# A Preemptive-Resume Priority MAC Protocol for Efficient BSM Transmission in UAV-Assisted VANETs
## 3 System Model
### Ground-Bound Vehicular Traffic Model  
This paper assumes that the considered segment D represents a low- to moderate-density free-flow ground transportation system. Such a transportation system has been widely applied in the literature. The macroscopic free-flow traffic model used in this study is based on Ref. [43]. Because the communication range of UAVs under the V2I scenario in a highway depends on multiple factors, including the frequency, power, antenna gain of its communication system, as well as environmental conditions, the communication range can vary from several hundred meters to several kilometers based on different UAV communication systems and specific configurations. Additionally, assuming a constant velocity can help study the worst-case scenario in V2I. Therefore, we assume that after each vehicle k reaches position \(x_{0}\), its velocity remains unchanged at the speed at position \(x_{0}\) until it exits the communication range of the UAV, \(\mathrm{v_{f}}\in[\mathrm{v_{min}},\mathrm{v_{max}}]\). We assume that the number of vehicles follows a Poisson distribution, and the vehicle density is \(\lambda_{v}\). The premise of our study is that the vehicle density is not high, as in the case of high vehicle density, and it is highly likely to find multiple vehicle-UAV paths for connection, which does not align with our design approach. We focus on the worst-case scenario, aiming to minimize the number of paths. In this scenario, each time a vehicle enters the communication range of a UAV, it needs to be processed individually. Additionally, we assume that the VANET includes a location service, such as Hierarchical Location Service (HLS) or Geographic Location Service (GLS), and the information related to the location service is included in the header of the transmitted data packets. We divide a time window \(\tau\) into several equal intervals \(\Delta t\). Since the traffic flow follows a Poisson random process with the parameter \(\mathrm{\lambda_{v}}\), the arrival time of vehicles is also a random variable denoted as \(\Delta t_{v}\) and follows an exponential distribution with the parameter \(1/\mathrm{\lambda_{v}}\). Assuming that there is one vehicle arriving at the entrance point \(\mathrm{x_{0}}\) in each time interval \(\Delta t_{v}\), the average value and probability density function (pdf) [44] of the vehicle arrival time can be written as follows:  
\[E[\Delta t_{v}]=\
icefrac{{1}}{{\lambda_{v}}}, \tag{1}\]  
\[f_{\Delta t_{v}}(t)=(\
icefrac{{1}}{{\lambda_{v}}})e^{-\
icefrac{{1}}{{ \lambda_{v}}}}. \tag{2}\] \begin{table}
\begin{tabular}{c c} \hline
**Notion** & **Definition** \\ \hline \(\mathrm{P_{k}}\) & The transmission power of vehicle k \\ \(\mathrm{I_{C}},N_{0}\) & Co-channel interference and Gaussian white noise \\ \(\mathrm{W_{up}}\) & A constant representing the total available bandwidth of the uplink path \\ \(\mathrm{R_{ku}}\) & The transmission rate of vehicles in the G2A channel \\ \(\mathrm{T_{ku}}\) & The time required to transmit a data packet \\ \(\mathrm{\beta}\) & Packet size \\ \(W_{j}\) & The corresponding contention window size \\ \(p\) & Collision probability \\ \(q\) & The probability that the cache queue is not empty \\ \(m\) & Maximum backoff stage \\ \(\tau\) & The transmission probability of the user in a random time slot \\ \(\mathrm{P_{s}}\) & The probability of detecting a busy channel due to successful \\  & transmissions from other stations \\ \(\mathrm{P_{idle}}\) & The probability of the channel being idle \\ \(\mathrm{T_{s}}\) & The duration of a successful transmission \\ \(\mathrm{T_{c}}\) & The duration of detecting channel busyness due to collisions \\ \(\sigma\) & The duration of an idle system time slot \\ \(\mathrm{p_{i}}\) & The system utilization for priority i \\ \hline \end{tabular}
\end{table} 
Table 2: _Cont._The speed \(v_{f}\) at point \(x_{0}\) is a continuous random variable, represented by \(\mu_{v}\) for the mean value and \(\sigma_{v}\) for the standard deviation.