Pricing lane changes

Highlights

• A micro-pricing method penalizing socially-detrimental lane changes is proposed.

• Safety vs. efficiency is quantified within the game-theoretic framework.

• Two approaches are introduced to engage public-good driving behaviors.

• The proposed pricing schemes are tested by microsimulation experiments.

Abstract

Risky and aggressive lane changes on highways reduce capacity and increase the risk of collision. We propose a lane-changing pricing scheme as an effective tool to penalize those maneuvers to reduce congestion as a societal goal while aiming for safe driving conditions. In this paper, we first model driver behavior and their payoffs under a game theory framework and find optimal lane-changing strategies for individuals and their peers in multiple pairwise games. Payoffs are estimated for two primary evaluation criteria: efficiency and safety, which are quantified by incorporating driver tradeoffs. After that, the discretionary lane-changing (DLC) model is calibrated and validated by real-world vehicular trajectory data. To manipulate drivers’ DLC behaviors, two types of lane-changing tolls based on local-optimal and global-optimal rules are introduced to align individual preferences with social benefits. We find prices can close this gap and achieve ‘win-win’ results by reducing drivers’ aggressive lane changes in the congested traffic. Meanwhile, the tolls collected can be used to compensate drivers who get delayed when yielding, to encourage appropriate yielding behavior and a pseudo-revenue neutral tolling system.

Introduction

Lane changing (LC) in traffic occurs often, and is a major source of road crashes and traffic congestion at merge bottlenecks (Jula et al., 2000, Coifman et al., 2006, Laval and Daganzo, 2006, Pande and Abdel-Aty, 2006, Li et al., 2020). Lane changing/merging accounted for 5.3% of all police-reported motor vehicle crashes in the United States in 2019, and resulted in about 1.8% of incapacitating injuries (National Highway Traffic Safety Administration, 2021). Meanwhile, it is found that lane changes can trigger road capacity reductions and traffic oscillations (Patire and Cassidy, 2011, Cassidy and Rudjanakanoknad, 2005, Mauch and Cassidy, 2002). A recent study also reveals that a single discretionary LC behavior delays 4–5 surrounding vehicles, and the impact duration is up to 12–13 s (He et al., 2022). When vehicles change lanes in congested traffic states, they simultaneously occupy space in two lanes. Lane changing is over-consumed because lane changers do not suffer the full cost they impose on other travelers. Motorists then drive and change lanes more frequently because of the low personal cost. In general, drivers need discretionary lane changes (DLCs) to gain a speed advantage or execute mandatory lane changes (MLCs) to enter or exit highways. All else equal, when changing lanes, they appreciate the yielding of other drivers, while they prefer not to yield themselves (Ji et al., 2022).

Most conventional microscopic LC models (e.g. acceleration models, MOBIL model, MITSIM model, gap-acceptance model, etc.) focus on safe and reasonable lane changes from the users’ view (Gipps, 1986, Hidas, 2005, Toledo et al., 2003). In contrast, macroscopic models describe LC behaviors as filling vacant gaps in a continuous fluid-like traffic flow (Lighthill and Whitham, 1955, Richards, 1956, Jin, 2010, Ramezani and Ye, 2019). From a different perspective, the LC maneuver can be regarded as a strategic interaction where drivers compete or cooperate. Game theory (GT), developed by Von Neumann and Morgenstern (1944), provides insights to understand interactions among multiple agents. It has wide application in recent transport studies (Littlechild and Thompson, 1977, Bell, 2000, Chen et al., 2018, Fisk, 1984, Ji and Levinson, 2020c), which complements the advantages of microscopic and macroscopic models and allows consideration of interactive behaviors. Although the LC maneuver is complicated in the real world, we argue modeling with simple rules of game theory helps reveal how drivers make decisions under different conditions and build on it to develop micro-pricing of LC to manipulate the frequency of lane changes.

The interaction among drivers can be described as a multi-player game, in which players (arguably) rationally adopt strategies based on how others behave. However, in some cases, their preferences may conflict with the mutually beneficial outcome, which causes a social dilemma wherein players make personally rational but socially costly choices. The present paper develops solutions to reduce or mitigate the dilemma.

To foster cooperative strategies among players, some studies propose reciprocity, such as direct and indirect mechanisms, by introducing Evolutionary Game Theory (EGT) (Cortés-Berrueco et al., 2016, Iwamura and Tanimoto, 2018). According to reciprocity, people are encouraged to cooperate after being recognized over repeated games. The EGT approach induces social identity for players to reduce the negative effect of the social dilemma. Because we cannot count on repeated encounters on the road between the same players in DLC maneuvers, we test externally-imposed enforcement (i.e. micro-pricing) to motivate cooperation among stranger drivers and demotivate socially detrimental behaviors.

Road pricing provides a possible solution for prompting cooperation, regarded as an effective social cost-minimizing mechanism (Levinson, 2005). It is designed to internalize negative externalities, aiming to increase road capacity and safety by aligning individual decision-making with social welfare. However, to date, road pricing strategies have been relatively macroscopic in nature and have aimed to regulate the presence of a vehicle in the network by general location or time, but not the maneuver dynamics of individual vehicles. The effect of pricing strategy on traffic oscillations caused by lane changes (microscopic behaviors) remains undetermined. Some similar insights were proposed by Lin et al. (2019) and Zimmermann et al. (2018) with utility transaction or virtual rewards designed in games, but which have yet to be specified as exact pricing schemes (see Table 1 for comparisons). The need for penalizing aggressive DLC serves as the motivation of this study.

In this paper, we propose a micro-pricing method to penalize socially-detrimental lane changes based on the local-optimal (LO) approach (microscopic scale) or the global-optimal (GO) approach (macroscopic scale) and compare their effects. This pricing does not aim to prevent intended lane changes strictly, but to engage public-good driving behaviors and incentivize drivers to consider the social consequences (delay or risk experienced by others) in their decision.

The main contribution of this study includes developing a DLC behavior paradigm to model the trade-off between safety and efficiency in real values. Furthermore, unlike existing road tolls, the proposed LC pricing focuses on micro-interactions. Besides, the proposed model and pricing schemes are tested through a microsimulation environment to examine their performance with various traffic demands.

The paper is structured as follows. In Section 2, a simultaneous two-player game theory LC model is first established and analyzed to discover drivers’ possible strategies and corresponding payoffs in LC games. From both microscopic and macroscopic perspectives, Section 3 proposes the possible improvements for LC games with the potential conflict of interests. Based on those optimization solutions, we apply two types of pricing rules to eliminate the social dilemma. Next, in Section 4, the model calibration and validation process are first conducted to capture human naturalistic driving behavior from real-world trajectories. It is then followed by the performance of pricing schemes in simulated experiments, and finally, the simulation results are presented in Section 5. In Section 6, model applicability and potential improvements are summarized and discussed.