## 4 Simulation Analysis  
Ride-hailing platforms have accumulated extensive regional order information and real-time traffic data. By studying the relationship between changes in regional order density and the probability of taxi drivers accepting offline orders, especially the tendency of taxis to choose offline orders when orders overflow, we can provide references for ride-hailing platforms to make dispatching decisions in overflow scenarios. This section simulates the scenario of taxi drivers accepting offline orders during order overflow and analyzes the relationship between order density and the probability of taxi drivers accepting offline orders. The decision-making of taxi drivers to accept rides online or offline is influenced by a combination of factors, such as expected income, road conditions, and personal preferences. This paper introduces a weighted function to calculate the driver's decision value, as shown in Equation (29). In this equation, \(L_{C}\) represents road conditions, reflecting driving elements such as traffic congestion that affect the driver's efficiency and pickup time. \(K_{I}\) denotes the driver's visual range, i.e., the distance within which the driver can observe potential passengers on the road, influencing offline ride acceptance opportunities. \(P_{J}\) indicates platform incentives, affecting the expected income from online ride acceptance. \(K_{E}\) signifies past experience, influencing the driver's comprehensive judgment of different ride acceptance methods, and \(\xi_{1},\xi_{2},\xi_{3}\)... are the weights of each factor, with \(\sum_{i=1}^{4}\xi_{i}=1\). When the decision value \(D_{cc}\) is above a threshold, the driver chooses to accept rides offline; otherwise, they choose to accept rides online. \[D_{cc}=\xi_{1}L_{C}+\xi_{2}K_{I}+\xi_{3}P_{J}+\xi_{4}K_{E} \tag{29}\]  
Based on relevant data released by the Wuxi Transportation Bureau, an experiment was conducted with 750 taxis and 4250 ride-hailing vehicles operating within a unit area of 100 square kilometers. The vehicle speed was set to 28 km/h, based on the average speed during peak hours in Wuxi's road network. Given limited vehicle resources, new orders will begin to queue when all vehicles are in service. Therefore, the simulation experiment started with a consistent order density of 5000 orders in the unit area (100 square kilometers). The results, as shown in Table 3, illustrate the number of offline taxi orders, the total number of completed orders within the area, and the proportion of offline taxi orders under different order densities. This section describes eight independent experiments that were conducted, and the mean proportion of offline taxi orders was calculated after each experiment, as shown in Table 4. Notably, the mean values of the proportion of offline orders accepted by taxis, \(\theta\), corresponding to different order densities, exhibited a stable trend, as illustrated in Figure 1. Therefore, when the Lagrange interpolation method is used, the correlation between order density, \(\rho\), and the proportion of offline orders accepted by taxis, \(\theta\), can be visualized more intuitively, as shown in Figure 2. This smooth curve illustrates the corresponding relationship between order density and the probability of offline taxi orders. \begin{table}
\begin{tabular}{l c c c c c c c c c c} \hline \hline
**Order Volume** & **5000** & **10,000** & **15,000** & **20,000** & **25,000** & **30,000** & **35,000** & **40,000** & **45,000** & **50,000** \\ \hline Number of orders completed by taxis & 3680 & 3717 & 3716 & 3746 & 3759 & 3720 & 3770 & 3768 & 3730 & 3761 \\ Number of orders completed offline & 847 & 1260 & 1611 & 1810 & 2045 & 2194 & 2360 & 2568 & 2749 & 2845 \\ Proportion of offline orders accepted by taxis & 23.02\% & 33.90\% & 43.35\% & 48.32\% & 54.40\% & 58.98\% & 62.60\% & 68.15\% & 73.70\% & 75.64\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Example of changes in order density and proportion of taxis’ offline order acceptance.