## 3 Markov Modeling Analysis of IEEE 802.11 Operations  
In this section, we will improve the model by adding the ICS procedure based on the Bianchi model [7]. i.e., if the node senses that the previous data frame has been successfully received and the channel is idle for a DIFS, the node will directly send a new data frame, which the process of the new data frame waits for sending is called the ICS procedure. As shown in Table 1, to further illustrate the difference between the proposed model and the original Bianchi model, we briefly summarize it, and we assume that after the node successfully transmits the previous frame, the node has a new data frame waiting to be sent (the successful transmission of the previous data frame can be seen in Figure 1). Obviously, the proposed model does not need to enter the backoff procedure after successfully transmitting the previous frame but directly starts the ICS procedure, which greatly reduces the idle time of the channel. This work can not only reduce the service delay of the network but also reduces the waste of the bandwidth so as to improve the network throughput and  
Figure 1: RTS/CTS transmission in the proposed model. channel utilization. In particular, a low delay and high throughput are the desired goals when the network is loaded with large amounts of emergency traffic. Next, we assume that the channel condition is a single-cell environment with n terminals. The channel has no defects, i.e., the data frames' collision (probability \(p\)) is the only factor that causes transmission errors. Furthermore, the terminal is always in three states, i.e., the transmission, ICS, or backoff procedure. Letting \(X(t)\) denote the state of the transmit queue at time \(t\), we can obtain:  
* the backoff state, \(X(t)=\{(i,\ k)|0\leq i\leq m,0\leq k\leq W_{i-1}\}\), where \(i\) denotes the value of the backoff stage, and \(k\) is the value of the backoff counter of the data frame at the head-of-line (HOL);
* The ICS state, \(X(t)=\{(-1,\ \sigma)|\sigma=0,\ 1,\ 2,\ \ldots,\ D\}\), where \(D=DIFS/\delta\), and \(\delta\) is a time slot length. The state means that the channel is sensed to be idle for the \((D-\sigma)*\delta\) period during the ICS procedure;  
Next, we obtain the state transition diagram (Figure 2) of the 2-D Markov chain, which considers all the major factors. The corresponding one-step transition probabilities are as follows (where \(p_{b}\) is the probability that the channel is busy): \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Markov Model** & **Channel State** & \begin{tabular}{c} **Terminal** \\ **Transmission Status** \\ \end{tabular} & \begin{tabular}{c} **Next MDPU** \\ **(The Legend is Shown** \\ **on the Right)** \\ \end{tabular} \\ \hline Bianchi model & \
\begin{tabular}{c} Busy \\ \end{tabular} & Backoff \\ \hline  & Idle & Backoff \\ \hline Proposed model & Busy & Backoff \\ \hline  & Idle &
\begin{tabular}{c} Initial carrier-sensing \\ (ICS) \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of transmission procedure between Bianchi model and proposed model in the 802.11 DCF protocol. 1. For \(0\leq i\leq m\), there are the following three state transitions: if the HOL data frame is successfully transmitted, start the backoff procedure: \[P(0,k|i,0)=\frac{(1-p)\times p_{b}}{W_{0}},0\leq k\leq W_{0}-1.\] (1) If the HOL data frame is unsuccessfully transmitted, the frame is retransmitted, resulting in an increase in the backoff stage: \[P(i,\ k|i-1,0)=\frac{p}{W_{i}},0\leq k\leq W_{i}-1.\] (2) If the HOL data frame is successfully transmitted and the channel is sensed to be idle for a DIFS, the ICS procedure is initiated: \[P(-1,D|i,0)=(1-p)(1-p_{b})\] (3)
2. For the case of \(0\leq\sigma\leq D\) during the ICS procedure: if the channel is sensed to be idle for a time slot, the counter decreases by one: \[P(-1,\sigma-1|-1,\sigma)=(1-p_{b})\] (4) If the channel is sensed to be busy, the backoff procedure is initiated: \[P(0,k|-1,\sigma)=\frac{p_{b}}{W_{0}},0\leq k\leq W_{0}-1.\] (5)
3.