## 2 System Model
```
Input: Service Arrival Event Output: Successful Service Transmission or Backoff Retry repeat ifService arrivesthen  Generate access information;  Perform access control;  Send access request to the access point; ifACK indicates no collisionthen  Establish transmission link;  Transmit service data; returnService transmitted successfully; else  ACK indicates collision occurred  end if  Calculate random backoff time \(T_{\text{backoff}}\leftarrow\text{Random}(1,W)\); //\(W\)is the current backoff window size Wait for \(T_{\text{backoff}}\) time units;  Update backoff window \(W\leftarrow\min(2W,W_{\text{max}})\); else  No message received  end if  Wait for a period of time; untilService is successfully transmitted;
```  
**Algorithm 1**Transmission-control separation algorithm  
As shown in Figure 3, these three types of spectra operate in a discrete-time mode and are composed of superframes, frames, slots, and minislots. The RAS only broadcasts the allocated frequency resources for each ACN at the beginning of the superframe. Since the CAS only needs to exchange identity information and the number of packets on the TTS, the duration of each CAS slot can be much shorter than the TTS slots; therefore, the frames of the CAS are composed of minislots. Within one superframe, the CAS contains \(I\) frames, each consisting of three parts: the first part is for broadcasting access information; the second part is for contention access, consisting of \(N_{\text{C}}\) minislots; the third part is for feedback of access results. The TTS contains \(N_{\text{T}}\) slots. More specifically, each CAS slot lasts \(T_{C}\) milliseconds, each RAS slot lasts \(T_{A}\) milliseconds, and each TTS slot lasts \(T_{T}\) (\(T_{T}>T_{\text{C}}\)) milliseconds. Hereafter, CAS slots will be referred to as minislots. To improve utilization efficiency, the TTS is also divided into  
Figure 3: Frame structure. multiple sub-channels, and each ACN has multiple sub-channels. During the uplink transmission of the CAS, each piece of SUE will randomly select several minislots at the beginning of frame \(i\) and transmit a contention packet over the chosen minislot. In the considered ISAG network, we assume that the SUE of different ACNs can use orthogonal CAS to contend for TTS slots. Since each minislot can support one contention packet, the contention result for each minislot can be success, collision, or idle:  
* Success indicates that one single piece of SUE transmits a contention packet over the CAS slot. The successful SUE transmits the traffic packet over the TTS slots. * Collision indicates that more than one piece of SUE transmits contention packets over the CAS slot. The collided pieces of SUE need to re-compete for another CAS slot in the next frame and store the traffic packets until no collision occurs over the chosen CAS slot. * Idle indicates that no SUE transmits contention packet over the CAS slot. Assume that the arrival of traffic packets from SUE is an independent Poisson process. The total arrival rate of pieces of SUE controlled by an ACN in frame \(i\) is denoted by \(\lambda_{i}\). To control the number of pieces of SUE gaining access in each frame, each piece of SUE has a probability \(P_{i}\) of being allowed to access in frame \(i\). \(m\) represents the number of pieces of SUE contending for access, and \(n\) represents the number of resources being contended for. The access load of an ACN in frame \(i\) is defined as  
\[G_{i}=\frac{m}{n}=\frac{M_{i}P_{i}}{N_{C}}. \tag{1}\]