## 3 System Model and Problem Formulation  
We consider concurrent V2I and V2V, based on Mode 3 specified in 3 GPP cellular V2X framework, which consists of multiple RRH and multiple vehicle equipment (VE). The RRHs are deployed at the center of intersections and connected to BBU pool through fronthaul link; the VEs are distributed across the network and move on the roads. The RRHs. In Mode 3, the RRHs allocate communication resources to V2I mode VEs, for the subsequent reuse by V2V mode VEs. A V2I mode VE can interfere with V2V mode VE while multiple V2V mode VEs share the same resources. The total VE set can be expressed as \(\mathbb{U}\), and consists of a V2I VE set \(\mathbb{C}\) and a V2V VE set \(\mathbb{V}\). We denote the set of RRHs as \(\mathbb{S}\) within the total available bandwidth \(W^{total}\). The total bandwidth \(W^{total}\) is divided into \(\mathbb{K}\) resource block (RB)s, allocated to each V2I VE. The used symbols are summarized in Table 1.  
In V2V communication, it is imperative to ensure stringent latency and reliability requirements when safety-critical messages are being transmitted. However, it is difficult to formulate the latency and reliability requirements as constraints of the optimization problem. Therefore, according to [PERSON]'s law, the latency requirement is converted into data queue length, and the reliability requirement is converted into outage probability [18]. The outage probability is defined as the probability that the signal to interference plus noise ratio (SINR) of the VEs is lower than the predefined SINR threshold [19]. Increasing the outage probability results in packet loss, and reveals re-transmission occurrence leading to reduced reliability. When reusing cellular resources, there is mutual interference between V2I and V2V communication. Thus, the SINR is derived to consider the interference between V2I and V2V communication. The SINR of \(c\)th V2I VE at the \(k\)th RB is  
\[\gamma_{k}^{c}=\frac{p_{tr}^{0}\cdot g_{k}^{sc}}{N+\sum_{v\in V}p_{k}^{v}\cdot g _{k}^{cv}+\sum_{f\in V,j\
eq v}p_{tr}^{0}\cdot g_{k}^{v^{c}c}} \tag{1}\]  
where \(p_{tr}^{0}\) is the transmission power of RRH; \(g^{sc}c_{k}\) is the channel gain between the V2I VE \(c\) and the associated RRH \(s\) on \(k\)th RB. \(N\) is the noise power spectral density and \(p_{k}^{v}\) is the transmission power of V2V VE \(v\) at the \(k\)th RB. The SINR of V2V VE \(v\) at the \(k\)th RB is  
\[\gamma_{k}^{v}=\frac{p_{k}^{v}\cdot g_{k}^{cv^{\prime}}}{N+p_{k}^{c}\cdot g_{ k}^{cv}+\sum_{f\in V,j\
eq v}p_{k}^{j}\cdot g_{k}^{v^{c}}} \tag{2}\]  
where \(p_{k}^{v}\) is the transmission power of V2V VE \(v\) at the \(k\)th RB. The total system capacity is  
\[R=W^{total}\cdot\sum_{c\in\mathbb{C}}\sum_{k\in\mathbb{K}}\Biggl{\{}log_{2}(1 +\gamma_{k}^{c})+\sum_{v\in\mathbb{V}}log_{2}(1+\gamma_{k}^{v})\Biggr{\}} \tag{3}\]  
where \(W^{total}\) is the system bandwidth. Only the power consumption of the RRHs and the associated fronthauls were considered. The macro BS is only involved in voice services; hence, its energy consumption is disregarded. The power consumption model of RRH is  
\[P_{\mathbb{S}}=\sum_{s=1}^{\mathbb{S}}\left(\pi_{\mathbb{S}}+\Delta slope\sum_{c =1}^{\mathbb{C}}a_{c}^{s}p_{tr}^{0}\right) \tag{4}\]  
where \(\pi_{\mathbb{S}}\) is the circuit power of the RRH, \(\Delta slope\) is the slope of load-dependent power consumption of RRH, as reported in [20], and \(a_{c}^{s}\) is the association indicator for V2I VE \(c\)