Abstract
With the dynamic voltage scaling (DVS) technology, the terminal node (TN) can dynamically adjust its computational speed, thus providing a new way to save energy during task offloading in fog computing. Focusing on the scenario of one TN and multiple fog nodes (FNs), this paper proposed an Energy-Minimized Partial Task Offloading (EMPTO) scheme for the first time to reduce the overall energy consumption based on DVS technology. Firstly, by modeling the energy consumption and processing delay of task offloading, we formulated the problem of minimizing energy consumption. Then, using the variable substitution method, we transformed this energy minimization problem into a univariate optimization problem about the TN’s computational speed. By solving this problem, EMPTO gets the optimal TN’s computational speed, task offloading size between each pair of TN and FN, and the overall energy consumption. Finally, EMPTO selects the offloading scheme with the lowest overall energy consumption as the final scheme. Theoretical proof and simulation results show that EMPTO can achieve the minimum energy consumption by DVS technology under delay constraint.
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Data Availability
The data used to support the findings of this study are available from the corresponding author upon request.
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Appendices
Appendix A
The energy consumption of the TN to calculate a unit bit of data is expressed as:
It is easy to know that \(E_{T}^{C}\) is a monotonically increasing function of the TN’s computational speed fT.
The delay generated by the TN calculating the unit bit of data is expressed as α/fT, which is a monotonically decreasing function of fT.
Therefore, when QT takes any value under the constraint of D < = Dmax, we can always reduce the local computing energy consumption by adjusting fT so that DT = Dmax, thereby minimizing the overall energy consumption.
The above proves Proposition 1.
Appendix B
According to (2) and (10), the processing delay of Qi is rewritten as:
To ensure that the optimization problem (8) is solvable, it needs to satisfy D ≤ Dmax. It has been proved in Proposition 1 that DT = Dmax, then Di ≤ Dmax must be satisfied:
The above proves Proposition 2.
Appendix C
To ensure that problem (8) is solvable, QT ≤ Q and Di ≤ Dmax should be satisfied.
According to QT ≤ Q, we have
According to Di ≤ Dmax, we have
We denote the upper and lower bounds of the effective value range of fT as \(\widetilde{{f_{T\max } }}\) and \(\widetilde{{f_{T\min } }}\). According to (27), (28) and \(0 \le f_{T} \le f_{T\max }\),\(\widetilde{{f_{T\max } }}\) and \(\widetilde{{f_{T\min } }}\) are expressed as:
The above proves Proposition 3.
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Qin, Y., Yao, Y., Feng, W. et al. Dynamic voltage scaling based energy-minimized partial task offloading in fog networks. Wireless Netw 28, 3337–3347 (2022). https://doi.org/10.1007/s11276-022-03052-3
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DOI: https://doi.org/10.1007/s11276-022-03052-3