# Optimal Lane Allocation Strategy in Toll Stations for Mixed Human-Driven and Autonomous Vehicles
## 2 Problem Statement, Notations, and Assumptions
### Study Area  
This study focuses on the Liulin Toll Station of the G30 Lianhuo Expressway in China. Located on the outer ring expressway of Zhengzhou, Henan Province, the Liulin Toll Station serves as a critical gateway to the city. Its proximity to major urban arterial roads, the city's northern bus terminal, universities, and densely populated residential areas underscores its significance in meeting substantial population and traffic demands. Figure 2 illustrates the spatial positions of Liulin toll station, urban main roads, and Lianhuo Expressway. As shown in Figure 3, the Liulin Toll Station currently features 14 bidirectional toll lanes. In the entry direction (onto the expressway), there are six lanes, including four inner ETC lanes and two outer MTC lanes. In the exit direction (off the expressway), there are eight lanes, comprising six inner ETC lanes and two outer MTC lanes. The toll lanes at the station are separated by isolation barriers (marked in yellow in Figure 3) and feature extended lane guidance and separation lines (marked in red Figure 3). These measures prevent vehicles entering the toll queue system from freely switching lanes. Figure 2 illustrates the spatial positions of Liulin toll station, urban main roads, and Lianhuo Expressway.  
Using the Henan Provincial Expressway Cloud Real-Time Monitoring Platform, video surveillance data from the Liulin Toll Station was collected for 31 October 2024, between 15:30 and 16:30. This time frame was selected for its typical and representative nature: it falls on a Thursday, a midweek working day, and is neither a holiday nor a special workday (e.g., Monday or Friday). The chosen period is also outside peak and off-peak traffic hours.  
Vehicles can be classified not only by toll collection method but also by factors such as vehicle size and weight, into passenger cars, buses, and trucks. Clearly, based on this classification, different vehicle types may exhibit varying service times on the same lane type. Following conventional methods, we do not adjust the service rate of the lanes but rather convert vehicle arrival rates (traffic flow) accordingly. Traffic flow data were  
Figure 2: The Liulin toll station and its surrounding roads.  
standardized using passenger cars as the reference vehicle type, with conversion factors of 1, 2, and 2.5 applied to passenger cars, buses, and trucks, respectively [30]. During this period, the vehicle arrival rates for the entry and exit directions were 23.64 veh/min (1418.5 veh/h) and 21.03 veh/min (1262 veh/h), respectively. The vehicle distribution between the entry and exit directions was similar, with MTC-HVs and ETC-HVs accounting for 0.26 and 0.74 of the traffic. For ETC lanes, the service rates for both entry and exit lanes were similar, at 13.95 veh/min. However, for MTC lanes, the service rates for the entry and exit lanes showed significant differences, at 4.05 veh/min and 2.79 veh/min, respectively. This discrepancy is due to the different processes: at the entry lanes, drivers only need to obtain a highway entry ticket from the toll staff; at the exit lanes, drivers must return the ticket, pay the toll, and sometimes the toll staff needs to provide change. As a result, the service rate for the exit lanes is lower than that for the entry lanes.