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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


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