# Urban Congestion Avoidance Methodology Based on Vehicular Traffic Thresholding
## 3 Vehicular Traffic Congestion Avoidance Methodology
In this paper, we considered 7 m;
* Lsegment--variable representing the length of a specific road segment in meters;
* lanesCountsegment--variable representing the number of lanes on a road segment. Its value depends on the corresponding road segment;
* t--variable representing the estimated timestamp when a vehicles enters on a road segment. Used as a local variable in the algorithms;
* vehiclesCountsegment(t)--variable representing the number of vehicles on a road segment at a specific moment t. It is used as a local variable in the algorithms;
* \(\mathrm{p_{segment}(t)}\)--variable representing the predicted vehicular density on a road segment at a timestamp, defined as \[\frac{\mathrm{vehiclesCount}_{\mathrm{segment}}(t)\times L_{\mathrm{vehicle}}}{\mathrm{L_{segment}}\times\mathrm{ lanesCount}_{\mathrm{segment}}}\] (1) and vehicular density can have value in interval [0...1]. Used as a local variable in the algorithms;
* Threshold levels represented by a set of constant numerical values--for the purpose of providing vehicular routes that avoid congestion, we use ten density threshold levels defined by the set. We found through testing that it is necessary and sufficient to split the density in ten threshold levels in order to obtain significant improvement on congestion reduction and avoidance: \[T=\{0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1\};\] (2)
* F\({}_{\mathrm{e}}\)--the set of numeric values representing the effort factors used to penalize congested road segments based on vehicular traffic density threshold levels in order to route traffic on less used road segments. It was experimentally identified by trying values between 1 and 100 and analysing the evolution of the traffic in time;
* F\({}_{\mathrm{e}}(\rho)\)--effort factor function based on vehicular traffic density threshold levels. It has 10 values;
* Esegment(\(\rho\))--the effort of a segment to become part of a route (during route computation algorithm), defined as a function based on vehicular traffic density threshold levels \[(\mathrm{E_{segment}}+\delta)\times\mathrm{F_{e}}(\rho)\] (3)speedLimitsegment--variable representing the speed limit for a specific segment from the road network. Its value depends on the corresponding road segment;
* F\({}_{\text{s}}\)--the set of numeric values representing the speed factors used to compute the speed of a vehicle based on vehicular traffic density threshold levels. This was experimentally identified by following the fundamental traffic flow speed-density diagram [23; 24];
* F\({}_{\text{s}}(\rho)\)--speed factor function based on vehicular traffic density threshold levels. It has 10 values;
* S\({}_{\text{segment}}(\rho)\)--computed speed of a segment defined as a function based on vehicular traffic density threshold levels \[\text{speedLimit}_{\text{segment}}\times\text{F}_{\text{s}}(\rho);\] (4)
* F\({}_{\text{d}}\)--the set of numeric values representing the delay factors used to compute the vehicular traffic delay based on vehicular traffic density threshold levels and \(\delta\). This was experimentally identified by comparing the estimated travel time with the corresponding metric of existing navigation solutions (e.g., Google Maps). * F\({}_{\text{d}}(\rho)\)--delay factor function based on vehicular traffic density threshold levels. It has 10 values;
* D\({}_{\text{segment}}(\rho)\)--the delay introduced by the vehicular traffic on a specific segment (in seconds), defined as a function based on vehicular traffic density threshold levels \[\delta\times\text{F}_{\text{d}}(\rho).\] (5)  
The route computation algorithm integrates the estimates of vehicular density, travel effort, speed and traffic delay defined above by the formulas (1)-(5). The following part of this section presents their corresponding algorithms. The vehicular density computation is performed in Algorithm 2 and uses the KEP tree query operation to count vehicular density on a segment at a specific moment. Details on KEP Tree data structure and its associated operations (store, update, query) may be found in [8].