## 2 Analysis of IEEE 802.11 DCF Mechanism and Modeling Ideas  
The basic operating principle of the 802.11 DCF mechanism is that the node should sense the channel activities before sending a data frame [25]. The channel is usually busy or idle, so the node sensing channel activities are divided into two situations: (1) If the channel is sensed to be idle for a DCF interframe space (DIFS), the data frame will be sent. (2) If the channel is sensed to be busy, the node will continuously sense the channel until it becomes idle for a DIFS. At this moment, in order to avoid collisions as much as possible, the nodes will generate a random backoff interval that follows the binary exponential backoff algorithm. That is, when a node tries to transmit a data frame, the backoff timer (or the backoff counter) is uniformly chosen in the range of \(t\in(0,W_{i}-1)\), and the backoff window length in the \(i\)-th backoff stage is \(W_{i}=2^{i}\times W_{0}\), \(0\leq i\leq m\). When the first attempt to send is made, the backoff window's original length is \(W_{0}=W_{min}\), and after each failed attempt to send, the backoff window length is two times that of the previous one until the maximum backoff stage is reached, \(W_{m}=W_{max}\). During the backoff, whenever the node senses that the channel is idle for a slot time, the backoff counter is decremented by one, and the node cannot send data frames until it decrements to zero. It should be noted that nodes send data frames only at the beginning of each slot time, where the time slot length is the time required by any node to sense the farthest node transmission. Furthermore, the value of the DIFS can be expressed as \(T_{DIFS}=DIFSN\times\delta+T_{SIFS}\), where \(DIFSN\), \(\delta\), and \(T_{SIFS}\) stand for the DIFS number, a time slot length, and a SIPS length, respectively. The DCF has two transmission modes [26]. In the basic mode, after the data frame is sent, its successful reception is confirmed by the receiving node sending an acknowledgment (ACK) frame. Additionally, if no ACK frame is received, it will go through a backoff procedure and start to retransmit. This mode does not solve the problem of conflicts that may be caused by hidden nodes. However, the ready-to-send (RTS)/clear-to-send (CTS) transmission mode avoids the conflicts caused by the hidden nodes during transmission [11]. Its main principle is to control the transmission status of the node (transmitting data or in the backoff procedure) using the transmitting data frames' information carried by the RTS/CTS frames. Therefore, we mainly discuss the RTS/CTS transmission mode. The main feature of this mode is that before sending data frames to the receiving node B, the sending node A must send the RTS frames to make a reservation channel and to inform the other nodes, except node B, to postpone sending while node B will send the CTS frames to node A after receiving the RTS frames. The specific transmission process is shown in Figure 1.  
In order to describe the service delay's behavior more accurately in real WLANs, different from existing research, this paper comprehensively considers the following four major factors to build a system model:  
1. ICS procedure: If a new data frame arrives when the channel is idle, the frame will start the ICS procedure, i.e., if the channel is idle for a DIFS, the data frame will be transmitted immediately at the end of the DIFS without entering the backoff procedure. Otherwise, if the channel is detected to be busy during the DIFS, the data frame will enter the backoff procedure;
2. Backoff counter freezing: When the channel is sensed to be busy, the backoff counter will pause its decrementing process. Once the channel is sensed to be idle, the backoff counter will be activated again to continue its decrement procedure;
3. Up-to-date standard parameters: to make our model suitable for the real network environment, some parameters need to be updated, including the DIFS, SIFS, time slot length, retransmission limit, and contention window size, and so on;
4.