# A Hybrid Traffic Sensor Deployment Model with Communication Consideration for Highways
## 2 The Optimization Model for the Hybrid Sensor Deployment  
This paper assumes that two kinds of sensors will be deployed along the researched highway, i.e., RSUs and camera sensors. As listed in Table 1, cameras can capture videos of the highway environment, which are utilized to extract information on traffic flow, traffic density, and vehicle trajectory. Meanwhile, RSUs can acquire information on vehicle speeds and vehicle positions recorded in the text. For the convenience of stating the multi-type sensor-deployment problem, the highway is divided into several uniform cells, as shown in Figure 1. Four combination types could be listed for two adjacent sensors, i.e., (camera, camera), {camera, RSU}, {RSU, camera}, and {RSU, RSU}, which are labeled as types 1, 2, 3, and 4, respectively, as shown in Table 2. With this configuration, the problem can be regarded as selecting appropriate cells to install sensors and combination types to monitor the researched road. Since sensors located along the road are not only used to capture traffic information of designated points, monitoring traffic conditions of the entire road by integrating traffic data from multiple sensor points is more meaningful for traffic managers. Thus, the monitoring efficiency of the area between two adjacent sensors becomes a critical indicator for evaluating sensor-deployment plans. To express the model in a simplified way, a binary coefficient \(\tau_{ij}^{k}\) is defined and denoted as the accuracy rate from cell \(i\) to \(j\) via the \(k\)th combination type of hybrid sensor. Therefore, the multi-type sensor-deployment problem will be converted into finding optimal combination types. Based on the above assumption, the optimization model of the multi-type sensor deployment problem will be introduced as follows. For a researched road with \(\mathbf{N}=\{1,2,3,\ldots,N\}\) cells, the length of each cell is \(\Delta d\), and sensors are assumed to be deployed in the middle of designated cells. The total investment cost is \(W\). The unit cost of each RSU and camera is, respectively, \(w_{r}\) and \(w_{c}\). The set of combination types is \(\mathbf{S}\), where \(\mathbf{S}=\{1,2,3,4\}\). Since directly sending video data to the control center usually takes some time, the idea of Multi-access Edge Computing (MEC) is widely adopted to preprocess data and reduce latency. The MEC server is one of the essential parts of complete edge computing. Thus, the number and location of MEC servers also need to be considered. Similar to locating sensors, the main concern of the MEC server-deployment problem is to search for the proper placement of cells. Therefore, two binary variables \(x_{ij}^{k}\) (\(\forall i,j\in\mathbf{N},k\in\mathbf{S}\)) and \(z_{u}\) (\(\forall u\in\mathbf{N}\)) are applied to formulate the researched problem, where \(x_{ij}^{k}\) is equal to 1 if the region between cell \(i\) and \(j\) is monitored via the \(k\)th combination type of sensors, and \(z_{u}\) is equal to 1 if an MEC server is located in the middle of cell \(u\). The process of decoding variable \(x_{ij}^{k}\) to obtain sensor location can be explained with the example shown in Figure 2. It should be noted that cells \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Equipment** & **Transferred Information** & **Format** \\ \hline \multirow{2}{*}{RSU} & vehicle speed & \multirow{2}{*}{text} \\  & vehicle position & \\ \hline \multirow{4}{*}{Camera} & traffic flow & text \\  & traffic density & \\ \cline{1-1}  & vehicle trajectory & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The data information for roadside equipment. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & & **Cell \(i\)** & \\ \cline{2-4}  & & **Camera** & **RSU** \\ \hline \multirow{2}{*}{Cell \(j\)} & Camera & type 1 & type 2 \\  & RSU & type 3 & type 4 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The type of required sensors and servers. Figure 1: A sketch map of sensor layout. \(0\) and \(n+1\) are two dummy cells, which are used to represent the origin and destination cells.