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SCIENCE CHINA Information Sciences, Volume 62, Issue 8: 082301(2019) https://doi.org/10.1007/s11432-018-9680-9

Delay-constrained sleeping mechanism for energy saving in cache-aided ultra-dense network

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  • ReceivedJul 15, 2018
  • AcceptedNov 29, 2018
  • PublishedMay 28, 2019

Abstract

We investigate an energy-saving sleeping mechanism in a cache-aided ultra-dense network (UDN) with delay constraints. As in existing works, we consider the video and file contents of the UDN. The video contents are cached at and delivered by a small-cell base-station (sBS). The cache-aided sBS cooperates with a macro-cell base-station (mBS) to service the file contents. The optimal sleeping strategy that conserves energy under the delay constraint is formulated as an energy-consumption minimization problem under the network stability condition with a guaranteed delay constraint. To find its solution, the minimization problem is transformed into a joint optimization problem of energy consumption and delay by the Lyapunov technique. A delay-constrained sleeping algorithm is proposed, and its effectiveness is confirmed by the numerical results of a simulation study. A tradeoff between energy consumption and delay, achieved by adjusting the weighting factor in the cache-aided UDN, is also demonstrated.


Acknowledgment

This work was partially supported by National Major Project (Grant No. 2017ZX03001002-004), National Natural Science Foundation Project of China (Grant No. 61521061), and 333 Program of Jiangsu (Grant No. BRA2017366).


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  • Figure 1

    (Color online) System model for a cache-aided UDN.

  • Figure 2

    (Color online) Time-averaged energy consumption vs. weighting factor $V$, calculated by Algorithm 1.

  • Figure 3

    (Color online) Time-averaged queue length vs. weighting factor $V$, obtained in the simulation study.

  • Figure 4

    (Color online) Time-averaged delays in file and video contents vs. weighting factor $V$, obtained in the simulation.

  • Figure 5

    (Color online) Weighting factor $V$ vs. the time-averaged energy consumption and the time-averaged delay of file contents at $C=5$.

  • Figure 6

    (Color online) Time-averaged energy consumption vs. weighting factor for different sleeping schemes and caching capacities.

  • Figure 7

    (Color online) Time-averaged delay vs. weighting factor for different sleeping schemes and caching capacities.

  • Table 1   System parameter
    Parameter Value Parameter Value
    ${\lambda~_m}$ $5\times10^{-6}$ ${\lambda~_s}$ $2.5\times10^{-5}$
    ${\lambda~_V}$ $0.5~~{\rm~s}^{-1}$ ${\lambda~_F}$ $1~~{\rm~s}^{-1}$
    $\Delta~p_{m}$ $10$ $\Delta~p_{s}$ $8$
    ${P_{s0}}$ $4.8$ W ${P_{m0}}$ $10$ W
    ${P_S}$ 2.4 W ${P_{mb}}$$8$ W
    ${P_{mt}}$ $46~$ dBm ${P_{st}}$$30$ dBm
    ${L_V}$ 10 MB $L_F$5 MB
    ${W_m}$ 10 MHz $W_s$ 10 MHz
    ${E_{S}}$ $1.5$ W ${{\omega~_{{{cs}}}}}$ $2\times10^{-9}$ J/byte
  •   

    Algorithm 1 A delay-constrained sleeping scheme

    01: Initialize: $\!{Q}(0)\!\!=\!0$, $\!{G}(0)\!\!=\!0$, $\!\rho(0)\!\!=\!0$, $\!\xi(0)\!=\!0$, $\!{\cal{B}}_{\rm~on}$, $\!{\cal{B}}_{\rm~off}$. 02: Repeat 03: Calculate $R_{k}(t)$, $r_{j}(t)$, $\rho_{k}(t)$, $\xi~_{j}(t)$ and ${{p}}_k^{F}$. 04: Compute $A_{k}(t)$ and $M_{j}(t)$ according to (6) and (15). 05: Update $Q_{k}(t)$ and $G_{j}(t)$ according to (10) and (17). 06: Calculate $P(t)$ according to (5). 07: $t=t+1$, 08: Update $\bar~\rho_{k}$ and $\bar~\xi~_{j}$ according to (14) and (21). 09: Update $\bar~Q_{k}$, $\bar~G_{j}$ and $\bar~P$, according to (13), (20) and (30). 10: End Repeat when $t=T$, $T$ is total number of time slots. 11: While $\Psi~>~1$, 12: Repeat 13: Calculate ${\Gamma~_{\rm~on}}\!\left(~k~\right)~\!=\!~F\!\left(~{{\cal~B}_{\rm~on}}\!~\cup~\!~\left\{~{k}~\right\}~\right)\!~-\!~F\!\left({\cal~B}_{\rm~on}~\right)~\!+~\!{E_s}$, $\forall~k~\!~\in~\!~{\cal~{B}}_{\rm~off}$. 14: If ${k^*}~\!=\!~\mathop~{\arg~\min~}\limits_{k~\in~{{\cal~B}_{{{\rm~on}}}}}~{\Gamma~_{\rm~on}}\left(~k~\right)$, Then ${{\cal~B}_{{{\rm~on}}}}\!~\leftarrow~\!~{{\cal~B}_{{{\rm~on}}}}~\cup~\{~{k^*}\}~$. 15: End Repeat when $0<\Psi~<~1$. 16: End While 17: While $0<\Psi<~1$, 18: Calculate ${\Gamma~_{\rm~off}}\!\left(~k~\right)~\!=\!~F\!\left({\cal~B}_{\rm~on}~\right)~\!-\!~F\!\left(~{{\cal~B}_{\rm~on}}\!-\!~\left\{~{k}~\right\}\!~\right)\!~-~\!{E_s}$, $\forall~k~\!~\in~\!~{\cal~{B}}_{\rm~on}$. 19: If ${\Gamma~_{\rm~off}}\!\left(~k~\right)~\!~>0$, Then ${{\cal~B}_{{{\rm~off}}}}~\leftarrow~{{\cal~B}_{{{\rm~off}}}}~\cup~\{~{k}\}~$. 20: End While

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