## 3 Collision Probability Analysis
So, the received power \(P_{r}(d_{1-2})\) can be calculated by  
\[P_{tr}(d_{1-2})=P_{r}+PL(d_{1-2})+P_{sd} \tag{9}\]  
where \(P_{t}r\) = power from transmitting node;  
\(P_{r}\) = power from receiving node;  
\(PL(d_{1-2})\) = path loss in between UE1 and UE2;  
\(P_{sd}\) = power from shadowing. Interference caused by the transmission range, \(I_{tr}(d_{1-2})\), can be calculated by  
\[I_{tr}(d_{1-2})=P(T_{tr}|T_{U_{tr}})\]0  
where \(fP_{tr}(d_{1-2})(\rho_{tr})\) represents the probability of transmitted power between distance \(d_{1}\) and \(d_{2}\). The threshold value is \(Th_{tr}\). Now, if we consider a normal distribution with a mean of 0 and a standard deviation \(\sigma\) = 1 in an urban area, \(I_{tr}(d_{1-2})\) becomes  
\[I_{tr}(d_{1-2})=P(T_{tr}|T_{U_{tr}})\]1  
* \(I_{col}(d_{1-2})\) calculation: In this scenario, there are two possibilities: 1. The probability of UE1 and UE2 selecting the same RBs. In that case, the packet will drop. 2. Probability of simultaneous RB selection, \(P_{sim}(d_{(1-2)})\): \[I_{tr}(d_{1-2})=P(T_{tr}|T_{U_{tr}})\]2 (12) where \(P_{overlap}\) is the probability of the \(T_{a}\) time becoming overlapped by both UE1 and UE2 but not sharing the allocated time. \(P_{Shared|overlap}\) is the probability of both getting the same allocated time given that they are overlapped. \(T_{c}\) is the number of time slots both UEs are sharing in a particular RB. \(T_{c}(avg)\) is the average number of allocation time slots that are used in a particular RB. \(P_{overlap}\) can be calculated by  
\[I_{tr}(d_{1-2})=P(T_{tr}|T_{U_{tr}})\]3  
\(T_{g}-T_{a}+1\): This part of the equation calculates the time window during which a packet can potentially make a Transmission Attempt. It considers the time difference between successive packet generations (\(T_{g}\)) and the allocation time (\(T_{a}\)) plus 1 to account for the starting point. \(100\cdot 2^{N}\): This part accounts for the total number of vehicles (N) in the network and each vehicle is transmitting 100 packets. So there will be \(100\cdot 2^{N}\) combination of packets. RRI: The Resource Reservation Interval represents the duration within which vehicles can make reservations for resource allocation [7; 31]. By dividing the time window during which Transmission Attempts can occur (Tg \(-\) Ta + 1) by the product of \(100\cdot 2^{N}\) and the Resource Reservation Interval (RRI), you obtain the probability (Poverlap) that two vehicles will attempt to transmit within the same time window. \(P_{Shared\left|overlap\right. }\) can be calculated by  
\[I_{tr}(d_{1-2})=P(T_{tr}|T_{U_{tr}})\]4  
where \(T_{sub-ch}\) is the number of total sub channel time slots, \(T_{sh-res}\) is the average number of shared time slots, and \(T_{t}\) represents total time slots [32]. \(T_{sub-ch}.T_{sh-res}\): This part of the equation calculates the product of two terms. The first term \(T_{sub-ch}\) represents the total subchannel time slots and the second term \(T_{sh-res}\) represents the average number of shared time slots. This product reflects the total number of possible combinations, where both vehicles share the same time slots. \((\frac{T_{sub-ch},T_{sh-res}}{T_{t}})^{2}\): Squaring the result from the previous step provides the probability that both vehicles will have their allocated time slots overlapping. This is the probability that two randomly selected time slots, chosen independently, are shared by the vehicles. \(P_{Shared\left|overlap\right. }\) quantifies the likelihood that in an overlapping scenario, both vehicles will get their individual, non-overlapping time slots within a sub-channel. \[I_{tr}(d_{1-2})=P(T_{tr}|T_{U_{tr}})\]5  
For both, UEs perform reselection within one RRI of each other. Thus, we can input the values from Equations (13)-(15) to Equation (12). We start with the following base expression:  
\[I_{tr}(d_{1-2})=P(T_{tr}|T_{U_{tr}})\]6  
Substitute the derived expressions for \(P_{overlap}\) and \(P_{Shared\left|overlap\right.