## 4 Proposal
### Proposed Algorithm
#### 4.2.2 Modified Dijkstra Algorithm (MD)
In the real live, this behavior is translated to drivers moving in the first in which they fit. The pseudo code is presented below (Algorithms 6 and 7), and is executed by the vehicle in the simulation. ```
0: Actual node actual
0: Destination node destination
1: Node \(k=\) get next node that connects the first available street (7)
2:if\(k\) exists then
3:if\(k=destination\)then
4: exit network
5:else
6: wait
7: end if
8: else
9: wait
10: end if
```
**Algorithm 6**Natural behavior
```
0: Actual node actual
0: Adjacent nodes \(Ad=\{k_{1},...,k_{n}\}\) not empty
1:for\(k\) in \(Ad\)do
2:if\(use_{(actual,k)}<capacity_{(actual,k)}\)then
3:return\(k\)
4: end if
5:end for
6:return not Exists
```

**Algorithm 7**Get first available node

This section describes how the validation process for the different approaches was. We defined a computational experiment based in two scenarios, a control scenario for small-scale examination of the results of each implementation, and a reference scenario that includes some features extracted from Google Maps. Additionally, the executed simulation is described and the evaluation metrics are specified for comparison between implementations. ### Scenarios Definition

#### 5.1.1 Control Scenario

For the control scenario we had a small vehicular network composed by 15 streets with random capacities in the interval [7,20] and a distance equal to that capacity. Additionally, we defined specific origin and destination nodes O, N. The same O/D is selected to evaluate if when a group of vehicles with the same origin / destination characteristics gets a new route, and the new route for those vehicles is the same, congestion is moved to the new route instead of get better. Two different ways of simulation were developed here: in the first we established a maximum number N of vehicles moving through the network and entering in the same turn in order to establish how the vehicular network state evolves as the number of vehicles gets larger; in the second a number F of vehicles was incorporated after X steps in the simulation, to compare different flows of vehicles. The corresponding configuration is shown in Figure 16:

#### 5.1.2 Reference Scenario

This scenario is based on the previous work realized in [2], which makes a proposal for congestion charging. This paper analyzed congestion in Colombian cities taking as a case study Bogota. As part of this work, areas of congestion were identified in the city of Bogota which are located in the expanded center where the main economic activities of the city are concentrated. One of the identified areas was selected to create the reference scenario. Its main characteristics are shown in Figure 17.

Figure 18 shows the vehicular network created for this area. The network posed does not intend to be an accurate representation of this area, so it only aims to map the main corridors, with some adjustments to get more connected nodes, and the traffic flow direction was decided by the author. Based on the proposed vehicular network graph, it was necessary to establish the capacity of each street, the approximate number of vehicles to go through them and their respective origins and destinations. Figure 16: Proposed control scenario. Figure 17: Desired congestion area, taken from Google Maps. (a) Street Capacity

To establish the capacity of each street, equation below was used:

\[capacity_{i}=\left| \begin{array}{c}length\ street_{i}\\ average\ length\end{array} \right| \tag{7}\]

The average length is defined as the floor function of average length of a vehicle coupled with a minimum separation. This minimum corresponds to what is defined as spacing in the Colombia's National Traffic Code [36], that is, the distance between two consecutive vehicles measured from the front end of a vehicle to the rear end of the other. * For \(length\ street_{i}\), approximate distances that provides Google Maps for each street network are taken.