## 3 Dynamic Algorithm of Resource Re-allocation
### Implementation of the Proposed Resource Allocation Scheme and Its Overhead  
In summary, the implementation of the proposed resource allocation scheme can be described as follows. First, at the beginning of each time slot, the MBS broadcasts information on the geographical location and channel occupation of all MUs to each platoon leader, and the members send the interference strength, the signal strength, the length of queue, and the data arrival rate to the corresponding platoon leader. Second, each platoon leader calculates \(\delta_{nk}(t)\) and \(\xi_{nk}(t)\) for each member. Lastly, according to the information including \(z_{n}\left(t-1\right)\), \(Q_{n}\left(t-1\right)\), \(a_{n}\left(t-1\right)\), \(R\left(t-1\right)\), \(\delta_{nk}(t)\), and \(\xi_{nk}(t)\), each platoon leader determines \(\mathbf{X}\) by solving the optimization problem in Equation (30) and allocates the channel to members. Therefore, the signaling overhead in the proposed scheme consists of two parts. The first part is the information of MUs transmitted by the MBS to the platoon leader, which includes the geographical location and channel occupation. The second part is the information of VUs transmitted by members to the platoon leader, which includes the interference and the signal strength, the length of queue, and the data arrival rate.  
A summary of notations in this paper is presented in Table 1.  
\begin{table}
\begin{tabular}{c l} \hline \hline
**Notations** & **Meaning** \\ \hline \(\Phi\) & The set of platoons \\ \(\lambda\) & The density of platoons \\ \(\mathcal{N}\) & The set of vehicles in a platoon \\ \(N\) & The cardinality of \(\mathcal{N}\) \\ \(\mathcal{K}=\left\{1,\ 2,\ \ldots,\ K\right\}\) & The set of orthogonal channels \\ \(N^{M}\) and \(N^{P}\) & The number of microcell users (MUs) and the number of platoons \\ \(\theta\) & The threshold of the signal-to-interference ratio (SIR) \\ \(p^{M}\) and \(p^{V}\) & The transmit power of the microcell base station (MBS) and the transmit power of the \\  & vehicle user (VU) \\ \(\alpha\) & The factor of the path loss \\ \(n\) & The member in the platoon \\ \(I_{nk}^{MV}\) & The interference from the MBS to member \(n\) in the platoon in channel \(k\) \\ \(\delta_{k}^{MV}\) & The small-scale fading from the MBS to member \(n\) in the platoon in channel \(k\) \\ \(d^{MV}\) & The distance between the MBS and the platoon \\ \(p^{M}\) & The probability of a channel being occupied by an MU \\ \(I_{nk}^{VV}\) & The aggregated interference from the other platoons to member \(n\) in the platoon in channel \(k\) \\ \(g_{ak}^{VV}\) & The small-scale fading from the VU interferer \(q\) to member \(n\) in the platoon in channel \(k\) \\ \(d_{q}^{VV}\) & The distance between the VU interferer \(q\) and the platoon \\ \(I_{nk}^{VV}\) & The total aggregated interference from the MBS and the other platoons to member \(n\) in the platoon in channel \(k\) \\ \(SIR_{mk}^{V}\) & The SIR of member \(n\) in the platoon in channel \(k\) \\ \(g_{nk}^{V}\) & The small-scale fading from the corresponding transmitter to member \(n\) in the platoon in channel \(k\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Summary of notations.