# Vehicle Lane Change Models--A Historical Review
## 2 Vehicle Lane Change Models
### Empirical Models of Lane Change
#### 2.1.1 Logit Models  
Logit models are commonly used empirical models for lane change, mainly used to build probabilistic models for vehicle lane-changing decision-making. The models mainly use the driver's observational information and the estimated parameters to describe the driver's decision process during a lane change. The assumed error terms of the traditional logit model are independent and identically distributed and Gumbel distributed, but this approach incorporates irrelevant properties. Aiming at overcoming the defects of this logit model, researchers have successively proposed the path-size logit (PLS) model [19], the cross-nested logit (CNL) model [20], and the mixed logit model [21]. However, when these algorithms analyze the route and road information of multiple accident locations, the results are not very satisfactory. In order to include more influential factors such as vehicle spacing, speed difference, and traffic flow density to improve the performance of the model, [PERSON] et al. [22] studied the logit model with fixed and random parameters and adopted more detailed data such as road shape, road condition, weather conditions, and traffic characteristics. The detailed data improve the accuracy of the model. [PERSON] et al. [23] introduced a logit lane allocation model to describe multi-lane traffic flow from a macroscopic perspective. Each available lane has a specific utility for the driver in the process of running the vehicle, and the driver will choose the lane with the highest utility. The model is represented using a system of conservation laws with smooth and implicitly defined flux functions. The cited paper discusses how the traffic data support traffic speed as an explanatory variable for lane assignment in the dataset, and then illustrates its convergence through several numerical schemes such as the Lax-Fredrich scheme, the Euler-Lagrange scheme, and the Lagrange scheme when dealing with the Riemannian problem. Lane change around large commercial vehicles is an extremely challenging task, and collisions resulting from dangerous lane changes can lead to serious collision consequences. To better analyze the relationship between collision factors and severity in commercial vehicle lane change crashes, [PERSON], [PERSON] et al. [24] constructed a mixed (random parameter) logit model based on Alabama traffic crash data from 2009 to 2016. According to the analysis, about 4% of traffic accidents are severe, and more than 50% of traffic accidents are caused by driver error. The results of the model evaluation showed that the likelihood of serious crashes increased when lane change crashes occurred in dark and unlit sections and involved older drivers, drivers who caused crashes through negligence, or female drivers. On the other hand, serious lane change accidents are less likely to occur on motorways with more lanes. These findings raise awareness of the dangers of changing lanes near large commercial vehicles or driving in the blind spots of large commercial vehicles. Lane changing requires a relatively high level of driving experience from the driver, and lane changing is a difficult driving task, especially for young, inexperienced drivers and older drivers. Incorrect lane changing can have a significant impact on traffic flow and road safety. [PERSON] et al. [25] analyzed collision data from the Critical Analysis Reporting Environment (CARE) system developed by the Center for Advanced Public Safety at the University of Alabama. The data analysis showed that 63.1% of the crashes were caused by young drivers. The authors determined the relationship between crash factors and crash outcomes by developing an average model with random logit and heterogeneity. In a complex urban environment, [PERSON] et al. [26] established a logical lane change prediction model based on macro cells [27], and combined it with the cell transport model (CTM) to improve the accuracy of macro traffic state estimation.