## 2 Packet Loss Model  
The channel-based packet loss model is introduced in this section. In the study of network packet loss, it is difficult to reproduce the actual network packet loss environment, so it is very important to find an effective prediction model for simulating the network environment with a specified packet loss rate. In most cases, there is no packet loss in the network. Once a packet is lost, the continuous packet loss may happen. This burst packet loss is closer to the real network transmission environment. In this paper, we use the discrete Gilbert Elliott channel (GEC) model [28; 29] to simulate burst packet loss. This model assumes that binary bit stream is transmitted in the channel. As shown in Figure 1, this model assumes that the channel has two states, that is, good state (G) and bad state or burst (B). For states G and B, the probabilities of remaining in the same states are (\(1-\mathrm{P}\)) and (\(1-\mathrm{Q}\)), respectively, where P is the probability of transition from state G to B, and Q is the probability of transition from state B to G. When the channel is in a certain state, the number of continuous packet loss follows the geometric distribution, that is, the probability of continuous transmission of j packets with good or bad state of the channel is (\(1-\mathrm{P}\))\({}^{j-1}\mathrm{P}\) or (\(1-\mathrm{Q}\))\({}^{j-1}\mathrm{Q}\). It can be deduced that in a good state (G) or a bad state (B), the average number of the transmitted packets is  
\[\sum_{j=1}^{\infty}{(1-\mathrm{P})^{j=1}\mathrm{P}\cdot j}=1\Big{/}\mathrm{P} \tag{1}\]  
or  
\[\sum_{j=1}^{\infty}{(1-\mathrm{Q})^{j-1}\mathrm{Q}\cdot j}=1\Big{/}\mathrm{Q} \tag{2}\]  
Figure 1: [PERSON] channel (GEC) model. Therefore, the probability that the channel is in a good state (G) or a bad state (B) is  
\[\mathrm{P(B)}=\frac{1\Big{/}\mathrm{Q}}{1\Big{/}\mathrm{P+1}\Big{/}\mathrm{Q}}= \frac{\mathrm{P}}{\mathrm{P+Q}} \tag{3}\]  
\[\mathrm{P(G)}=\frac{1\Big{/}\mathrm{P}}{1\Big{/}\mathrm{P+1}\Big{/}\mathrm{Q}}= \frac{\mathrm{Q}}{\mathrm{P+Q}} \tag{4}\]  
In fact, in an actual network packet loss environment, when the channel is in a good state, packet loss may occur, or when the channel is in a bad state, packet loss may not occur. Therefore, in order to move closer to an actual environment, as shown in Figure 2, it is supposed that the probability of packet loss in the good state G or bad state B is \(\mathrm{P_{G}}\) or \(\mathrm{P_{B}}\). In summary, the calculation formula of the packet loss rate (PLR) can be determined as follows:  
\[\mathrm{PLR} =\mathrm{P(G)}\mathrm{P_{G}}+\mathrm{P(B)}\mathrm{P_{B}} \tag{5}\] \[=\frac{\mathrm{Q}}{\mathrm{P+Q}}\mathrm{P_{G}}+\frac{\mathrm{P}}{ \mathrm{P+Q}}\mathrm{P_{B}}=\frac{\mathrm{Q}}{\mathrm{P-\gamma}}\mathrm{P_{G} }+\frac{\mathrm{P}}{\mathrm{1-\gamma}}\mathrm{P_{B}},\]  
where \(\gamma=1-(\mathrm{P+Q})\) represents the characteristics of random packet loss or burst packet loss in the channel. When \(\gamma\) is close to 0, it indicates that the channel packet loss is random packet loss, and when \(\gamma\) is close to 1, it indicates that the channel packet loss is burst packet loss. When the channel is in a good state, the probability of packet loss (\(\mathrm{P_{G}}\)) is low, and when the channel is in a bad state, the probability of packet loss (\(\mathrm{P_{B}}\)) is high. Thus, the values of \(\mathrm{P_{G}}\) and \(\mathrm{P_{B}}\) need reasonable ranges [30]. It is known from the literature that \(\mathrm{P_{G}}\) and \(\mathrm{P_{B}}\) follow the constraints \(0\leq\mathrm{P_{G}}<\mathrm{P_{B}}\leq 0.5\). In this paper, the special values \(\mathrm{P_{G}}=0\) and \(\mathrm{P_{B}}=0.5\) are used. This is related to the fact that when the channel is in a good state, there will be no packet loss in the channel, that is, \(\mathrm{P_{G}}=0\). When the channel is in a bad state, the packet loss in the channel is in a completely uncertain state. Considering the principle of equivalent possibility, \(\mathrm{P_{B}}\) is set to 0.5.