# Priority-Driven Resource Allocation with Reuse for Platooning in 5G Vehicular Network
## 4 System Modeling and Resource Allocation Algorithm
### Proposed Resource Allocation Algorithm  
The following objective function aims to minimize the number of resource re-requests while maximizing the resource allocation rate in the process where general vehicles are allocated resources and engage in communication within the overall communication process. Constraints \(C_{1}\) to \(C_{4}\) below represent the conditions of the proposed resource allocation algorithm. \(Ra(i)\) represents the resource block allocated to vehicle \(i\), and \(t_{i}\) denotes the resource allocation order of vehicle \(i\). \(n_{i}\) denotes the number of times vehicle \(i\) re-requests a resource, while \(n_{\max}\) represents the maximum number of resource re-requests allowed for a vehicle. \[\max\frac{1}{m}\sum_{i=1}^{m}\left(\frac{Ra(i)}{Ra(i)}-\frac{n_{i}}{n_{\max}} \right)\quad(i\in G_{t},\ G_{t}=\{1,\ldots,m\}) \tag{6}\]  
\[C_{1}:\quad Ra(i)\in\{0,Rq(i)\}\quad(i\in V_{t}) \tag{6a}\] \[C_{2}:\quad t_{p}<t_{g}\quad(p\in P_{t},\ \delta\in G_{t})\] (6b) \[C_{3}:\quad x_{i,j}+x_{k,j}\leq 1\quad(i,k\in V_{p}^{(m)}\ \text{or}\ i,k\in G_{t},\ d_{i,k}<d_{0})\] (6c) \[C_{4}:\quad\gamma_{i,k}^{(j)}\geq\gamma_{\min}\quad(i,k\in P_{t}) \tag{6d}\]  
The SINR \(\gamma_{i,k}^{(j)}\) is given by  
\[\gamma_{i,k}^{(j)}=\frac{P_{0}h_{i,k}^{(j)}}{N_{0}+\sum_{i^{\prime}\
eq i}x_{ i^{\prime},j}P_{0}h_{i^{\prime},k}^{(j)}}\quad\left(\forall\,i,\ x_{i,j}=1,\ \forall\,i^{\prime},\ x_{i^{\prime},j}=1\right) \tag{6f}\]  
\(C_{1}\) specifies that each vehicle either receives all requested resources or none at all. In other words, vehicle i is either allocated the requested resource requirement or does not receive the requested allocation. In \(C_{2}\), the resource allocation order for platoon vehicles must always precede that of general vehicles. \(C_{3}\) ensures that vehicles in the same platoon, or general vehicles within the resource reuse distance, cannot use the same resource simultaneously. Specifically, if the distance between vehicle i and vehicle k is less than a defined threshold, the same resource cannot be allocated. \(C_{4}\) states that when platoon vehicles reuse resources, the SINR must be equal to or greater than the minimum threshold SINR value. In this case, the resource for platoon vehicles can only be reused if the SINR constraint is satisfied. The resource allocation problem is classified as NP-Hard, indicating that the process of deriving an optimal solution is computationally complex and time-consuming [45]. In NP-Hard problems, the computational time required to explore feasible solutions increases exponentially as the problem size grows. Furthermore, since resource allocation must adapt to continuously changing conditions, finding solutions for the objective function in real-time within dynamic network environments becomes highly challenging in practice. In particular, finding solutions that optimize system performance across multiple time slots is significantly more challenging. The allocation in one-time slot can affect outcomes in subsequent time slots, making it difficult to achieve a globally optimal solution for the objective function. Given these complexities, instead of pursuing a theoretically optimal solution to the objective function, this paper focuses on the empirical evaluation of the proposed resource allocation algorithm. We use heuristic algorithms suitable for real-time vehicular networks and assess the practical performance of the algorithm. The objective function aims to improve network efficiency by maximizing resource utilization and minimizing communication delay to meet real-time requirements. Therefore, we evaluate the effectiveness of the algorithm by comparing its performance with existing algorithms using performance evaluation metrics such as the average resource allocation rate and communication delay. These metrics are directly linked to the objectives of maximizing resource utilization and minimizing delays, providing a meaningful assessment of how well the algorithm meets the goals set by the objective function.