## 3 Income Model of Roadside Units
### Roadside RSU Coverage Negative Income  
#### 3.2.1 Information Transmission Deficit  
In the construction of the negative income model, the negative income mainly includes two aspects: the information transmission deficit \(C_{L}(\alpha)\) and the network construction and maintenance cost \(C_{P}(\alpha)\). In the first part, when the information is transmitted in the wireless sensor network, the information received by some nodes is defective and distorted due to the interference of equipment and the external environment. Based on assumption (3), this paper uses node information transmission energy loss to represent the economic loss caused by information distortion and transforms the abstract problem into a quantitative problem. In addition, the energy loss problem of the node can be carried out from multiple angles, which will be explained in this section.  
Three main types of energy loss occur in the process of information transmission between nodes, which are the transmission energy loss \(E_{TX}\), receiving energy loss \(E_{RX}\), and unit data fusion energy loss \(E_{c}\). Depending on the distance between the roadside unit nodes to the vehicle nodes, the free-space model and the multi-path fading model [22] are applied, in which the free-space model is used within the threshold range and the multi-path fading model is used outside the range.  
Based on the assumption (3) that the distance between nodes is proportional to the energy loss, the model is selected by whether the distance between nodes is greater than a set threshold value \(d_{c}\), as in Equation (19). The energy loss generated by nodes transmitting information is as in Equation (20).  
\[d_{c}=\sqrt{\frac{\varepsilon_{fx}}{\varepsilon_{mp}}} \tag{19}\]  
\[E_{TX}(l,d)=\left\{\begin{array}{l}1E_{elc}+l\varepsilon_{fx}d^{2},d<d_{c}\\ l\varepsilon_{elc}+l\varepsilon_{mp}d^{4},d\geq d_{c}\end{array}\right. \tag{20}\]  
In the equation, \(l\) represents the data length of information transmission; \(E_{elc}\) represents the circuit energy loss per bit of data transmitted or received by the node; \(d\) represents the distance between the transmitting node and the receiving node; and \(\varepsilon_{fx}\) and \(\varepsilon_{mp}\) represent the circuit energy loss amplification factor of the free space model and the multi-path fading model. The free-space model is used when \(d<d_{c}\) and the multi-path fading model is used when \(d\geq d_{c}\).  
In addition, the energy loss generated by the node receiving information is as in Equation (21). To facilitate the description, a single vehicle cluster is taken as an example to illustrate and explain with. After the cluster head receives the information transmitted by each node, the energy loss generated during the information fusion process is as in Equation (22).  
\[E_{RX}(l)=lE_{elc} \tag{21}\]  
\[E_{c}(l)=n_{i}lE_{DA} \tag{22}\]  
In the equation, \(n_{i}\) is the number of nodes in the cluster and \(E_{DA}\) is the energy loss per unit of data fusion. In summary, the information transmission energy loss \(C_{L}(\alpha)\) is as in Equation (23).  
\[C_{L}(\alpha)=\alpha n\Big{[}\Big{(}\overline{k}+1\Big{)}(E_{TX}+E_{RX})+n_{ j}E_{c}\Big{]} \tag{23}\]  
In the equation, \(n_{j}\) is the number of vehicles in a vehicle cluster for data fusion. If there are no special requirements, \(n_{j}\) is equivalent to the hops of information transmission.