# An Optimization Framework for Data Collection in Software Defined Vehicular Networks
## 3 Materials and Methods
### Proposed Data Collection Optimization Model
#### 3.3.1 Objective Function
\[\mathcal{B}_{i}=\ \mathcal  
collected at a constant rate (\(p_{i}=1,q_{i}=0,L_{i},f\) are constants). As the RSUs are stationary, their velocity and acceleration are zero, and the position is fixed. Thus, broadcasting status as I2I (from an RSU to another RSU) is not necessary. However, both vehicular nodes and RSUs can broadcast status in the DSRC communication channel (V2V, I2V, V2I). Thus, the combined communication cost for broadcasting from a given node \(i\) to its neighbor \(m\) (\(\mathcal{B}_{im}\)) can be assumed to be constant as the communication cost and delay within the same communication channel (DSRC) is almost the same. Therefore, both the first and third terms in the generic objective function in Equation (10) can be reduced to one term and the objective function for this special case of status data collection can be written as in Equation (11). Our simulations will include only the status data collection, and thus they will be conducted only for the special case objective function derived in Equation (11). However, if sensor data is collected, the objective function in Equation (10) must be used, and as we simulate only status data collection, we use the objective function in Equation (11). However, it can be argued that solving the simplified case is almost equivalent to the generic case as terms 2 and 3 of Equation (11) are exactly the same as terms 2 and 4 of Equation (10), and the effect of term 1 of Equation (11) is equivalent to the effect of the combination of terms 1 and 3 of Equation (10), as term 1 of Equation (11) is formed by combining terms 1 and 3 of Equation (10).  
\[minimize\;C_{CN}\sum_{i=1}^{\mathcal{N}}\mathcal{N}_{i}z_{i}+C_{CA}\sum_{i=1}^ {\mathcal{N}}\mathcal{B}_{i}x_{i}-C_{O}\sum_{i=1}^{\mathcal{N}}(x_{i}\sum_{m \in\mathcal{S}_{i}}z_{m}) \tag{11}\]  
The objective function will be the same for any SDVN architecture. However, constraints will be different from SDVN architecture to architecture. Table 1 summarizes the notations used in the optimization model. Some common facts regarding the optimization of data collection are given below. \begin{table}
\begin{tabular}{p{142.3 pt} p{142.3 pt}} \hline \hline
**Notation** & **Description** \\ \hline \(x_{i}\,z_{i}\) & Decision variable to represent the association of a node \(i\) for data collection as an agent, as a broadcasting node, respectively \\ \hline \(\mathcal{S}_{i}\), \(\mathcal{S}\) & Node ID set of all one-hop neighbors of node \(i\), Set of one-hop neighbors of the whole network, respectively \\ \hline \(\mathcal{N},\mathcal{N}_{i}\) & Total number of nodes in the network, Total one-hop neighbors of node \(i\), respectively \\ \hline \(\mathcal{B}_{im},\mathcal{C}_{im},\mathcal{D}_{im}\) & Combined communication cost, communication cost, and delay for communication between \(i^{th}\) node and its \(m^{th}\) neighbor, respectively \\ \hline \(\mathcal{B}_{i},\mathcal{C}_{i},\mathcal{D}_{i}\) & Combined communication cost, communication cost, and delay for communication from \(i^{th}\) agent to controller, respectively \\ \hline \(f,f^{\prime}\) & Update/Data collection frequency, optimization frequency, respectively \\ \hline \(\mathcal{L}_{stj},\mathcal{L}_{seqj},\mathcal{L}_{i}\) & Status data payload, sensor data payload, and combined data payload of \(i^{th}\) node, respectively \\ \hline \(p_{i}\,q_{i}\) & Binary variable to represent the state of the collection of status data and sensor data from \(i^{th}\) node, respectively \\ \hline \(\mathcal{C}_{N},\mathcal{C}_{DN},\mathcal{C}_{DA},\mathcal{C}_{CN},\mathcal{C }_{CA},\mathcal{C}_{IN},\mathcal{C}_{O}\) & Optimization coefficients \\ \hline \(H_{hom},H_{het}\) & Homogeneous normalized network entropy, Heterogeneous normalized network entropy, respectively \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of notations used in the proposed data collection optimization model.