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Network traffic prediction based on INGARCH model

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Abstract

In this paper, we introduce the integer-valued generalized autoregressive conditional heteroscedasticity (INGARCH) as a network traffic prediction model. As the INGARCH is known as a non-linear analytical model that could capture the characteristics of network traffic such as Poisson packet arrival and long-range dependence property, INGARCH seems to be an adequate model for network traffic prediction. Based on the investigation for the traffic arrival process in various network topologies including IoT and VANET, we could confirm that assuming the Poisson process as packet arrival works for some networks and environments of networks. The prediction model is generated by estimating parameters of the INGARCH process and predicting the Poisson parameters of future-steps ahead process using the conditional maximum likelihood estimation method and prediction procedure, respectively. Its performance is compared with those of three different models; autoregressive integrated moving average, GARCH, and long short-term memory recurrent neural network. Anonymized passive traffic traces provided by the Center for Applied Internet Data Analysis are used in the experiment. Numerical results show that the proposed model predicts better than the three models in terms of measurements used in prediction models. Based on the study, we can conclude the followings: INGARCH can capture the characteristics of network traffic better than other statistic models, it is more tractable than neural networks (NNs) overcoming the black-box nature of NNs, and the performances of some statistical models are comparable or even superior to those of NNs, especially when the data is insufficient to apply deep NNs.

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Acknowledgements

The author would like to thank the editor and the anonymous reviewers for their constructive and valuable comments. Support for CAIDA’s Internet Traces is provided by the National Science Foundation, the US Department of Homeland Security, and CAIDA Members. This work was supported by the Mid-career Research Program and Basic Science Research Program through the NRF Grant funded by the MEST (NRF-2019R1A2C1002706, NRF-2016R1D1A1B03931037) and supported by the Korea University Grant.

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    Meejoung Kim

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Appendix: Proof of Theorem 1

Appendix: Proof of Theorem 1

Since

$$\hat{\lambda }_{t} (n) = w + \sum\limits_{i = 1}^{p} {\alpha_{i} E(\lambda_{t + n - i} |{\mathcal{F}}_{t} )} + \sum\limits_{j = 1}^{q} {\beta_{j} E(X_{t + n - j} |{\mathcal{F}}_{t} )} ,$$
(15)

\(E(\lambda_{t + n - i} |{\mathcal{F}}_{t} )\) and \(E(X_{t + n - j} |{\mathcal{F}}_{t} )\) are obtained as

$$\begin{aligned}E(\lambda_{t + n - i} |{\mathcal{F}}_{t} ) &= \left\{ {\begin{array}{*{20}l} {\lambda_{t + n - i} ,} \hfill & {{\text{if}}\;n - i < 0} \hfill \\ {\hat{\lambda }_{t} (n - i),} \hfill & {{\text{if}}\;n - i \ge 0} \hfill \\ \end{array} } \right.,\;{\text{and}}\\E(X_{t + n - j} |{\mathcal{F}}_{t} ) &= \left\{ {\begin{array}{*{20}l} {X_{t + n - j} ,} \hfill & {{\text{if}}\;n - j < 0} \hfill \\ {\hat{\lambda }_{t} (n - j),} \hfill & {{\text{if}}\;n - j \ge 0} \hfill \\ \end{array} } \right.,\end{aligned}$$
(16)

respectively, and the result follows.

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Kim, M. Network traffic prediction based on INGARCH model. Wireless Netw 26, 6189–6202 (2020). https://doi.org/10.1007/s11276-020-02431-y

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