## 4 Discussion
### Bus Corridor's Distance  
Because a bus corridor's distance is affected by the number of stops (\(s_{n}\)) and the average stop spacing (\(\overline{s}\)), the impacts of the two parameters were studied. When \(s_{n}\) was analyzed, the values in the matrices \(\mathbf{P}\) and \(\mathbf{D}\) of the non-exited stops were also removed. The other parameters remained the same. When \(\overline{s}\) was analyzed, the other parameters remained the same.  
In Figure 5, with the increase in \(s_{n}\), the costs of the two types of services increased. The mixed service performed better than the local-only service with the different values of \(s_{n}\) owing to the stop-skipping mechanism of the limited-stop service. For the bus agency, when the number of stops changed, the design of the mixed service was not affected. \(H_{e}\) varied greatly, whereas \(H_{L}\) was relatively stable. The average waiting time for the limited stop service increased by approximately 5 min. The bus agency should add limited-stop vehicles to shorten the waiting time and maintain its competitiveness.  
In Figure 6, when \(\overline{s}\) < 0.5 km, the local service performed better than the mixed service. When \(\overline{s}\) > 0.5 km and \(L\) > 16.5 km, the total cost of the mixed service was lower than that of the local service. With a longer average stop spacing, the advantage is that the decline in the in-vehicle time of the limited-stop service was more evident. The average stop spacing had a great impact on the efficiency of the mixed service and the local service. When the length of the bus corridor was longer than 16.5 km and the average bus stop spacing was longer than 0.5 km, the mixed service design was more conducive to improving the performance of the bus. When \(\overline{s}\) changed from 0.3 to 0.6 km, the average waiting time increased by approximately 2 min, which is within acceptable bounds for passengers. The change in waiting time had no notable impact on the service level of the limited-stop service.  
Figure 4: The variations in the objective function and decision variables with changes to \(g\).  
Stops for the limited-stop service were primarily affected by the OD matrix; therefore, when a unit change in the hyper-parametrizations occurs, stops for the limited-stop service remain unchanged. Adding vehicles and increasing the travel speed decreased the headway of the local service by \(24\%\). The effects of the other hyper-parametrizations were smaller for the headways. The variation in the headway of the local service was between \(-17.5\%\) and \(15\%\), and the variation in the headway of the limited-stop service was between \(-4\%\) and \(12\%\). Overall, the model's stability was good.  
The elasticity coefficient of the total cost was small, and the model was robust. The passenger cost showed inelastic results for most of the parameters. The elasticity coefficient of the passengers' speed when entering or leaving the bus system to the passenger cost was \(-1\); thus, the passenger cost significantly decreased when passengers entered or left the bus system using faster methods such as by bike-sharing, \"P + R\", and \"K + R\". The elasticity coefficients of the bus cruising speed and the number of vehicles to the agency cost were \(-1\) and \(1\), respectively. Therefore, increasing the cruising speed, such as by implementing bus lanes, can help to significantly reduce the agency cost. Adding to the number of vehicles significantly raised the agency cost. The other input parameters produced a small effect on the costs.