# Emerging Data-Driven Calibration Research on an Improved Link Performance Function in an Urban Area
## 1 Introduction  
An effective urban transportation system not only makes sure that individuals have access to high-quality transportation services but also fosters the development of the entire society and economy. As urbanization and the density of the urban population increase, transportation in cities faces a growing number of challenging problems. Due to the high traffic flow, city roads become disorganized and inefficient, which causes enormous economic losses for both individual users and society as a whole. As a result, the objective of current research--both local and foreign--is to lessen this long-standing problem of urban congestion. Traffic flow is essentially the set of all travel users' path selection behaviors, and it corresponds to traffic assignment in traffic planning [1; 2; 3; 4]. Within modern traffic assignment methodologies, constraints on road capacity that affect travel speed or travel time are characterized through the use of link performance functions [5; 6]. These performance functions mathematically illustrate the relationship between traffic volume and travel time (or cost) on the road. The link performance function is an essential component of a transportation system, as it describes the relationship between the link travel time and loading for road transportation. The link performance function is used to determine the optimal routes for travelers and, in turn, the overall efficiency of the road system. Over the years, many scholars have worked on this topic with the aim of better understanding the mechanism of the performance function and improving its accuracy [7; 8; 9; 10; 11; 12]. Link performance functions can be used to predict traffic flows on specific road segments or a road network. They help decision makers develop traffic policies to deal with differing traffic conditions. A linkperformance function model is very important in road network analysis, and it serves as the foundation for a network's traffic distribution and the evaluation of the quality of network traffic. However, the complexity of traffic flow and the peculiarities of diverse surroundings bring a huge challenge. It is difficult to determine a trustworthy set of parameters for a link performance function with universal applicability [13]. Therefore, it is necessary to recalibrate the function according to the traffic flow data in different spatial and temporal environments [14; 15; 16; 17; 18; 19; 20]. Parameter calibration problems have also been extensively studied in the transportation field [14; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30]. The general form of the link performance function is shown below. This is a first example of such an equation:  
\[T=f(T_{0},v,c). \tag{1}\]  
Here, \(T_{0}\) denotes the link's free-flow journey time (when the traffic flow equals zero), \(v\) signifies the link's traffic volume, \(c\) denotes the link's capacity, and \(T\) denotes the estimated link travel time. Several of the most commonly used link performance functions are shown in Table 1.  
One of the earliest studies on link performance functions was performed by the U.S. Bureau of Public Roads (BPR), which is still widely used today [31]. The set of its parameters is \([\alpha,\beta]=[0.15,4]\). Since then, many researchers have proposed modifications to the original formula, including additional variables of road conditions, traffic flow, and driver behavior. It has the advantage that the roadway flow is not limited by roadway capacity. It is unnecessary to detect feasible solutions when assigning traffic, thus making the assignment algorithm significantly simpler. This model was established based on the velocity-flow curve from the 1965 version of the Highway Capacity Manual (HCM). However, a limitation of this model is that it tends to produce high-velocity estimates when the saturation rate is greater than 1 and low estimates when the saturation rate is smaller than 1. With the introduction of the 1994 version of the HCM, the velocity-flow curve became flatter.