## 3 Proposed Work
### Length Distortion  
The premise that travelers evaluate road length based on actual travel time instead of the actual measurements of a road section motivated us to build an algorithm that dynamically alters the lengths of a particular line section. As said before, journey time is also a significant issue in spatial choice models. Figure 2 shows how, depending on traffic density, the perceived distance between two points along a path can differ from the actual metric distance. The perceived distance is not easily quantified in terms of metrics, unlike the metric distance between two places along a road section, since it is not a set score and changes based on individual variances in human perception of space and time.  
We utilized the PUSH software [19], which contains an expanded option to scale objects by a component, to deform the lengths of a line segment. PUSH is a software application that was created to dynamically generalize cartographic items and, in specific, eliminate spatial conflicts through dislocation. It provides for a very flexible description of object behavior during dislocation by specifying numerous characteristics, such as the permissible degree of distortion or the minimal space needed by an object. Each object's attributes could be customized separately. To determine the enlarged factor autonomously, we firstly determine the expected perceived length (\(t\)) of a road segment using the equation:  
\[\begin{split} plenght(t)=len(t).\frac{\theta dens(t)+(dens(t)- \theta dens(t)).w_{g}}{\theta dens(t)}\end{split} \tag{2}\]  
The estimations are dependent on the present traffic density \(dens\) (\(t\)), calculated for every individual road section as contrasted to the mean traffic density \(\theta dens(t)\) for the road section during a similar period.  
We also present a weight factor \(w_{g}\), that permits to dynamically modify the intensity of the variation of the attained length value from the actual length value len (\(t\)), using  
\[w_{g}=\{0,\ 2\}\ \in\ Q \tag{3}\]  
This weighting factor allows for individual variances in observed road length to be addressed, as well as for traffic control to intervene if the strength of aberrations needs to be physically increased or decreased. The enlarge factor is then computed as the ratio of the estimated observed length of the line segment to its actual length:  
\[\begin{split} enlarge=\frac{plenght(t)}{len(t)}\end{split} \tag{4}\]  
Once the individual enlarges factors have been set to the line segments that need to be scaled, the global optimization finds a holistic solution that takes all of the other objects into consideration (i.e., relocating them suitably if necessary). The line segments of the generated polyline will be scaled based on the provided traffic volume estimates. That is, high-volume segments grow in size while low-density segments shrink in size. If the estimated traffic volume is equal to the mean volume for the road section at a given moment, the expand factor does not affect the segment's depiction. Since the entire picture is optimized in one step, bigger scores for the aura specification for the matching line sections can be defined. This dislocation of map elements shall be extremely helpful in visually distinguishing between diverse pathways in a system.  
Figure 2: The actual length of a road segment as contrasted to the perceived length.