## 4 Analytical Model for FASBA  
The main focus of the FASBA protocol is to support guaranteed QoS for life-saving emergency nodes during emergency situations. In this work, we considered frame aggregation with a protected Block ACK mechanism. In protected Block ACK (shown in Figure 2a), the sender will transmit a single data packet and wait for an ACK from the recipient before sending an entire data burst. If the ACK message is successfully received, the sender initiates the TXOP period to transmit the data burst. This protected mechanism helps to avoid bulk data loss due to channel error or multi-user channel contention. \begin{table}
\begin{tabular}{c l c} \hline \hline
**Two Bits** & **Purpose** & **Next Packets** \\ \hline
11 & All frame/packet received successfully. Transmit another one & 4, 5, and 6 \\ \hline
01 & Only resend packet 1, (packet #2 and #3 received successfully) & 1, 4, and 5 \\ \hline
10 & Only resend packet 3, (packet #1 and #2 received successfully) & 3, 4, and 5 \\ \hline
00/None & Resend (all three packets) & 1, 2, and 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: FASBA’s simple 2-bit BlockAck algorithm. Figure 1: Illustrating frame aggregation (three packets) and two-bit acknowledgement of FASBA. This section presents an analytical model to evaluate the performance of FASBA. A two-dimensional Markov model is used to derive the throughput and end-to-end delays of successful data transmission with the following assumptions listed in Table 3. The developed Markov model is an extension of the Bianchi model [38] under saturated load conditions. We extend the Bianchi model to accommodate frame aggregation and protected block ACK with error-prone channel conditions. In the 802.11 distributed coordination function (DCF), a station with a new packet performs carrier sensing for distributed inter-frame space (DIFS) period and transmits the packet if the channel is idle. If the channel is busy, the station continues monitoring the channel until it becomes free for the DIFS period. Afterwards, the station generates a random backoff period before sending the packet. In saturation load conditions, each station always has a packet available for transmission after the completion of each successful transmission. Moreover, being that all packets are consecutive, the packet needs to wait for a random backoff time before transmitting. The purpose of the random backoff period is to minimise collisions due to multiple users. Let us consider \(b(t)\) and \(s(t)\) to be the stochastic process representing the random backoff counter and backoff stage, respectively. The value of \(b(t)\) is decremented at the start \begin{table}
\begin{tabular}{l l} \hline Attributes & Value \\ \hline Number of states & Finite \\ \hline Load condition & Saturated \\ \hline Channel condition & Error-prone \\ \hline Hidden terminals & No \\ \hline Packet length & Equal \\ \hline \end{tabular}
\end{table} 
Table 3: Markov model assumptions. Figure 2: Frame aggregation with Block ACK mechanism. of every idle timeslot, and the contending station wins the channel. Then, it reaches zero and can start data transmission according to the basic handshake scheme. To further reduce the chance of collision, the communication parties exchange RTS/CTS control frames to make the surrounding users aware of ongoing communication. The backoff counter value \(k=b(t)\) is chosen from \(k\in[0,CW_{i}]\), where \(CW_{i}\) represents the contention window (CW) size. The collision happens when two stations end up with the same \(b(t)\) values. Therefore, the contention window size starts with a minimum value (\(CW_{min}\)) and doubles after each unsuccessful transmission. The maximum value of the contention window is \(CW_{max}=2m^{{}^{\prime}}CW_{min}=CW_{m}\), where \(m^{{}^{\prime}}\) is a positive integer by which the contention window can be doubled and m is used to represent the maximum backoff stage. The value of \(m\) is also used to bind the retry limit.