# A Hybrid Forecasting Model for Self-Similar Traffic in LEO Mega-Constellation Networks
## 2 Materials and Methods  
Traditional network traffic models are generally derived from Poisson processes, including the Poisson and Markov models [13], which can only describe SRD properties. For satellite network traffic with LRD properties, it is difficult for traditional models to accurately characterize the network. Since the discovery of the self-similarity properties of network traffic in 1994 [14], various self-similarity-based traffic forecasting models have been proposed. One class of models describe the observed traffic by constructing physical models, including ON/OFF models with heavy-tailed distribution [15], \(M/G/\infty\) queuing models [7], etc. Another category is statistics-based models, which attempt to simulate network traffic through data fitting. Statistics-based models mainly include linear models and non-linear models. Linear models, i.e., the autoregressive model (AR), moving average model (MA), autoregressive moving average model (ARMA) and autoregressive integrated moving average model (ARIMA) [8], need to set a variety of parameters based on experience. Linear models are only suitable for short-term forecasting and find it difficult to deal with the self-similarity and LRD properties of satellite network traffic. Due to the limitations of linear models, non-linear models such as the fractional autoregressive integration moving average model (FARIMA), wavelet model and grey model are utilized to forecast network traffic. [PERSON] et al. [16] proposed the Markov-modulated deterministic model to simulate satellite network traffic, which converts the acquisition, storage and transmission of network traffic into an MMDP/D/1/K queued model. [PERSON] et al. [17] proposed a satellite network traffic forecasting model based on ARMA, which represents current traffic through the weighted summation of multiple historical traffic data. Considering the limited onboard computing and storage capacity, ARMA(2, 1) is adopted to reduce the computational complexity. [PERSON] et al. [18] established a traffic forecasting model with two variables: the geographic longitude of ascending nodes and the time from passing ascending nodes. A prediction method based on a surrogate model is adopted to solve the traffic prediction problem with a time-independent ground traffic distribution. Accordingto the above analysis, statistics-based forecasting methods have limitations in describing the self-similarity, SRD and LRD laws of satellite network traffic [16]. In view of the limitations of statistics-based models, neural network models are applied to forecast network traffic. Compared with statistics-based models, neural network models outperform them in terms of non-linear mapping capabilities [19]. [PERSON] et al. [20] proposed a forecasting method, SSA-AWELM, by combing singular spectrum analysis (SSA) and an AdaBoost weighted extreme learning machine (AWELM). In the proposed method, SSA decomposes raw traffic into three parts: trend, periodicity and residual. The AWELM is designed to predict each part separately. [PERSON] et al. [10] combined a recurrent neural network (RNN) and a gated recurrent unit (GRU). The experiment results demonstrated that the proposed RNN-GRU model had advantages in forecasting accuracy. [PERSON] et al. [21] combined a graph convolutional neural network (GCN) and a generative adversarial network (GAN). In GCN-GAN, a GCN is utilized to extract the complex properties of network traffic, whereas a GAN is utilized to model the data structures. [PERSON] et al. [22] proposed a forecasting model (LA-ResNet) that utilizes attention mechanism to solve spatiotemporal modeling and predict wireless network traffic. However, the computation complexity of LA-ResNet is too considerable to be applied in LEO mega-constellations. According to the above analysis, increasing the number of hyperparameters will greatly increase the complexity of neural networks. In order to reduce the computation complexity and improve forecasting accuracy, [PERSON] et al.