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SCIENCE CHINA Information Sciences, Volume 63 , Issue 4 : 142301(2020) https://doi.org/10.1007/s11432-019-2695-6

Prophet model and Gaussian process regression based user traffic prediction in wireless networks

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  • ReceivedJun 16, 2019
  • AcceptedOct 25, 2019
  • PublishedMar 9, 2020

Abstract

User traffic prediction is an important topic for wireless network operators. A user traffic prediction method based on Prophet and Gaussian process regression is proposed in this paper. The proposed method first employs discrete wavelet transform to decompose the user traffic time series to high-frequency component and low-frequency component. The low-frequency component bears the long-range dependence of user network traffic, while the high-frequency component reveals the gusty and irregular fluctuations of user network traffic. Then Prophet model and Gaussian process regression are applied to predict the two components respectively based on the characteristics of the two components. Experimental results demonstrate that the proposed model outperforms the existing time series prediction method.


Acknowledgment

This work was partially supported by National Key Research and Development Project (Grant No. 2018YFB1802402) and Huawei Tech. Co., Ltd.


References

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  • Figure 1

    (Color online) Prediction result for a user.

  •   

    Algorithm 1 Traffic prediction algorithm

    Require:Per-user traffic time series $x_{i}(t)$.

    Output:Prediction $\hat{x}_{i}(t+1)$.

    for User $i=1$ to $P$

    ${c}_{i}(n)=\frac{1}{\sqrt{2}}\sum_{t=1}^{N}x_{i}(t)\varphi(\frac{t}{2}-n),{d}_{i}(n)=\frac{1}{\sqrt{2}}\sum_{t=1}^{N}x_{i}(t)\psi(\frac{t}{2}-n)$;

    for time slot $n=1$ to $N/2$

    $g(n)=\frac{B(n)}{1+{\rm{exp}}(-(k+\boldsymbol{a}(n)^{\rm~T}\boldsymbol{\delta})(n-(m+\boldsymbol{a}(n)^{\rm~T}\gamma)))}$;

    $s(n)={\boldsymbol{e}}(n)\boldsymbol{\beta}=\sum_{l=1}^{L}(a_{l}~{\rm{cos}}(\frac{2\pi~nl}{P})+b_{l}~{\rm{sin}}(\frac{2\pi~nl}{P}))$;

    $h(n)={\boldsymbol{z}}(n)~\boldsymbol{\kappa}=\sum_{i=1}^{M}\kappa_{i}\cdot~\mathbf{1}_{\left\{~n\in~D_{i}\right\}}$;

    end for

    ${\boldsymbol~X}_{c}=\left\{[\boldsymbol{e}(n)~~~~\boldsymbol{z}(n)]\right\}_{n=1}^{N/2},\boldsymbol{c}_{i}=\left\{~c_{i}(n)\right\}_{n=1}^{N/2},{\boldsymbol~A}=\left\{~\boldsymbol{a}(n)~\right~\}~_{n=1}^{N/2}$;

    $\boldsymbol{\lambda}=(k,m,\boldsymbol{\delta,\beta,\kappa}),p(\boldsymbol{c}_{i}|{\boldsymbol~X}_{c},\boldsymbol{\lambda})=N(\boldsymbol{\mu}_{ci},\varepsilon),\boldsymbol{\mu}_{ci}=\frac{B}{(1+{\rm{exp}}(-(k+{\boldsymbol~A}\boldsymbol{\delta})\cdot(n-(m+{\boldsymbol~A}\boldsymbol{\gamma}))))}+{\boldsymbol~X}_{c}{\tiny[{\boldsymbol{\beta}~\atop\boldsymbol{\kappa}}]}$;

    $\boldsymbol{\lambda}^{\rm~MAP}={\rm{argmin}}(-{\rm{log}}~p(\boldsymbol{c}_{i}|{\boldsymbol~X}_{c},\boldsymbol{\lambda})-{\rm{log}}~~p(\boldsymbol{\lambda}))$;

    $\hat{c}_{i}(n+1)=g(n+1)+s(n+1)+h(n+1)$;

    for time slot $n=1$ to $N/2$

    $\boldsymbol{x}_{n}=[d_{i}(n-3),d_{i}(n-2),d_{i}(n-1)]$;

    $y_{n}=d_{i}(n)$;

    end for

    ${\boldsymbol~X}_{d}=\left\{~\boldsymbol{x}_{n}~\right\}_{n=1}^{N/2},\boldsymbol{y}=\left\{y_{n}\right\}_{n=1}^{N/2}$;

    $p(\boldsymbol{y}|{\boldsymbol~X}_{d},\theta)=N(\mathbf{0,K}_{T}),{\boldsymbol~K}_{T}={\boldsymbol~K}+\sigma_{n}^{2}\mathbf{I},k(\boldsymbol{x}_{i},\boldsymbol{x}_{j})={\rm{exp}}(-\frac{1}{2\theta^{2}}(\boldsymbol{x}_{i}-\boldsymbol{x}_{j})^{\rm~T}(\boldsymbol{x}_{i}-\boldsymbol{x}_{j}))$;

    $\theta^{ML}={\rm{argmin}}(-{\rm{log}}~~p(\boldsymbol{y}|{\boldsymbol~X}_{d},\theta))$;

    $\boldsymbol{x}_{*}=[d_{i}(n-2),d_{i}(n-1),d_{i}(n)],\boldsymbol{k}_{*}=(k(\boldsymbol{x}_{*},\boldsymbol{x}_{1}),\ldots,k(\boldsymbol{x}_{*},\boldsymbol{x}_{N/2}))^{\rm~T}$;

    $\hat{d}_{i}(n+1)~=~\boldsymbol{k}_{*}{\boldsymbol~K}_{T}^{-1}\boldsymbol{y}$;

    $\hat{x}_{i}(t+1)=\sum_{n=1}^{\frac{N}{2}}\hat{c}_{i}(n+1)\varphi(\frac{t+1}{2}-n-1)+\sum_{n=1}^{\frac{N}{2}}\hat{d}_{i}(n+1)\psi(\frac{t+1}{2}-n-1)$.

    end for

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