# Data-Driven Modular Vehicle Scheduling in Scenic Areas
## 4 Experimental Results and Analysis
### Effectiveness Analysis of M2  
While M2 shows superior performance over M1 in terms of cost and vehicle utilization, the reliability of M2's results warrants further discussion. Since the results of the M3 model represent the theoretically global optimal solution, we compare the outcomes of M2 against M3 to assess the validity of M2. Figure 10: Difference in vehicle utilization between M2 and M1 in each simulation for different parameter variations. Figure 11 presents the cost savings of M2 and M3 compared to M1 across 30 simulation experiments. Overall, both M2 and M3 achieve lower total costs than M1 over these simulations, with M3 generally yielding higher savings. Notably, M3's savings are highly variable, reaching over USD 600 at the high end but dropping to less than USD 10 at the low end. In contrast, M2's savings fall within a more stable range of USD 10-USD 300. Although M2 is not as effective as that of M3, the variation in savings is more stable. To further evaluate M2's optimization effectiveness, we calculate the optimization rates of both M2 and M3 relative to M1. The detailed results are presented in Figure 12.  
Figure 11: The total cost savings of M2 and M3 over M1 in each simulation for different parameter variations. Figure 12 examines the model's effectiveness in terms of optimization rates, highlighting the impact of variations in vehicle capacity and penalty. Overall, the optimization range spans from 0% to 6%, with M3 generally showing a higher optimization rate than M2. Figure 12a,c,e indicate that both M2 and M3 achieve higher optimization rates with increased vehicle capacity. This trend may be attributed to the instant response approach in M1, which, under higher vehicle capacity conditions, is more susceptible to high unloaded rates, thereby enhancing the average optimization effect of M2 and M3. Additionally, the optimization rate of M2 generally hovers around or above 2% when penalties fluctuate, while it remains below 2% when penalties are constant. This suggests that optimization improves with variable penalties, likely because the M2 and M3 strategies can more effectively align real-time conditions with scheduling plans, achieving greater optimization when penalties are dynamic. Figure 12: Optimization rate of M2 and M3 compared to M1 in each simulation for different parameter variations. Since M3 represents the theoretically maximal achievable optimization margin, a statistical analysis of the optimization effects of M2 and M3 is conducted across each scenario to better understand the optimization gap between them. In addition, the ratio of M2's average optimization rate to M3's average optimization rate is defined as the \"solution quality rate\" of M2. This metric provides a measure of M2's optimization level relative to the theoretical optimum. The final results are presented in Tables 3 and 4. Table 4 presents the average optimization rate and standard deviation for M2 and M3 across all scenarios. A clear pattern emerges: while M3 consistently achieves a higher average optimization rate than M2, M2 shows a lower standard deviation than M3 in all scenarios except scenario (f). These findings suggest that, although M2 does not reach the theoretical optimal level, it demonstrates greater stability and adaptability, managing fluctuations in passenger demand, vehicle load, and penalty changes more effectively than the theoretical optimum. Consequently, M2 maintains a steady optimization effect, even in complex scenarios. Furthermore, our optimization results consistently show a cost difference of no more than 1.5% from the global optimum across all scenarios, whereas in similar scenarios--assuming uniform passenger numbers--heuristic algorithms such as genetic algorithms still typically exhibit a gap of around 3% from the optimal solution [51]. We further investigate the solution quality obtained by M2 by comparing its solution with that of the optimal solution under a deterministic setting. This measure will provide insight into M2's performance relative to the best possible outcome.