# A New Hybrid Hierarchical Roadside Unit Deployment Scheme Combined with Parking Cars
## 5 Simulation Analyses and Results  
### Simulation Analyses  
The experimental simulation software is built on the following hardware configuration: AMD Ryzen 7 1800X Eight-Core Processor 3.60 GHz CPU processor (AMD, Santa Clara, CA, USA), Ubuntu 20.04 operating system, 8 GB RAM, NVIDIA GeForce GTX 1060 6 GB graphics processor (NVIDIA, Santa Clara, CA, USA). In the simulation, a 3D map of the real-world road network is obtained from OpenStreetMap and projected onto a 2D plane using the standard WGS84 coordinate system. SUMO is employed to simulate real traffic scenes with parked vehicles, which are considered to be t-RSUs. In this section, the simulations that are conducted using OpenStreetMap and SUMO (version 1.11.0) with its interface TraCI interacted with Python are described. The simulations use a 1.91 km by 2.01 km real-world road topology from the area around Nenjiang Road, which is located at the Wujiaochang area of Jiangwan, Yangpu District, Shanghai, the downtown area of Shanghai, China. The parameters in the SUMO simulator (version 1.11.10) are shown in Table 2. \begin{table}
\begin{tabular}{l l} \hline \hline
**Step** & **Description** \\ \hline Step 1 & If the problem is to minimize the solution, the current optimal solution is set as \(\infty\). \\ \hline Step 2 & According to the branch rule, a node is selected from the nodes that have not been searched at present, and it is divided into several new nodes in the next level of the node. \\ \hline Step 3 & Calculate the lower limit of each new branch node. \\ \hline Step 4 & If either of the following conditions is satisfied, it is not considered: \\  & 1. The node does not contain a feasible solution. \\  & 2. The lower limit of the node is greater than or equal to the current A value. \\  & 3. If a feasible solution with a minimum lower limit value in the node is found, it is necessary to further compare the feasible solution with the current A value. If the latter is small, it needs to be discarded. \\ \hline Step 5 & Determine whether there are nodes that have not yet been searched. If there are, step 2 is performed. If not, the calculation is stopped, and the optimal solution \\  & is obtained. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Branch and bound algorithm steps. \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter** & **Value** \\ \hline Density of Vehicles (veh/km\({}^{2}\)) & 37.5, 112.5, 187.5 \\ Total Given Cost & 5 units \\ Simulated Area & Downtown area of Shanghai, China \\ Communication Range & 100 m, 300 m, 500 m \\ Traffic Data Source & Historical traffic data in Shanghai \\ Car-Following Model & CarFollowingModel-Krauss [27] \\ Lane-Changing Model & LC2013 [28] \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of Simulation. In the simulation, considering a confined geographical region, vehicles are entering and leaving the region continuously and the RSUs can be deployed at any position along the roads. Meanwhile, it is assumed that all drivers use the fastest routes through the network using the Djikstra routing algorithm. During the simulation, we compare our deployment algorithm with two other algorithms: the Random Deployment algorithm (RandDeploy) and the Maximum Vehicle Coverage Deployment (MVCD) algorithm. The RandDeploy algorithm randomly selects a vertex in a road network until the set visiting probability (SVP) of all the vertices to the result set meets or exceeds a predefined threshold [29]. The MVCD algorithm employs a greedy algorithm to maximize the coverage area of vehicles within the given cost, which consequently often leads to the inclination to deploy the RSUs in the intersections. Both the RandDeploy and MVCD are conventional algorithms and do not include the procedure of choosing the candidate virtual t-RSUs. To evaluate the performance of the hybrid hierarchical RSU deployment scheme with parked cars as t-RSUs against the other two deployment strategies, a critical cost constraint of 5 RSU units is applied.