## 3 System Model  
Since the uplink resources are under-utilized compared with the downlink ones [29], we only consider uplink cellular resource allocation.  
As illustrated in Figure 1, an uplink scenario in a single cell system is considered. BS was lying in the center of the cell. The road configuration for vehicular communication is defined as an urban setting [30]. The cell consists of multiple V2I links, denoted as \(M=\{1,\ldots,M\}\) and multiple V2V pairs denoted as \(N=\{1,\ldots,N\}\). In order to improve the spectrum efficiency and ensure the data rate requirements of the V2I links. We assume that each V2I user has assigned one orthogonal subcarrier resource and each V2I user allows more than one V2V pair to share its resource.  
We define the channel power gain of the desired transmission for \(m\)th V2I link and \(n\)th V2V pair on the \(m\)th channel as \(g_{m^{\prime}}^{m}\), \(g_{n^{\prime}}^{m}\). Similarly, let \(g_{m,n}^{m}\) represent the interfering channel power gain from the \(m\)th V2I transmitter to the V2V pair \(n^{\prime}\)s receiver. The interference channel power gain between \(n\)th V2V link and the BS is denoted as \(g_{n,b}^{m}\), and the interference channel gain from the V2 Vpair \(l^{\prime}\)s transmitter to the V2V pair \(n^{\prime}\)s receiver is denoted as \(g_{l,n}^{m}\). In the simulation in this article, all the channel gains mentioned above include path loss, shadow fading, and small-scale fading.  
Then, we can respectively express the signal-to-interference-plus-noise-ratio (SINR) for the \(m\)th V2I link and \(n\)th V2V pair on subcarrier \(m\) as  
\[\gamma_{m}^{m}=\frac{p_{m}g_{m}^{m}}{\sum_{n=1}^{N}\rho_{n}^{m}p_{n}g_{n,b}^{m }+\sigma^{2}} \tag{1}\]  
\[\gamma_{n}^{m}=\frac{p_{n}g_{n}^{m}}{\sum_{l^{\prime}\
eq n}^{N}\rho_{l}^{m}p_ {l}g_{l,n}^{m}+p_{m}g_{m,n}^{m}+\sigma^{2}} \tag{2}\]  
where \(p_{m}\), \(p_{n}\), \(p_{l}\) denotes the transmit powers of the \(m\)th V2I, \(n\)th V2V pair, and \(l\)th V2 Vpair. \(\rho_{n}^{m}\) is the subcarrier access indicator, \(\rho_{n}^{m}\in\{0,1\}\), \(\rho_{n}^{m}\)\(=1\) if \(n\)th V2V pair is allowed to use subcarrier \(m\), otherwise, \(\rho_{n}^{m}=0\). \(\sigma^{2}\) indicates the noise power.  
Furthermore, to reduce interference between V2V links, we assume each V2V link can only access one V2I link resource. Accordingly, the sum data rate of \(m\)th V2I link and \(n\)th V2V pair on subcarrier \(m\) can be respectively given by  
\[R_{m}^{m}=\log_{2}(1+\gamma_{m}^{m}) \tag{3}\]  
\[R_{n}^{m}=\log_{2}(1+\gamma_{n}^{m}) \tag{4}\]  
Figure 1: System model for vehicular communication underlaying cellular network in uplink.  
We model the latency requirements of V2V links as the successful delivery of packets of size L within a limited time budget T\({}_{\max}\). Therefore, if the following constraint holds, the latency requirements of a V2V link will be satisfied:  
\[\Pr\left\{\sum_{t=1}^{T_{\max}}\sum_{m=1}^{M}\rho_{n}[m]R_{n}^{m}[t]\geq\
icefrac{{ L}}{{\Delta T}}\right\} \tag{5}\]  
where \(\Delta T\) is channel coherence time, and the index \(t\) is added in \(R_{n}^{m}[t]\) to indicate the capacity of the \(n\)th V2V link at different coherence time slots.