# Emerging Data-Driven Calibration Research on an Improved Link Performance Function in an Urban Area
## 1 Introduction
To accommodate this change, the BPR function was modified, leading to the Metropolitan Transportation Commission (MTC) model [34]. The structure of the MTC model is similar to that of the BPR model, except that the parameter values have been adjusted. Additionally, a new BPR function model for urban trunk roads was proposed with \([\alpha,\beta]=[0.05,10]\) as the set of model parameters [35]. According to [PERSON] [5], excessive values of \(\beta\) can result in numerical problems. These include overflow circumstances, loss of precision, and a low rate of convergence by unfairly penalizing overloaded links during the initial iterations of an equilibrium assignment. Additionally, a BPR function with high values of \(\beta\) always produces free-flow speeds; it does not correspond to the real traffic volumes for lines with volumes that are significantly below capacity. [PERSON] [32] proposed a link performance function based on the queuing theory to improve the BPR model. It failed to adapt to actual traffic conditions when the flow was close to capacity. The Davidson function can be applied to any type of road infrastructure. However, the model has been the subject of considerable debate due to some contradictions in interpreting its parameters. As a result, several researchers proposed various improved models based on the Davidson function [33; 36; 37], among which the [PERSON] model has gained extensive usage. \begin{table}
\begin{tabular}{c c} \hline \hline
**Model** & **Mathematical Formula** \\ \hline BPR [31] & \(T(T_{0},v,c)=T_{0}\left[1+\alpha(\frac{p}{c})^{\beta}\right]\) \\ [PERSON] [32] & \(T(T_{0},v,c)=T_{0}^{\left[1+\frac{av}{c-v}\right]}\) \\ [PERSON] [33] & \(T(T_{0},v,c)=T_{0}\Big{\{}1+0.25\frac{d}{T_{0}}\Big{[}\frac{v}{c}-1+\sqrt{ \frac{p}{c}-1+8\frac{l}{QT}\frac{v}{c}}\Big{]}\Big{\}}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Several link performance functions. By using the coordinate transformation method, [PERSON] [33] suggested a time-dependent version of the Davidson function that sought to account for the intersection delay. When intersection delays give a sizable amount of link travel speed, this delay function enhances the modeling of the link travel speed. A parameter is used to capture the delay. Higher values are preferred for arterial highways without coordinated signal systems, whereas lower values are recommended for motorways. When comparing other speed delay functions to data gathered from 119 freeway segments in California, it was found that the Akcelik function was frequently the best fit for planning applications [35]. According to [PERSON] [38], applying the Akcelik function in traffic assignment also has some additional benefits, such as improved convergence and more accurate speed prediction in crowded areas. The compactness of the Akcelik function makes it beneficial because it allows for the universal use of a single functional form and the avoidance of complicated parameters while determining intersection delays. This paper aims to report on data-driven calibration research for an improved link performance function. It provides a comprehensive overview of the calibration and validation of the link performance function and then provides a sensitivity analysis to evaluate the effect of different parameter levels on link performance. Three solution algorithms are proposed to cope with the calibration problem. In addition, a value of the time parameter is introduced and calibrated against income data to measure the value of time for different populations and trip types. The rest of this paper is organized as follows. Section 2 describes the model in depth and examines the model parameters. The recommended solution approaches are presented in Section 3. The efficiency of the proposed methodology is validated in a genuine case study in Section 4. Finally, some concluding remarks are provided.