# Comprehensive Review of Traffic Modeling: Towards Autonomous Vehicles
## 5 Traffic Flow Models
### Microscopic Models
#### 5.2.5 Lane-Changing Models  
While car-following models describe the rules for vehicular longitudinal interactions on the road, lane-changing models focus on lateral interactions, which are crucial for understanding overall traffic dynamics. Lane-changing behavior is often categorized into mandatory and discretionary lane changing. Mandatory lane changes are necessary for reaching a planned destination, such as when a vehicle needs to exit a freeway. In contrast, discretionary lane changing is voluntary and more complex, as it involves evaluating the necessity and desirability of the maneuver in addition to the safety considerations typically associated with mandatory lane changes. The modeling of lane-changing behavior generally focuses on two key aspects: the decision-making process of the driver and the impact of lane changing on surrounding vehicles. This dual focus is essential for capturing the full range of influences that lane changing can have on traffic flow and safety. [PERSON] and [PERSON] (2018) contributed to this area by developing a model that explains the reduction in traffic flow following the onset of congestion at freeway lane drops, as well as the relationship between the speed of moving bottlenecks and their capacities. Their work provided significant insights into how lane-changing behavior can exacerbate congestion under certain conditions. [PERSON] and [PERSON] (2018) further expanded on this by modeling the relaxation phenomenon using a macroscopic lane-changing model, which helped to understand how traffic stabilizes after a disruption caused by lane changes. Initial lane-changing decision models were predominantly rule-based, focusing on a stepwise process where drivers first select a target lane and then assess whether there is an acceptable gap in the traffic to make the lane change. [PERSON] (2018) proposed a model that considered the structure of lane-changing decisions within urban infrastructures, accounting for variables such as traffic signals, obstructions, and different vehicle types. This early work laid the groundwork for understanding how lane-changing decisions are influenced by various environmental factors. [PERSON] (2018) added to this by analyzing bottleneck situations, while [PERSON] and [PERSON] (2019) developed a model for lane-changing behavior on multi-lane unidirectional roadways, building on the framework established by [PERSON]. [PERSON] and [PERSON] (2017) introduced a continuum model for a two-lane traffic flow,which, although not microscopic, provided valuable insights into lane-changing behavior at a macroscopic level. Despite these advancements, early models were often simplistic and did not fully capture the complexities of cooperative or forced lane-changing behavior. For example, [PERSON] and [PERSON] [191] presented software programs capable of replicating lane-changing behavior, but these models were limited in scope and did not address the full range of factors influencing lane changes. To address these limitations, later models incorporated more sophisticated theories, including utility theory, artificial intelligence, and game theory. [PERSON] and [PERSON] [192] developed a driver decision-making model using neural networks, which allowed for more nuanced simulations of lane-changing behavior. [PERSON] and [PERSON] [193] introduced cellular automata models that included multi-lane traffic, further advancing the field by enabling more detailed and realistic simulations. [PERSON] [194] presented a multi-agent simulation system in which driver-vehicle objects are modeled as autonomous agents. This system included detailed lane-changing and merging algorithms that considered both forced and cooperative lane-changing, providing a more comprehensive understanding of how drivers interact with each other in complex traffic environments. Utility theory has also been applied to lane-changing decisions, as demonstrated by [PERSON] and [PERSON] et al., who explored how drivers make decisions based on perceived utilities or benefits.