# An Extended Game-Theoretic Model for Aggregate Lane Choice Behavior of Vehicles at Traffic Diverges with a Bifurcating Lane

## TL;DR

This paper introduces a game-theoretic model for vehicle lane choice behavior at complex diverging junctions, capturing congestion patterns caused by lane changing and enabling better traffic management strategies.

## Contribution

It develops a novel aggregate lane-changing model based on Wardrop equilibrium, with proven existence and uniqueness, and demonstrates its effectiveness in predicting congestion.

## Key findings

- Model accurately predicts aggregate lane choice behavior.
- Model can be calibrated with real or simulation data.
- Predicts congestion patterns at bifurcating diverges.

## Abstract

Road network junctions, such as merges and diverges, often act as bottlenecks that initiate and exacerbate congestion. More complex junction configurations lead to more complex driver behaviors, resulting in aggregate congestion patterns that are more difficult to predict and mitigate. In this paper, we discuss diverge configurations where vehicles on some lanes can enter only one of the downstream roads, but vehicles on other lanes can enter one of several downstream roads. Counterintuitively, these bifurcating lanes, rather than relieving congestion (by acting as a versatile resource that can serve either downstream road as the demand changes), often cause enormous congestion due to lane changing. We develop an aggregate lane--changing model for this situation that is expressive enough to model drivers' choices and the resultant congestion, but simple enough to easily analyze. We use a game-theoretic framework to model the aggregate lane choice behavior of selfish vehicles as a Wardrop equilibrium (an aggregate type of Nash equilibrium). We then establish the existence and uniqueness of this equilibrium. We explain how our model can be easily calibrated using simulation data or real data, and we present results showing that our model successfully predicts the aggregate behavior that emerges from widely-used behavioral lane-changing models. Our model's expressiveness, ease of calibration, and accuracy may make it a useful tool for mitigating congestion at these complex diverges.