# Layout Model of Bike-Sharing Facilities in the Transfer-Influenced Area of a Subway Station
## 3 Results and Discussion
### Parameter Sensitivity Analysis
#### 3.5.3 Upper- and Lower-Limit Parameters of Bike-Sharing Allocation  
The upper- and lower-limit parameters of the facilities determine the threshold of bike-sharing allocation for a single facility. The lower limit for a single facility is limited by the economic cost of a single facility and the accuracy of the electronic fence, and generally cannot be less than 10 bikes. The upper limit is limited by the actual available parking space on urban roads, and can theoretically affect the results of the optimal facility point scheme. In order to analyze the influence of the change in the upper limit parameter on the optimal layout and configuration scheme, the upper limit parameter is selected to change according to the step size of 10. The change trend of each key index is shown in Table 7 and Figure 10, and the Figure 11 shows the optimal scheme with 80 bikes. Table 8 shows the number of bikes allocated to the alternative facilities.  
The main discussions are as follows.  
1. Under the premise that other parameters remain unchanged, the number of selected bike-sharing facilities would firstly decrease and then remain stable with the increase in the upper limit of bike-sharing allocation. If the upper limit parameter of a single facility is less than 80, the optimal layout and configuration scheme provides more choice for transferring and riding for travelers by adding facilities, and shares the ride demand of a single facility point as much as possible, so as to avoid the overload penalty of excessive demand on the comprehensive benefit value of a single point. If the upper limit parameter exceeds 80, as shown in Figure 10, theoretically all the travel needs of each traffic zone can be met by a single facility, and only the corresponding optimal facility points need to be deployed, so the layout and configuration scheme will no longer change, and the number of optimal facilities also no longer decrease. Compared with the first-generation scheme (Figure 6), we found that multiple sub-optimal facilities (such as 2, 4, 12) were selected. The transfer cost of bike-sharing was affected by the sub-optimal facility. Compared with the optimal facility scheme (Figure 7), the basic layout and configuration scheme is similar, because it is possible to build some facilities with large numbers of bikes (such as 1, 25, 26), so as to reduce the number of facility points.  
Figure 11: Optimal scheme of bike-sharing facilities with an upper limit of 80.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Alternative Point ID** & **Bicycle Allocation** & **Alternative Point ID** & **Bicycle Allocation** & **Alternative Point ID** & **Bicycle Allocation** \\ \hline
1 & 72 & 11 & 18 & 21 & 0 \\
2 & 0 & 12 & 0 & 22 & 39 \\
3 & 0 & 13 & 38 & 23 & 28 \\
4 & 0 & 14 & 28 & 24 & 42 \\
5 & 33 & 15 & 0 & 25 & 74 \\
6 & 39 & 16 & 0 & 26 & 67 \\
7 & 0 & 17 & 43 & 27 & 0 \\
8 & 0 & 18 & 0 & 28 & 0 \\
9 & 25 & 19 & 27 & 29 & 0 \\
10 & 29 & 20 & 0 & 30 & 48 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Optimal scheme and the number of bikes allocated with an upper limit of 80.  
With the increase in the upper limit parameter, the transfer-ride volume increases at first and then remains stable. When the upper limit parameter is less than 80, the maximum supply of the optimal facility relative to a travel zone cannot meet all the transfer-ride needs, and travelers need to choose the next best neighboring facility, which affects the transfer-ride volume. When the upper limit parameter is greater than 80, this indicates that the supply of single facility point is sufficient, the original problem is equivalent to finding the scheme with the largest transfer-ride volume and the least number of facilities in the influenced area. At this time, all travelers in different traffic zones can meet the demand of transfer and riding by choosing the nearest facility, without causing overload penalty and reducing the comprehensive benefit value; therefore, the optimal scheme will no longer change, and the volume will no longer increase.