# A Novel Base-Station Selection Strategy for Cellular Vehicle-to-Everything (C-V2X) Communications
## 4 Proposed Mechanism
### Markov Decision Policy  
In the [PERSON] decision policy, we treat each vehicle as a competitor. We enumerate the sequence of all vehicle choices and allow all vehicles to select base stations in sequence. The choice of the previous vehicle affects the conversion probability of the next vehicle selection. In other words, vehicles that prefer femtocell base station resources reduce the opportunity to choose the femtocell base station. The process is shown in Algorithm 1. For all vehicles, the opportunity to select the macrocell or femtocell base station is the same. We had all vehicles compete for femtocell base station resources. Vehicles that prefer the femtocell base station first have an advantage in receiving femtocell base station services. Other vehicles have fewer opportunities to use the femtocell base station. Signal strength obtained by vehicles from the macrocell and femtocell base stations is predicted by the vehicles' position in the next second. To reflect the priority of vehicle selection, we use the Markov decision policy to choose. 1. Sort \(n\) vehicles in order with all permutations and combinations. Then, select the femtocell base station for the first user so there is a total of \(n!\) Sort the results. 2. Left vehicles have the same opportunity to choose the macrocell or femtocell base station. Therefore, there are \(n!2^{(n-1)}\) choice possibilities. 3. Obtain the conversion probability of each user's choice. 4. The corresponding predicted RSS and transition probability are treated as the value function of the vehicle. 5. The value-function sum of all sequences is the sequence value of the selection sequence. 6. The sequence with the highest value is the optimal selection sequence, and the base station of each vehicle in the sequence selects the best base station selection for the next second. Figure 3: Workflow of the Markov decision policy. To clearly describe the above mechanism, we provide an example in Figure 4. The number means marked vehicles (ex. 1,2,3...n). M means the macrocell base station that the vehicle selected, and F means the femtocell base station that the vehicle selected. Here, we emphasize that the \(j\)-th vehicle's selected base station corresponds to the corresponding \(RSS_{j}\). Figure 4: Permutations and combinations of vehicle sorting. When the \(j\)-th vehicle chooses the femtocell base station, \(\widehat{F_{H_{j}}}\) represents the higher probability of the vehicle's displacement; \(\widehat{F_{M_{j}}}\) represents the normal possibility of the vehicle's displacement; \(\widehat{F_{L_{j}}}\) represents the low probability of the vehicle's displacement in the range of values. In Figure 6, we define the current position co-ordination of the \(j\)-th vehicle with \((0,0)\). Then, we take any direction as the polar co-ordinates' positive direction. \(\theta\) represents the angle between the vehicle and the positive direction; \(\theta_{0_{j}}\) represents the angle between the previous motion step and the positive direction; \(\theta_{M_{j}}\) represents the angle between the macrocell base station and the positive direction; and \(\theta_{F_{j}}\) represents the angle between the femtocell base station and the positive direction. The polar co-ordinates of the macrocell base station can be expressed as (\(D_{M_{j}}\), \(\theta_{M_{j}}\)). The polar co-ordinates from the vehicle to the femtocell base station can be expressed as (\(D_{F_{j}}\), \(\theta_{F_{j}}\)). The displacement vector to the next second can be expressed as (\(r_{j}\), \(\theta_{0_{j}}\)). The probability set could be presented by \(\widehat{M_{H_{j}}}\), \(\widehat{M_{M_{j}}}\), \(\widehat{M_{L_{j}}}\), \(\widehat{F_{H_{j}}}\), \(\widehat{F_{M_{j}}}\).