## 6 Example: Results and Discussion  
The example we consider is a single-entrance parking lot, see Figure 2. The layout of the parking lot has been redesigned according to the Engineering Construction Industry Standard JGJ100-98 and the layout of the example parking lot is shown in Figure 3. Since the entrance is located in the lower right of the entire layout, we define the coordinate system with the origin at the lower right corner, as shown in Figure 4.  
Figure 3: Layout of the parking lot (distance unit in meter). Figure 2: Aerial view of the parking lot of our example problem. As shown in Figure 4, in order to design the route selection, we denote each parking space and each turning intersection as a node (1-24) and a number (T1-T8). Additionally, considering the differences in sizes of vehicles entering the parking lot, we define the coordinates of each of the nodes and intersection numbers as the centered position of the parking space and the central line of the route at the turning. The coordinates of all nodes are listed in Table 1.  
In this section, we have designed three specific parking scenarios to test our proposed algorithm via Python. In the following, we will take scenario 1 as an example to explain the application of our method in detail. As shown in Figure 5, red nodes represent the parking spaces that are occupied, brown ones are those that are currently available, and the light blue node (node 11) represents the parking space that is being parked by a vehicle. A blue vehicle, which is an AV, is just entering into the intelligent parking lot and sending a parking request to the central command station. Meanwhile, an orange vehicle, which is a HV and cannut communicate with the central command station, is seeking an available parking space. Under this situation, the problem is to allocate an available parking space for the blue autonomous vehicle by the central command station. In order to solve this problem, we need to first determine which parking space that the driver of the orange vehicle would choose and offer the shortest path between the entrance and the allocated parking space. The overview scheme is described as a flowchart (Figure 6). The specific steps in the parking spaces selection and the shortest path planning are shown as follows: \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \(T1\) & (2.1, 17.0) & 1 & (9.7, 17.0) & 9 & (13.0, 17.0) & 17 & (8.0, 39.5) \\ \hline \(T2\) & (2.1, 28.5) & 2 & (12.2, 17.0) & 10 & (15.5, 17.0) & 18 & (10.5, 39.5) \\ \hline \(T3\) & (2.1, 39.5) & 3 & (14.7, 17.0) & 11 & (5.5, 28.5) & 19 & (13.0, 39.5) \\ \hline \(T4\) & (2.1, 50.4) & 4 & (17.2, 17.0) & 12 & (8.0,28.5) & 20 & (5.2, 50.5) \\ \hline \(T5\) & (15.7, 50.4) & 5 & (19.7, 17.0) & 13 & (10.5, 28.5) & 21 & (7.8, 50.5) \\ \hline \(T6\) & (19.7, 39.5) & 6 & (5.5, 17.0) & 14 & (13.0, 28.5) & 22 & (10.4, 50.5) \\ \hline \(T7\) & (19.7, 28.5) & 7 & (8.0, 17.0) & 15 & (15.5, 28.5) & 23 & (13.1, 50.5) \\ \hline \(T8\) & (19.7, 17.0) & 8 & (10.5, 17.0) & 16 & (5.5, 39.5) & 24 & (15.7, 50.5) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Coordinates in metric units of all nodes in test graph  
Figure 4: Layout of nodes in the parking lot and reference to a coordinate system. Figure 5: Example of a parking scenario 1. Figure 6: Flowchart for parking space selection and the shortest path planning. For the walking distance and distance to parking, distances in metric units are used in evaluating the values in matrix \(A\), as defined in Section 4. For the status of lane and status of available parking spaces, fuzzy evaluation is assigned with values proposed in Section 3. Based on the values from Table 2, the evaluation matrix \(A\) is:  
\[A=\left( \begin{array}{cccc}51.0&36.7&9.0&6.0\\ 44.3&30.0&9.0&5.0\\ 27.8&36.5&3.0&5.0\\ 41.8&27.5&9.0&5.0\\ 11.1&63.6&9.0&5.0\\ \end{array} \right)\]  
Step 2: Normalize the evaluation matrix \(A\) to form the fuzzy comprehensive evaluation matrix \(R=\left(r_{ij}\right)_{n\times m}\) according to Equations (2) and (3):  
\[R=\ \left(