## 3 Experiments and Results
### Satellite Network Delay Prediction Based on GMACC  
In most ground network research, the network delay is directly measured, but in the large-scale propagation space of a satellite network, the time difference between the measured delay and the actual delay cannot be ignored. If the measured delay is used in a link-switching mechanism, remote control, and other scenarios, the accuracy of these algorithms is reduced, so it is necessary to predict the delay of the satellite network in these scenarios. In this paper, the autoregressive (AR) model was used to model the time series of the satellite network delay, and the adaptive filter was used to estimate the model parameters, so as to predict the network delay. Generally speaking, the satellite network delay includes four parts: processing delay, queuing delay, transmission delay, and propagation delay. Figure 5 shows the components of the delay in the satellite network. The processing delay includes the time that the node checks the packet header and determines how to send or process the packet according to the packet header information, as well as the time to check whether the packet is misplaced, etc. The processing time is usually negligibly small. The transmission delay refers to the time required for the router to send packets onto the wire. The time is related to the length of the packets and the speed of the router to send packets. According to the actual packet length and network bandwidth parameter level, the transmission delay is small, and accounts for a low proportion in the overall network delay. The propagation delay refers to the time spent by an electromagnetic wave carrying data information going through the propagation channel, which can be calculated by dividing the channel length by the propagation rate of the electromagnetic wave in the channel. In the long-distance and dynamic channel of a satellite network, the influence of the propagation delay is obvious, while in the medium- and short-distance channel of a ground network, the influence of the propagation delay on the overall delay is limited. In most networks, the queuing delay accounts for a high proportion of the total network delay and is the decisive factor of the network delay variation. The queuing delay refers to the time that a packet is waiting to be sent in the router queue after it arrives at the router. For a specific packet, the queuing delay depends on the length of the queue in which the packet is located and the speed at which the router processes and sends the packet. For a specific queue, the queuing delay depends on the arrival strength and distribution characteristics of packets. Studies have shown that if there are 10 IP packets queued by 10 routers on average, the queuing delay on this path can reach hundreds of milliseconds [37; 38]. Figure 4: Theoretical and simulated steady-state EMSEs with different variances. In most time series analyses, an AR model or autoregressive moving average (ARMA) model and autoregressive integrated moving average (ARIMA) are very useful models, which can well reflect the autocorrelation of time series and is very suitable for modeling the time series of the network delay or its differential variation [39; 40]. In this paper, considering that the delay time series may not satisfy the stationary condition, we refer to the idea of ARIMA, and take the first-order difference of the network delay time series to build the AR model. The AR model of the satellite network delay can be expressed as  
\[y_{k}=\Phi_{k}^{\mathrm{T}}\Gamma_{k}+v_{k}=\sum_{n}^{i=1}a_{ki}\tau_{k-i}+v_{ k}, \tag{38}\]  
\[\epsilon_{k}=\tau_{k}-y_{k}, \tag{39}\]  
where \(n\) is the order of the AR model, \(\Phi_{k}=[a_{k1},a_{k2},\cdots,a_{kn}]^{\mathrm{T}}\) is the weight vector or the system parameter of the model, and \(\Gamma_{k}=[\tau_{k-1},\tau_{k-2},\cdots,\tau_{k-n}]^{\mathrm{T}}\) is the measured value of a continuous \(p\) delay before time \(k\).