### The Problem  
The scenario selected in this work is a real street network where the current infrastructure is not sufficient to achieve sustainable average speed on each link and period of time, considering a constant flow at the entry points of the network. The speeds on the links of a street network depends on different factors: the infrastructure (e.g., the traffic lights control, the length and width of the streets), the traffic enforcement authority, the drivers' behaviors, the right of way rules, the vehicles' origin-destination table, the vehicles' routes, the input flow, among others. In undeveloped and developing cities a few drivers follow a planned route according to the current traffic conditions and commonly have simple controls for traffic lights, but even if most of the drivers follow a planned route the network links can experience low speeds since the number of vehicles circulating is not adequate. In a street network, it always seems convenient to put in operation an intelligent control for traffic lights and a system for monitoring the traffic state and establishing optimal routes, these can be simple or complex implementations, in the latter (likely) requiring sensors and machines for storing and processing data, therefore expensive.  
In the street network presented in this work, the traffic light control is limited to fixed times, since in the real location is not in use a more advanced control. We introduced a procedure to estimate (periodically) the links' travel time, with this intel and a simulator built-in method the vehicles (optimal) routes are chosen, since real drivers select, intuitively or with the help of technology, the route they consider the best. If the selected network is under a constant flow at the entry points, a traffic light control based on fixed times and a procedure for selecting routes based on estimating the links' travel time at time intervals are insufficient to avoid unacceptable speed on the network's links. According to the imposed flow, this work aims to find which vehicles can enter the study area (the network), and which not, for not saturating the network. The main problem is, during 1 h of continuous flow at each entry point of the network and with a previously defined origin-destination table (abbreviated OD, in which randomness is involved), design a method to reduce the number of vehicles gradually and systematically from one simulation to another until reaching a (final) simulation in which no link, at any period, presents a particular speed (\(\mathit{vp}\)) less than or equal to the speed threshold (\(\mathit{v}\_b\)). Therefore, the number of vehicles allowed in the final simulation is, approximately, the maximum number supported by the network (for an hour) that provides sustainable average speed on links. In this work when we mention sustainable (or acceptable) speed we refer to traffic conditions where \(\mathit{vp}>\mathit{v}\_b\) and low (or unacceptable) speed where \(\mathit{vp}<=\mathit{v}\_b\). Additionally, regarding the notation \(\mathit{DG}\) and \(\mathit{DP}\) are the vectors containing the general density (\(\mathit{dg}\)) and particular density (\(\mathit{dp}\)) of each period, respectively, which are average densities (vehicles/m).