simulation step. This number is in the interval [90, 600] where 90 is the average capacity of the set of ingress streets (the streets connected with the origin nodes). Vehicles enter an empty network and simulation stops when a number N of vehicles arrive at the destination node. The results in Figures 29 and 30, correspond to the average value for each group of 50 vehicles, in a sample of 1000 vehicles of the total N vehicles that completed their trip. Figure 29 presents the obtained efficiency and Figure 30 presents the best-value comparison for efficiency and trip distance. In addition, the results in Figure 31 correspond to the behavior of Fairness and Congestion, that is, the value obtained for the state k, where k is one of 10 intermediate states of the simulation. Those 10 states where selected randomly with a uniform distribution to try to represent the initial, intermediate and final state of the vehicular network Obtained results are presented below:

Figure 19:8 Obtained Average Congestion in a state k for each F-vehicle value. (**a**) Avg. congestion obtained in a state k when F is 10; (**b**) Avg. congestion obtained in a state k when F is 20; (**c**) Avg. congestion obtained in a state k when F is 30; (**d**) Avg. congestion obtained in a state k when F is 40.