## 4 Simulation  
In this section, we verify our analytical results and evaluate the proposed scheme using MATLAB (R2017a, The MathWorks, Natick, MA, USA) as the simulation platform. The parameters are listed in Table 2. In this simulation, the MBS is located in the middle of the road and the MUs are uniformly and randomly distributed on the road. To represent the difference of the data arrival rates of multiple users, the data arrival rates of users are uniformly and randomly distributed throughout the segment \(\left[a^{\min},\ a^{\max}\right]\).  
\begin{table}
\begin{tabular}{c l} \hline \hline
**Notations** & **Meaning** \\ \hline \(d^{V}\) & The distance between the corresponding transmitter and receiver in the platoon \\ \(g_{k}^{M}\) & The small-scale fading from the MBS to the corresponding MU that is active in \\ \(d_{k}^{M}\) & The distance between the MBS and the corresponding MU that is active in \\ \(g_{k}^{VM}\) & The small-scale fading from the VU interferer to the MU that is active in channel \(k\) \\ \(d_{k}^{VM}\) & The distance between the VU interferer and the MU that is active in channel \(k\) \\ \(\beta\) & The threshold of the ratio of the interference from the MBS to the interference \\  & from the other platoons \\ \(b_{k}\) & The binary variable of channel allocation for the MUs in channel \(k\) \\ \(\rho_{nk}\) & The availability probability of channel \(k\) for member \(n\) in the platoon \\ \(\delta_{nk}(t)\) & The binary variable that indicates whether channel \(k\) is available to member \(n\) in \\  & the platoon at time slot \(t\) \\ \(\phi_{nk}\) & The non-outage probability of channel \(k\) for member \(n\) in the platoon \\ \(\tilde{\xi}_{nk}(t)\) & The binary variable that indicates whether channel \(k\) is in a non-outage state for \\  & member \(n\) in the platoon at time slot \(t\) \\ \(Q_{n}(t)\) & The data queue for member \(n\) in the platoon at time slot \(t\) \\ \(\mu_{n}(t)\) & The rate of service for member \(n\) in the platoon at time slot \(t\) \\ \(a_{n}\) & The rate of data arrival for member \(n\) in the platoon \\ \(\mathbf{X}\) and \(x_{nk}\) & The channel allocation matrix and its element \\ \(\mathbb{S}=\{D_{1},\ D_{2},\ D_{3},\ D_{4},\ D_{5}\}\) & The set of decisions for member \(n\) in the platoon \\ \(r(t)\) & The indicator of re-allocation at time slot \(t\) \\ \(\gamma\) & The threshold of re-allocation rate \\ \(z_{n}(t)\) & The notation that indicates whether member \(n\) in the platoon is a service-guaranteed user at time slot \(t\) \\ \(R(t)\) & The virtual cost queue for the re-allocation rate of the platoon at time slot \(t\) \\ \(L(t)\) and \(\Delta L(t)\) & The Lyapunov function and the Lyapunov drift at time slot \(t\) \\ \(V\) & The control parameter \\ \hline \hline \end{tabular}
\end{table}
Table 1: _Cont._  
\begin{table}
\begin{tabular}{l c} \hline \hline
**Simulation Parameters** & **Value** \\ \hline The threshold of the SIR, \(\theta\) & 5 \\ The path loss factor, \(\alpha\) & 4 \\ The transmit power of the MBS, \(P^{M}\) & 10 w \\ The transmit power of the VU, \(P^{V}\) & 3 w \\ The threshold of the re-allocation rate, \(\gamma\) & 0.2 \\ The length of each slot, \(\Delta t\) & 10 ms \\ The velocity of the platoon and MU & 40 km/h \\ The length of the road & 2000 m \\ The maximum data arrival rate of the VUs, \(a^{\max}\) & 1 packet/slot \\ The minimum data arrival rate of the VUs, \(a^{\min}\) & 0.1 packet/slot \\ The number of MUs, \(N^{M}\) & 2 \\ The threshold of the ratio of the interference from the MBS to the interference from the other platoons, \(\beta\) & 1 \\ The window of the service-guaranteed user, \(W\) & 10 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Simulation parameters.  
The parameters including \(N\), \(\theta\), \(\alpha\), \(P^{M}\), \(P^{V}\), \(\gamma\), and \(\Delta t\) refer to those in References [22; 23].