# Distributed Triggered Access for BSM Dissemination in 802.11 bd V2V Networks
## 3 Numerical Analysis  
In this section, we provide the numerical analysis of the proposed DTA scheme. The goal of this section is to obtain the transmission delay of the proposed scheme. In order to do so, we provide the Markov chain analysis of the proposed scheme and the Probability Generating Function (PGF) of the service time of a BSM using M/G/1 queuing model. In this paper, the impact of the mobility of VSTAs is not considered, since VSTAs are almost stationary within one packet transmission time in platooning communication. According to [36], high mobility of nodes (up to 120 mph) has very minor impact on the performance of the one-hop direct message broadcast network with high data rates. Also, in order to concentrate on the effect of the vehicle density and traffic intensity on the delay aspect and packet delivery rate of the proposed scheme, we only considers the packet collision and the hidden terminal effect and neglect the packet error rate as well as the capture effect [37] in this analysis. In this paper, we consider a one-dimensional highway model for our numerical analysis as shown in Figure 4. For inter-VSTA distance, an exponential distribution is applied, assuming that the VSTAs are placed on the line according to a Poisson point process with network density \(\beta\) (in VSTAs per meter). From the definition of Poisson distribution, the probability of j VSTAs existing within length L, \(P(j,\beta L)\), is given by  
\[P_{p}(j,\beta L)=\frac{(\beta L)^{j}e^{-(\beta L)}}{j!} \tag{1}\]  
The IEEE 802.11 specification defines two types of carrier sensing: Preamble Detection (PD) and Energy Detection (ED). A channel is considered busy as PD, when the preamble of a PPDU, e.g., the Short Training Field (STF), is detected by the physical layer of the receiver. If a preamble is detected, the receiving VSTA can obtain necessary information to decode the MAC-layer Protocol Data Unit (MPDU) of the PPDU. Unless the Frame Check Sequence of the MPDU fails caused by the channel error, the transmission is regarded as success. Nevertheless, the received power of a PPDU is not sufficient to detect the preamble, the recipient may be aware of the presence of ongoing transmission on the channel. If an energy is detected and is greater than a threshold value, the receiving VSTA regards the channel as busy and waits until the energy level decreases less than the threshold. Regarding the relationship between the radio range and transmission power, we apply the same approach as described in [24]. Assuming all VSTAs have the same transmission power and receiver sensitivity, the ED range of a transmission, \(L_{ed}\), is greater than the PD range, \(L_{pd}\). By assuming the interference range greater than \(L_{pd}\) and less than \(L_{ed}\), the VSTAs within the region \((L_{ed},2\cdot L_{pd})\)  
Figure 4: One-dimensional highway model. become hidden VSTAs of which the transmission might cause an interference to the tagged VSTAs if the transmission duration is overlapped to each other. Based on the assumption, the average number of VSTAs in the triggering region, \(N_{tr}\), the PD region, \(N_{pd}\), the ED region, \(N_{ed}\), and the hidden region, \(N_{int}\), can be respectively obtained as the following:  
\[ \begin{cases}N_{tr}=2\beta L_{tr}\\ N_{pd}=2\beta L_{pd}\\ N_{ed}=2\beta(L_{ed})\\ N_{int}=2\beta(2L_{pd}-L_{ed})\end{cases}  \tag{2}\]  
In DTA, VSTA can transmit a BSM using two methods: (1) EDCA: the VSTA becomes the TXOP holder by backoff contention and transmits a Trigger frame followed by a BSM transmission using a scheduled RU, (2) Triggered Access: transmitting a BSM in response to a Trigger frame from other VSTAs. Since all transmission sequences are initiated by the EDCA transmission, the backoff procedure needs to be analyzed first. According to the IEEE 802.11 standard, broadcast frames, such as BSM, do not require an acknowledgement from the recipients, so the transmitter cannot determine whether the transmission has succeeded or not.