# Optimal Lane Allocation Strategy in Toll Stations for Mixed Human-Driven and Autonomous Vehicles
## 1 Introduction
### Literature Review  
Under heterogeneous traffic flow conditions, significant progress has been made in research on toll station lane allocation. Researchers have analyzed the traffic characteristics  
Figure 1: The selectable lanes for different types of vehicles. of different vehicle types, driver decision preferences, and behavioral patterns, uncovering key insights into how various vehicles navigate toll stations within diverse traffic flows [17; 19; 20; 21]. Specifically, studies have developed driver decision models to predict lane choices, examined behavioral changes under congestion to optimize lane allocation strategies, and introduced intelligent guidance technologies to enhance passage efficiency. These findings have not only deepened the understanding of driver behavior but also provided a foundation for devising rational lane management strategies, effectively alleviating toll station congestion and improving overall traffic system efficiency and safety. In toll lane optimization research based on queuing theory, researchers have developed allocation models for multi-lane and multi-vehicle scenarios [13; 22]. Queuing theory, particularly the classical \(M/M/1\)[8; 14] model and its extensions (e.g., \(M/M/N\)[23; 24], \(M/G/1\)[25] and \(M/G/N\)[22; 26] models), have been widely applied in traffic engineering and toll plaza analysis, such as capacity planning, real-time traffic control strategies, automated tolling system evaluation, and so on. The \(M/M/1\) model has the advantages of simplicity in computation, intuitive analysis, and ease of application. It is particularly effective when vehicle arrival intervals and service times follow exponential distributions, allowing for the quick calculation of system performance metrics such as average waiting time and queue length. Despite its simplicity and frequent use, traffic flows can sometimes be more complex, with vehicle arrival intervals and service times not necessarily following exponential distributions. The \(M/M/N\) model extends the \(M/M/1\) model by considering systems with multiple parallel servers (lanes) to handle vehicle traffic. Sometimes users are unable to switch service lanes after entering the queue system, forming N independent \(M/M/1\) queuing systems. Similarly, the \(M/G/N\) model generalizes the \(M/M/N\) model by allowing both arrival intervals and service times to follow general distributions. This model is suited for scenarios where the assumption of exponential distribution no longer holds for either arrival or service processes. These models provide a solid theoretical foundation for more accurate simulations of toll station traffic. Additionally, with the integration of intelligent optimization algorithms (e.g., genetic algorithms, simulated annealing, and particle swarm optimization), these models can efficiently converge to optimal or near-optimal solutions under multi-variable and multi-constraint conditions, significantly improving passage efficiency [8; 27]. By combining dynamic traffic flow theory with real-time data, researchers have also developed models capable of dynamically adjusting lane allocation strategies to adapt to changing traffic volumes, thereby further reducing congestion. This body of research not only supports the efficient utilization of toll station resources but also demonstrates substantial potential for designing intelligent traffic management systems. With advancements in predictive analytics and machine learning technologies, toll station management has progressively shifted towards a data-driven paradigm. By modeling and analyzing historical and real-time data, predictive analytics accurately forecasts traffic volume and congestion, offering proactive guidance for flow management [28; 4; 29]. Concurrently, machine learning refines dynamic scheduling and resource allocation models by extracting complex patterns from large-scale data, significantly enhancing efficiency [12].