Energy-Optimal Latency-Constrained Application Offloading in Mobile-Edge Computing
<p>System model. (<b>a</b>) Mobile-edge computing (MEC) platform. (<b>b</b>) The offloading workflow.</p> "> Figure 2
<p>Dependence of <math display="inline"><semantics> <msub> <mi>α</mi> <mi>Max</mi> </msub> </semantics></math>, <math display="inline"><semantics> <msub> <mi>α</mi> <mi>Min</mi> </msub> </semantics></math>, and <math display="inline"><semantics> <msubsup> <mi>e</mi> <mrow> <mi>Tot</mi> </mrow> <mo>*</mo> </msubsup> </semantics></math> versus <math display="inline"><semantics> <msub> <mi>T</mi> <mi>Max</mi> </msub> </semantics></math> for <math display="inline"><semantics> <mrow> <msub> <mi>g</mi> <mi>s</mi> </msub> <mo>></mo> <msub> <mi>g</mi> <mi>Th</mi> </msub> </mrow> </semantics></math>.</p> "> Figure 3
<p>Dependence of <math display="inline"><semantics> <msub> <mi>α</mi> <mi>Max</mi> </msub> </semantics></math>, <math display="inline"><semantics> <msub> <mi>α</mi> <mi>Min</mi> </msub> </semantics></math>, and <math display="inline"><semantics> <msubsup> <mi>e</mi> <mrow> <mi>Tot</mi> </mrow> <mo>*</mo> </msubsup> </semantics></math> versus <math display="inline"><semantics> <msub> <mi>T</mi> <mi>Max</mi> </msub> </semantics></math> for <math display="inline"><semantics> <mrow> <msub> <mi>g</mi> <mi>s</mi> </msub> <mo>≤</mo> <msub> <mi>g</mi> <mi>Th</mi> </msub> </mrow> </semantics></math>.</p> "> Figure 4
<p>The effective coverage of MEC versus the energy efficiency of MD and task complexity (<math display="inline"><semantics> <mrow> <msub> <mi>h</mi> <mi>MD</mi> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> GHz, <math display="inline"><semantics> <mrow> <msub> <mi>h</mi> <mi>MEC</mi> </msub> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math> GHz, <math display="inline"><semantics> <mrow> <mi>B</mi> <mo>=</mo> <mn>5</mn> </mrow> </semantics></math> MHz, and <math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mn>0</mn> </msub> <mo>+</mo> <mi>I</mi> <mo>=</mo> <mo>−</mo> <mn>145</mn> </mrow> </semantics></math> dBm).</p> "> Figure 5
<p>Channel gain threshold <math display="inline"><semantics> <msub> <mi>g</mi> <mi>Th</mi> </msub> </semantics></math>. (<b>a</b>) <math display="inline"><semantics> <msub> <mi>g</mi> <mi>Th</mi> </msub> </semantics></math> versus B. (<b>b</b>) <math display="inline"><semantics> <msub> <mi>g</mi> <mi>Th</mi> </msub> </semantics></math> versus <math display="inline"><semantics> <msub> <mi>C</mi> <mi>App</mi> </msub> </semantics></math>.</p> "> Figure 6
<p>The transmission energy versus transmission time.</p> "> Figure 7
<p>The energy consumption and percentage of energy savings due to offloading under different latency constraints versus the distance between the BS and mobile device (MD). (<b>a</b>) Energy consumption. (<b>b</b>) Energy savings.</p> "> Figure 8
<p>The completion energy consumption versus the distance from the BS under different latency constraints. (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi>T</mi> <mi>Max</mi> </msub> <mo>=</mo> <mn>6</mn> <mo>.</mo> <mn>5</mn> </mrow> </semantics></math> s. (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>T</mi> <mi>Max</mi> </msub> <mo>=</mo> <mn>7</mn> <mo>.</mo> <mn>5</mn> </mrow> </semantics></math> s. (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mi>T</mi> <mi>Max</mi> </msub> <mo>=</mo> <mn>8</mn> <mo>.</mo> <mn>5</mn> </mrow> </semantics></math> s. (<b>d</b>) <math display="inline"><semantics> <mrow> <msub> <mi>T</mi> <mi>Max</mi> </msub> <mo>=</mo> <mn>9</mn> <mo>.</mo> <mn>5</mn> </mrow> </semantics></math> s.</p> "> Figure 9
<p>The completion energy and time consumption versus the distance from the BS under different latency constraints. (<b>a</b>) Energy consumption. (<b>b</b>) Time consumption.</p> "> Figure 10
<p>Percentage of the task remotely processed at the MEC server versus the distance from the BS under different latency constraints.</p> ">
Abstract
:1. Introduction
- Based on the offloading model above, we formulate an offloading-optimization problem that minimizes the MD energy usage while ensuring the task is completed within a prescribed deadline, by jointly optimizing the transmitting time and offloading ratio.
- We transform the latency-constrained problem into a two-stage optimization problem, which can be analytically solved using standard convex optimization techniques. In the solution, a channel condition threshold is derived above which full offloading is the optimal decision, whereas below the threshold, partial offloading is performed to trade off between the time and energy cost of offloading. For the partial offloading policy, the optimal transmission time and offloading ratio are derived in closed form expression.
- This paper also discusses in detail various practical aspects of the offloading strategy, including the conditions under which total offloading or non offloading is optimal, the minimum admissible latency constraint that renders the problem feasible, and how the system parameters affect the offloading decision, including the energy efficiency of MD, the task complexity, and the computing capacity of local devices.
2. System Model
- Input data size : the number of data bits as the input to the application;
- Required CPU cycles : the number of CPU cycles required to complete the application;
- Application completion deadline : the maximum latency, before which the application should be completed.
2.1. Communication Model
2.2. Computation Model
2.3. Partial Offloading Model
3. Joint Optimization of the Communication and Computation Resources with Partial Offloading
3.1. Optimization Formulation
3.2. Offloading Policy in Good Channel Conditions
3.3. Offloading Policy for the Channel Condition below the Threshold
Solution to the Sub-Problem
3.4. Special Cases of Full Offloading and Non Offloading
3.4.1. Optimality Condition of Total Offloading
3.4.2. Optimality of Non Offloading
4. Analysis of the System Parameters
4.1. The Latency Constraint and Feasibility of
4.1.1. Channel Gain
4.1.2. Channel Gain
- , ;
- .
4.2. The Channel Gain Threshold as a Function of the System Parameters
5. Simulation Results
6. Conclusions
Author Contributions
Funding
Conflicts of Interest
Appendix A. Monotonicity of eTot as a Function of tTr
Appendix B. The Existence of Channel Threshold gTh
- If , then offloading has to be performed because the time constraint cannot be totally satisfied by full local computing. Now, assume if there exists some fraction yet to be locally processed, then it must not be the optimal choice because offloading requires less energy than local computing for under the same time constraint.
- If , then . By Lemma 1, offloading will further reduce energy consumption due to the longer transmission time, which is advantageous to local computing.
Appendix C. Proof the Monotonicity of eTot with Respect to α When gs < gTh
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Latency | |||
---|---|---|---|
Channel | |||
Full offloading | Full offloading | ||
Partial offloading | Non offloading |
Parameter | Value |
---|---|
B | 5 MHz |
−174 dBm | |
I | −145 dBm |
5000 kBytes | |
1000 Megacycles | |
J/cycle | |
1 GHz | |
10 GHz |
200 | 700 | 1300 | 2000 | 4000 | 6000 | ||
---|---|---|---|---|---|---|---|
I | |||||||
−145 dBm | 200 | 433 | 606 | 759 | 1085 | 1333 | |
−135 dBm | 62 | 134 | 187 | 235 | 335 | 412 | |
−125 dBm | 20 | 42 | 59 | 74 | 106 | 130 | |
−115 dBm | 6 | 13 | 19 | 23 | 33 | 41 | |
−105 dBm | 2 | 4 | 6 | 7 | 10 | 13 |
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Gu, X.; Ji, C.; Zhang, G. Energy-Optimal Latency-Constrained Application Offloading in Mobile-Edge Computing. Sensors 2020, 20, 3064. https://doi.org/10.3390/s20113064
Gu X, Ji C, Zhang G. Energy-Optimal Latency-Constrained Application Offloading in Mobile-Edge Computing. Sensors. 2020; 20(11):3064. https://doi.org/10.3390/s20113064
Chicago/Turabian StyleGu, Xiaohui, Chen Ji, and Guoan Zhang. 2020. "Energy-Optimal Latency-Constrained Application Offloading in Mobile-Edge Computing" Sensors 20, no. 11: 3064. https://doi.org/10.3390/s20113064