## 4 Proposal
### Proposed Algorithm
#### 4.2.2 Modified Dijkstra Algorithm (MD)
### Obtained Results Presentation

For each scenario we present two kinds of figures: those representing the general behavior of the corresponding metric, and those representing the result of comparing the metric value with the best value obtained. The description of each one is presented below. #### 6.1.1 General Behavior

Figures 20, 22-25, 27-29 and 31 present the values obtained for each implementation under the same scenario. The presented values correspond to (a) the mean value of each metric for a group of vehicles when the metric described is efficiency or distance; or (b) the specific value obtained for a state k of the simulation when the metric described is Fairness or average congestion. Specific details on the scenario are described in each one. #### 6.1.2 Comparison against the Best Value

To get a better view of how good is an implementation with respect to another, a comparison percentage based on the best result for each metric is performed indicating how far from the best result is each implementation. When the best result should be the maximum value of the whole, this percentage is calculated as in Equation [12] and when the best value should be the minimum, the percentage is calculated as in Equation [13]:

\[\% =\frac{(Best-Real)}{Best} \tag{12}\] \[\% =\frac{(Real-Best)}{Best} \tag{13}\]

In Equation [12], if the value obtained by the implementation is the maximum, the comparison percentage is in the line x = 0, and the following values are in the set of positive values above this line. This definition is used for _Fairness_ and _Efficiency_. In the same way, in Equation [13], when the value obtained is the minimum, the comparison percentage is in line x = 0. This definition is used for _Distance_ and _Congestion_. In both cases, as the percentage is bigger, the result is farther from the best value, and should be interpreted, for example, as _value X_ is 30% worse than the best. ### Control Scenario Results

#### 6.2.1 N Vehicles

In this scenario, 10, 20, 30, 40, 50, 60, 70, 80, 90 and 100 vehicles were moved along the vehicular network to examine each metric as the number of vehicles rises. Vehicles enter an empty network at the same time and simulation stops when all vehicles in the set arrive to the destination node, which means the network is empty after the final simulation step. (a) Efficiency and Distance

The results correspond to the average value for the total set of N vehicles passed during the simulation (_i.e._, mean efficiency/total trip distance for 10 vehicles, 20 vehicles, and so on). The behavior in Figure 20 represents the obtained efficiency and trip distance, while the best-value comparison in Figure 21 represents the comparison percentage as described in Section 6.1.2. The main conclusions of this simulation with respect to the behavior of efficiency and distance are:

* The route efficiency in all implementations decreases as the set of vehicles in the network is bigger. * The trip distance is affected by the amount of vehicles in the network and it increases as the number of vehicles grows, even for the MD solution. Figure 21: Best value comparison for route efficiency and trip distance in the N-vehicles scenario. (**a**) Percentage comparison against the best value obtained for efficiency; (**b**) Percentage comparison against the best value obtained for trip distance. Figure 20: Behavior for route efficiency and trip distance in the N-vehicles scenario. (**a**) Mean efficiency value for each N-vehicles set; (**b**) Mean distance value for each N-vehicles set. * Even when the efficiency levels are always between 0.8 and 1 and the variability in the results is not very large, GC had a better result with respect to the other implementations, followed by LC. * On the other hand, that implementation has one of the biggest average trip distance among the vehicles, which means it exists a trade-off between the travelled distance and the route efficiency. The behavior of _Natural_ and MD implementations is only differentiated by the trip distance.