## 3 Efficient Network AOS Comprehensive Multiplexing Algorithm
### Asynchronous Real-Time Traffic
#### 3.2.2 Virtual Channel Scheduling Algorithm  
In the virtual channel multiplexing layer, this paper proposes a virtual channel scheduling algorithm based on the comprehensive channel status. The algorithm introduces four channel status parameters, including the virtual channel scheduling status, the transmission frame scheduling status, the virtual channel priority status, and the traffic prediction status. Virtual channel scheduling status:  
The virtual channel scheduling status parameter is used to represent the time interval from the last scheduling moment of the virtual channel to the current scheduling moment. According to the virtual channel scheduling principles, the VC scheduling status parameter at the current scheduling moment is determined by the scheduling status at the previous scheduling moment. There are three possible VC scheduling statuses, as follows: no transmission frame (Status 1, 51), a transmission frame available and scheduled (Status 2, 52), and a transmission frame available but not scheduled (Status 3, 53). Let \(s_{s\_j}(r,k)\) denote the VC scheduling status at the previous scheduling moment of \(\left(r,k\right)_{sche}\). Then, the virtual channel scheduling status parameter at the \(\left(r,k\right)_{sche}\) scheduling moment for the \(j\)-th VC is expressed as follows:  
\[U_{s1\_j}(r,k)=\left\{ \begin{array}{c}0,\quad\quad\quad s_{s\_j}=S1\;or\;s_ {s\_j}=S2\\ \\ U_{s1\_j}(r-1,K-1)+1,\quad r>0,k=0\;and\;s_{s\_lj}=S3\\ \\ U_{s1\_j}(r,k-1)+1,\quad r\geq 0,k>0\;and\;s_{s\_lj}=S3\end{array} \right. \tag{6}\]  
where \(K\) represents the number of scheduling slots in a scheduling cycle, which is defined in the multiplexing model parameters presented in Section 2. Transmission frame scheduling status:  
The transmission frame scheduling status parameter is used to represent the accumulated waiting time of the first data frame in the VC buffer. This is measured based on the waiting time of data frames in the current VC. Let \(t_{s\_aj}\) denote the arrival time of the first data frame in the current VC. Then, at the \((r,k)_{sche}\) scheduling moment, the waiting time interval for the current frame is given by the following:  
\[t_{s\_aj}(r,k)=(r\cdot K+k)\Delta t-t_{s\_aj} \tag{7}\]  
where \(K\) represents the number of scheduling slots in a scheduling cycle and \(\Delta t\) represents the occupied time of a scheduling slot, which are defined in the multiplexing model parameters presented in Section 2. Converting the time into the measurement of scheduling slots, the transmission frame scheduling state parameter for the \(j\)-th VC is defined as follows:  
\[U_{s\_aj}(r,k)=\frac{t_{s\_aj}(r,k)}{\Delta t}=\frac{(r\cdot K+k)\Delta t-t_{s \_aj}}{\Delta t} \tag{8}\]  
Traffic prediction status:  
The traffic prediction status parameter is used to represent the predicted data arrival volume for the current scheduling cycle. By employing a certain traffic prediction method, the traffic arrival for the next scheduling cycle is forecasted at the scheduling moment \((r,0)_{sche}\). For the \(j\)-th VC, the actual amount of data arriving in each scheduling slot from \((r,0)_{sche}\) to \((r,K-1)_{sche}\) is statistically accumulated. Let \(a_{s\_j}(r,k)\) denote the traffic that arrives at the \((r,k)_{sche}\) scheduling moment. Then, the traffic prediction status parameter for the \(j\)-th VC is expressed as follows:  
\[U_{s\_j}(r,k)=\left\{ \begin{array}{ll}\frac{p_{s\_j}(r)}{V},&k=0\\ U_{s\_j}(r,k-1)-\frac{a_{s\_j}(r,k)}{V},&0<k\leq K-1\end{array} \right. \tag{9}\]  
where \(p_{s\_j}(r)\) is defined in the frame generation algorithm presented in Section 3.2.1 and \(V\) is defined in the multiplexing model parameters presented in Section 2. Virtual channel priority status:  
The virtual channel priority status parameter is used to represent the priority of data transmission for the VC. Let \(m_{s\_j}\) denote the scheduling priority of virtual channel \(j\), which is specified by the specific application based on the criticality of the data.