## 3 Materials and Methods
### Simulation Model Calibration
#### 3.4.2 Simulation Model Calibration Method
Therefore, through trials with various K values (including 5, 10, 20, 25, 30, and 50), this study evaluates the calibration effectiveness for the first time period. Considering both accuracy and efficiency, K is ultimately set to 20, slightly lower than half of the total number of target road segments (50). This setting aims to balance calibration effectiveness with practical convenience and can serve as a reference for other calibration studies. Step 3: Calculating the rescaling factor for OD demand on key links. By analyzing the simulation's travel path output files, the travel paths containing the identified critical roads are extracted, and the current demand for the critical OD pairs is further quantified. Adjustments to the travel demand on these roads are made based on the ratio of simulated link speeds to actual link speeds. Specifically, the rescaling factor for OD pairs on critical road segment m is calculated as follows:  
\\[F^{\\prime}_{m,t}=\\frac{S^{\\prime}_{m,t}}{S_{m,t}} \\tag{7}\\]  
where \\(F^{\\prime}_{m,t}\\) is the rescaling factor for OD pairs using key link \\(m\\) during time period \\(t\\) in the current iteration; \\(S^{\\prime}_{m,t}\\) and \\(S_{m,t}\\) are the average speeds observed on link \\(m\\) during time period \\(t\\) from the simulation model and LBS data, respectively. When the simulated link speed is higher than the actual speed, the ratio in the rescaling factor will be greater than 1, indicating smoother traffic flow on the same link in the simulation compared to reality. This implies that the current simulation underestimates the travel demand on this link, necessitating the expansion of demand to simulate more congested conditions. Conversely, when the simulated link speed is lower than the reality, the ratio will be less than 1, reflecting more congestion in the simulation than in reality. In this case, the current simulation overestimates the travel demand, requiring a reduction in demand to simulate smoother traffic. Step 4: Determining the OD volume on key links for the next calibration iteration. During the calibration iterations, a coefficient that gradually decreases from 1 to 0 as the calibration process for the current time period progresses is introduced. This ensures efficient adjustments during the initial stages of calibration and finer, more stable adjustments later on. Based on the current number of vehicles (or OD pairs) using the key link during the current time period in the current simulation calibration iteration and its rescaling factor, the number of vehicles (or OD pairs) expected to use the key link during the same time period in the next calibration iteration is calculated as follows:  
\\[N^{\\prime}_{it+1,m,t}=\ \begin{cases}N^{\\prime}_{it,m,t}*\\begin{bmatrix}1+k* \\left(F^{\\prime}_{m,t}-1\\right)\\end{bmatrix},&F^{\\prime}_{m,t}>1\\\\ N^{\\prime}_{it,m,t}*\\begin{bmatrix}1-k*\\left(1-F^{\\prime}_{m,t}\\right)\\end{bmatrix},& F^{\\prime}_{m,t}<1\\end{cases}  \\tag{8}\\]  
where \\(F^{\\prime}_{m,t}\\) is the rescaling factor for the OD volume using key link m in time period \\(t\\) during the current iteration \\(it\\), \\(S_{m,t}\\) and \\(S^{\\prime}_{m,t}\\) denote the average speeds of the link as observed from LBS data and in the simulation model, respectively. \\(N^{\\prime}_{it+1,m,t}\\) is the number of vehicles (or OD) that will use key link \\(m\\) in time period \\(t\\) during the next calibration iteration \\(it+1\\) in simulation model, \\(N^{\\prime}_{it,m,t}\\) is the number of vehicles (or OD) that will use key link \\(m\\) in time period \\(t\\) during the current calibration iteration \\(it\\) in simulation model, \\(k\\) is a speed coefficient for the calibration process, gradually decreasing from 1 to 0 as the current time period calibration progresses. During the process of demand resampling on links, we initially retain all travel demands passing through the key links within the current time period.