## 2 Vehicle-Road Intelligent Capability Allocation Model
### Model Framework
#### 2.2.1 Quantified Assessment Sub-Model of Perception Scheme
By integrating the perception reliability of the vehicle scheme with that of the roadside scheme, the perception reliability of vehicle-road collaborative perception within each sub-region of the effective perception area can be obtained, as illustrated in Equation (2). \[ \begin{array}{ll}Reliability=& reliability_{camera}+sign(m-1)\times(1- reliability_{camera})\times reliability_{radar}\\ &+sign(m-2)\times[ reliability_{camera}+(1- reliability_{camera})\times reliability_{radar}]\\ &\times reliability_{lidar}\\ \end{array}  \tag{1}\]  
\[ \begin{array}{ll}Reliability_{vr}=Reliability_{v}+(1-Reliability_{v})\times Reliability _{r}\\ &\\ reliability_{camera}, reliability_{radar}, reliability_{lidar}\\ \end{array}  \tag{2}\]  
represent the reliability of a single sensor for the camera, millimeter-wave radar, and LiDAR, respectively. Their values are obtained by normalizing the average of the performance evaluations across five dimensions for the three types of sensors. \( reliability_{v}\), \( reliability_{r}\) represent the perceived reliability of the vehicle scheme and the roadside scheme, respectively. \( reliability_{vr}\) is the comprehensive reliability of vehicle-road collaborative perception. \[ \begin{array}{ll} Integrated\_Reliability_{v}=(\sum_{i=1}^{6}{(Range_{v,i} \times Reliability_{v,i}))/Range_{effective}}\end{array}  \tag{3}\]  
Figure 4: The effective perception area of vehicle. \[ \begin{split} Integrated_{Reliability_{vr}}\\ &=(\sum\limits_{i=1}^{6}\left(Range_{vr,i}\times Reliability_{vr,i} \right)+\left(Range_{r,i}\times Reliability_{r,i}\right))/Range_{effective}\\ \end{split}  \tag{4}\]  
\(Range_{v,i}\) represents the effective coverage area of vehicle perception scheme \(v\) in sub-region \(i\); \(Reliability_{v,i}\) denotes the reliability of vehicle perception scheme \(v\) in sub-region \(i\); \(Range_{vr,i}\) indicates the joint coverage area in sub-region \(i\) where both are covered by vehicle perception and roadside perception; \(Reliability_{vr,i}\) is the perception reliability within the joint coverage area; \(Range_{r,i}\) is the coverage area of the standalone roadside perception within sub-region \(i\); \(Reliability_{r,i}\) is the perception reliability of the roadside perception scheme \(r\) in its coverage area within sub-region \(i\); \(Range_{effective}\) is the area of the effective perception region. In terms of perception stability, vehicles often face obstructions from surrounding vehicles for most of the travel time, which results in the actual perception range being significantly lower than the vehicle's perception capability. By conducting a statistical analysis of the time probability density of the different range intervals of the actual perception area of vehicles traveling in Beijing at various times, the perception stability coefficient for single-vehicle intelligence is obtained as 0.13. Due to the high-dimensional perspective of roadside perception, the issue of occlusion blind spots inherent in vehicle-based perception will become nonexistent through collaborative intelligence. Therefore, the perception stability coefficient for vehicle-road collaborative intelligence is set to 1. Taking into account the three key indicators of perception range, perception reliability, and perception stability, the capabilities of vehicle-based perception and vehicle-road collaborative perception can be calculated using Equations (5) and (6), respectively. \[ \begin{split} Performance_{v,perception}=(\sum\limits_{i=1}^{6}Range_{ v,i}\times Reliability_{v,i})\times Stability_{v}\\ \end{split}  \tag{5}\]  
\[ \begin{split} Performance_{vr,perception}\\ &=(\sum\limits_{i=1}^{6}\left(Range_{vr,i}\times Reliability_ {vr,i}\right)+\left(Range_{r,i}\times Reliability_{r,i}\right))\times stability _{vr}\\ \end{split}  \tag{6}\]  
\(Stability_{v}\) represents the stability coefficient for vehicle-based perception; \(Stability_{vr}\) is the stability coefficient for vehicle-road collaborative perception.