## 3 Strategy and Model
### Parameter Optimization  
The control strategy of the IBA setting method based on lane multiplexing has been elaborated in the previous subsections, which addresses the key issues (_a_) and (_b_) in Section 2.2. However, there is a key parameter in its lane system that has not yet been determined, which is the length of the intersection space slice. The length of the intersection space slice actually corresponds to the set distance between the VMS and the downstream intersection in the lane system, and its size will affect the operation effect of the lane system. When the length of the intersection space slice is set too small, cars will not be able to change lanes in time in the relatively congested near-intersection area, resulting in the formation of queues in the lane-changing area, which  
Figure 5: Logic control flow of dynamic time slice division strategy of intersection space slices. may interfere with the normal running of the rear buses, and increase the suffering of cars added by the IBA strategy. On the other hand, if the intersection space slice is too long, the prediction error of the vehicle travel time of the space slice will become larger, resulting in the decline of the control accuracy of lane system, which will reduce the lane utilization rate, and even the bus priority cannot be guaranteed. Thus, how to set the optimal length of the intersection space slice under the premise of ensuring that the cars can smoothly merge into the intersection space slice and taking into account the control accuracy of the lane system, is the key issue to be addressed in this subsection. As shown in Figure 4, the intersection space slice is composed of three parts: the merging section, the weaving section, and the bus approach. Among them, the weaving section and the bus approach are the original intersection road infrastructure, and their length depends on the road traffic characteristics of the intersection, which belongs to the traditional intersection planning and design. The IBA based on lane multiplexing does not involve changes to the existing road infrastructure, so here we only optimize the design for the length of the merging section in the intersection space slice. The merging section is set to allow the cars to have enough space and time to merge into the bus lane, and its length is defined as \(l\). By analyzing the lane-changing behavior of the IBA lane system, an optimal model of the length of the merging section for the intersection space slice is established by using the gap acceptance theory and the differential method. Whether the headway of adjacent lanes is greater than the acceptable gap of lane-changing is the key factor when determining the smooth lane change of merging vehicles. Therefore, the successful merging of vehicles depends on the headway of adjacent lanes. Common headway distribution functions are shown in Table 1.  
In view of the traffic scene in which the lanes near the intersection of urban roads are crowded and have obvious vehicle queuing, the M3 distribution function is used to describe the headway distribution of vehicles in the merging area [37], as shown in the following formula:  
\[F(h)= \begin{cases}1-\alpha e^{-\lambda(h-\tau)}&h>\tau\\ 1-\alpha&h=\tau\\ 0&h<\tau\end{cases}  \tag{13}\]  
where \(F\) (\(h\)) is the probability distribution of vehicle headway \(l_{t}\); \(\alpha\) is the proportion of free-flow vehicles in adjacent lanes; \(\lambda\) is the attenuation constant; \(\tau\) is the minimum headway. The M3 distribution assumes that the vehicle travels in two states: the vehicle queuing state and the free-flow state. 1. Vehicle queuing status: vehicles are queuing up to keep the minimum headway. 2. Free-flow state: the headway of vehicles is randomly distributed and greater than the minimum headway. As the vehicle approaches the end of the merging section, the critical gap of lane-changing will decrease due to the driver's anxiety about not being able to change lanes smoothly.