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Optimal Energy Allocation and Task Offloading Policy for Wireless Powered Mobile Edge Computing Systems
Feng Wang, Jie Xu, Shuguang Cui
TL;DR
Prior work focused on one-shot optimization, leaving optimization with task arrivals insufficiently addressed. This paper develops offline and heuristic online energy and task allocation designs, with the offline solution yielding uniform transmission energy allocation and staircase task allocation.
Problem
Prior works focused on one-shot optimization, while optimization with task arrivals remained insufficiently addressed.
Method
The paper studies offline energy minimization and develops heuristic online designs inspired by the offline solution.
Results
The offline solution allocates transmission energy uniformly over time and uses staircase task allocation for local computing and offloading.
Takeaways & Limitations
The structured offline solution provides design insights that motivate the heuristic online designs.
Abstract
from arXiv · showhide
This paper studies a wireless powered mobile edge computing (MEC) system with fluctuating channels and dynamic task arrivals over time. We jointly optimize the transmission energy allocation at the energy transmitter (ET) for WPT and the task allocation at the user for local computing and offloading over a particular finite horizon, with the objective of minimizing the total transmission energy consumption at the ET while ensuring the user's successful task execution. First, in order to characterize the fundamental performance limit, we consider the offline optimization by assuming that the perfect knowledge of channel state information and task state information (i.e., task arrival timing and amounts) is known a-priori. In this case, we obtain the well-structured optimal solution in a closed form to the energy minimization problem via convex optimization techniques. Next, inspired by the structured offline solutions obtained above, we develop heuristic online designs for the joint energy and task allocation when the knowledge of CSI/TSI is only causally known. Finally, numerical results are provided to show that the proposed joint designs achieve significantly smaller energy consumption than benchmark schemes with only local computing or full offloading at the user, and the proposed heuristic online designs perform close to the optimal offline solutions.
I. INTRODUCTION
The paper addresses wireless powered MEC with fluctuating channels and dynamic task arrivals by jointly optimizing WPT energy and user task allocation over time. It develops structured offline policies and heuristic online designs, with simulations showing lower energy use than benchmark strategies and online performance close to offline solutions.
- Motivation: Prior wireless powered MEC studies largely considered one-shot optimization with static channels and given tasks, overlooking time dynamics in WPT and task arrivals.Practical systems instead face fluctuating wireless energy and bursty computation traffic, creating coupled energy and task causality constraints.
- System model: The paper studies a single-user system with a multi-antenna ET, an AP-integrated MEC server, and a user receiving dynamic task arrivals.The user executes some tasks locally and offloads the remainder using energy harvested through WPT.
- Problem formulation: The objective is to minimize ET transmission energy while satisfying user energy and task causality through joint WPT and local/offloading allocation.Cumulative executed energy and tasks cannot exceed cumulative harvested energy and arrived tasks at any time.
- Offline optimization: With perfect future CSI and TSI, offline optimization reveals structured policies that characterize the fundamental performance limit.For static channels, ET energy is allocated uniformly, while local computing and offloading use staircase task allocation with monotonically increasing executed bits.
- Offline optimization: For time-varying channels, convex optimization yields sporadic ET transmission at causally dominating channel gains, staircase local computing, and staircase water-filling for offloading.The resulting computation levels increase monotonically over time.
- Online optimization: With only causal CSI and TSI, heuristic online designs are developed from the structured offline solutions for practical implementation.The proposed online designs use past and present information while future channel and task states remain unknown.
- Numerical results: The proposed designs consume significantly less energy than local-only or full-offloading benchmarks, while online designs perform close to offline solutions and outperform myopic designs.These comparisons are reported for both static and time-varying channel scenarios.
II. SYSTEM MODEL AND PROBLEM FORMULATION
The paper models a single-user wireless powered MEC system over a finite, slotted horizon, where harvested wireless energy supports local computing and task offloading under a common completion deadline.
- The system contains a multi-antenna energy transmitter, an access point with an integrated MEC server, and a single-antenna user with dynamically arriving tasks.
- The ET wirelessly charges the user, which uses harvested energy for local computation or offloading tasks to the AP.
- Wireless power transfer and computation offloading occur simultaneously over orthogonal frequency bands.
- The finite horizon has duration T and is divided into N equal-duration time slots, with tasks arriving at the beginning of each slot.Each slot has duration τ = T/N.
- All arrived tasks must be successfully executed by the end of the horizon under a common computation deadline.The common deadline is motivated by applications that aggregate sensing tasks before taking an action.
A. Task Execution at User
Task execution combines partitionable local computing and offloading, both powered by harvested energy. Local execution uses DVFS, while offloading is modeled through transmission over the user–AP channel under energy and task causality constraints.
- Task allocation: Each slot partitions task input-bits between local computing ℓ_i and offloading d_i, and the tasks are assumed partitionable.This partitionability assumption provides a performance upper bound for nonpartitionable or discretely partitionable tasks.
- Causality constraints: Task causality and energy causality require cumulative execution and consumption to remain feasible relative to arrivals and harvested energy.Harvested energy is usable in the current and subsequent slots.
- Local computing: DVFS makes the local CPU frequency Cℓ_i/τ, yielding a slot energy determined by the locally processed bits and effective switched capacitance.C denotes the CPU cycles required per input-bit, while ζ denotes the effective switched capacitance coefficient.
- Task offloading: Offloading proceeds through task transmission, remote execution, and result downloading, but the model focuses on transmission because the latter two times are treated as constants.The offloading time in each slot is set to the slot length τ.
- Wireless power transfer: The ET uses maximum-ratio-transmission energy beamforming, and the user’s local computing and offloading are powered by the harvested wireless energy.The linear RF-to-DC model uses conversion efficiency η and allows the ET to adjust transmit power within the assumed linear regime.
C. Problem Formulation
The paper minimizes ET transmission energy while ensuring task completion and causal operation. Offline optimization uses non-causal CSI and TSI to characterize a performance bound, while causal-information designs are developed from the resulting structure.
- Optimization objective: The objective is to minimize total WPT transmission energy at the ET while sustaining the user’s communication and computation.The design variables include ET energy allocation and user allocation between local computing and offloading.
- Optimization constraints: The formulation imposes task causality, a final task-completion constraint, and energy causality constraints.
- Model scope: The AP/MEC server’s offloading-related energy is excluded because it can generally be modeled as a constant.The paper also assumes fixed peak CPU frequency for executing offloaded tasks with minimum delay.
- Offline and online information: Offline optimization assumes non-causal CSI and TSI known a-priori, making its ET energy consumption a lower bound for designs with imperfect or causal information.This offline solution is used to provide fundamental performance limits and motivate practical designs.
- Solution approach: Because the local-computing and offloading energy functions are convex, the optimization problem can be solved efficiently using convex optimization techniques.The paper derives well-structured optimal solutions for static and time-varying channels, then studies causal CSI/TSI online optimization.
III. OPTIMAL ENERGY AND TASK ALLOCATION UNDER STATIC CHANNELS
Under static channels, the offline problem is reduced to a convex task-allocation optimization whose solution has a monotone staircase structure and yields optimal energy allocation.
- Offline optimization: The static-channel offline problem is formulated as a convex optimization and solved using KKT conditions with zero duality gap.The resulting optimal local-computing and offloading task allocations are given in closed form.
- Structural properties: The computation level is nonnegative and increases monotonically over slots, defining transition slots where it strictly rises.The last slot is always a transition slot.
- Structural properties: At each transition slot, cumulative tasks at the user are completely cleared, producing a staircase allocation for local computing and offloading.Both task-input sequences increase across transition intervals, and the queue is emptied after each transition slot.
- Energy allocation: The optimal energy allocation for WPT can be obtained after task allocation, with the resulting offline solution combining both allocations.The paper illustrates the structure through dynamic task arrivals and the corresponding optimal solution.
IV. OPTIMAL ENERGY AND TASK ALLOCATION UNDER TIME-VARYING CHANNELS
The paper next extends the offline optimization to general time-varying WPT and offloading channels, where both channel-gain sequences may change over time.
- General scenario: The time-varying-channel scenario allows the WPT gains {h_i} and offloading gains {g_i} to change over the finite horizon.The objective remains the offline joint energy and task allocation problem under the general channel setting.
A. Decomposition of Problem (P1)
For time-varying channels, the paper decomposes the offline problem into task allocation and energy allocation, then exploits effective channel gains and transition slots to derive structured solutions.
- Problem decomposition: The problem is decomposed into optimizing task allocation at the user and energy allocation at the ET.The task-allocation subproblem is solved first, followed by optimal WPT energy allocation.
- Energy allocation: Under fixed task allocation, optimal WPT energy is transmitted only at causality-dominating slots, which are selected according to the channel structure.Energy at each such slot covers the user’s consumption over the corresponding interval.
- Task allocation: The task-allocation subproblem is convex and has closed-form local-computing and offloading solutions obtained from KKT conditions.The offloading rule has a staircase water-filling form governed by the computation level and effective channel gain.
- Structural properties: The computation level is nonnegative and monotone, producing staircase local computing and staircase water-filling offloading allocations.At transition slots, cumulative tasks are cleared before the next transition interval begins.
- Solution procedure: Algorithm 2 searches transition-slot sets forward and solves convex interval subproblems to obtain the optimal task allocation for the time-varying case.The procedure uses transition intervals and their minimum weighted-sum energy costs.
V. HEURISTIC ONLINE DESIGNS FOR JOINT ENERGY AND TASK ALLOCATION
When only causal CSI and TSI are available, the paper develops heuristic online joint energy and task allocation designs inspired by the offline solution structure.
- Online setting: The online setting provides only past and current CSI and TSI, unlike the offline setting with perfect a-priori knowledge.Task arrivals and channel gains are modeled through stochastic processes whose means are known.
- Online designs: The proposed heuristic online designs are inspired by the structures of the optimal offline solutions.They address scenarios with static and time-varying channels.
- Online designs: At each slot, the online design minimizes energy consumption from the current slot through the end of the horizon.Mean channel gains and mean task arrivals are used as estimates for future slots.
A. Static Channel Scenario
For static channels, the paper develops a causal online design based on residual tasks and future task estimates, using the offline solution structure to allocate energy and tasks over the remaining horizon.
- Static Channel Scenario: The online design considers the current slot as the first slot and minimizes ET transmission energy through the horizon.The remaining problem is formulated similarly to the offline problem using the current residual task state.
- Static Channel Scenario: It uses the exact task amount arriving in the current slot together with an estimated mean arrival amount for subsequent slots.
- Static Channel Scenario: The resulting task allocation follows the staircase structure established by the offline solution.
- Static Channel Scenario: At each slot, wireless energy transferred to the user equals the energy consumed by local computing and offloading.
B. Time-varying Channel Scenario
For time-varying channels, the paper adapts the remaining-horizon optimization using estimated future channels and task arrivals, then adds a threshold-based energy allocation rule for causal operation.
- Time-varying Channel Scenario: The time-varying-channel design replaces future channel gains and task arrivals with estimates when optimizing from the current slot to the horizon.The resulting problem is formulated similarly to the offline formulation with estimated future parameters.
- Time-varying Channel Scenario: The proposed online design computes task and energy allocations using the time-varying-channel optimal structure and an efficiently computable algorithm.
- Time-varying Channel Scenario: The threshold policy allocates more energy when the current WPT channel gain exceeds its average threshold.The parameter γ balances energy supply against the current channel power gain, with γ = 2 used in the design.
- Time-varying Channel Scenario: Otherwise, the ET allocates the minimum energy needed to meet the user’s computation demand in that slot.
VI. NUMERICAL RESULTS
Numerical experiments evaluate energy consumption under static and time-varying channels, varying distance, horizon length, and task size. Joint designs outperform restricted benchmarks, while causal online designs approach offline performance.
- Simulation Setup: The simulations average results over 10^3 randomized channel and task realizations using distance-dependent Rician fading models.The ET and access point are 10 m apart, and d denotes the user-to-ET distance.
- Offline Designs: The proposed offline designs achieve significant gains over local-computing-only and full-offloading benchmarks.This demonstrates the energy-saving benefit of jointly allocating tasks between local computing and offloading.
- Offline Designs: Time-varying channels produce significantly more energy consumption than static channels for all three schemes.The passage attributes this difference to wireless channel fluctuations over time.
- Online Designs: As the horizon length N increases, proposed offline and online energy consumption decreases, while myopic performance remains unchanged.The proposed designs exploit time dynamics in channel fluctuations and task arrivals, unlike the myopic scheme.
- Online Designs: The proposed online designs increasingly outperform myopic designs as N or Amax grows and remain close to offline designs.
VII. CONCLUDING REMARK
The paper formulates single-user wireless powered MEC as a joint energy and task allocation problem, deriving offline solutions with noncausal information and heuristic online designs with causal information. Results show lower energy than local-only or full-offloading benchmarks and online performance close to offline solutions, while several extensions remain challenging.
- Conclusion: The study targets joint energy and task allocation for a single-user wireless powered MEC system with dynamic task arrivals.
- Conclusion: Convex optimization yields well-structured offline solutions when CSI and TSI are known noncausally.
- Conclusion: Heuristic online joint designs are proposed using only causal CSI and TSI.
- Conclusion: The proposed designs consume significantly less energy than local-only or full-offloading benchmarks, while online designs remain close to offline solutions and outperform myopic designs.
- Limitations and Extensions: The paper assumes linear energy harvesting and partial offloading, while nonlinear harvesting, binary offloading, individual task latencies, and multiple users are identified as extensions.
- Limitations and Extensions: Binary offloading makes the energy minimization problem mixed-integer and generally NP-hard.
- Limitations and Extensions: Individual task latency constraints preserve convexity, but the monotonically increasing task allocation structure may no longer hold.
APPENDIX
The appendix proves structural properties of an optimal energy allocation for problem (P1) by contradiction and feasible-allocation transformations. It shows that energy is assigned only to designated CDS slots and that the resulting allocation achieves the minimum objective.
- If a non-CDS slot receives positive energy, reallocating energy to an earlier CDS with a higher channel gain preserves feasibility and lowers the objective.
- Any energy allocation solution to problem (P1) must satisfy p_i = 0 for all i ∈ N \ NCDS.
- For the last CDS, reducing its allocation until τηh_φ|NCDS|p_φ|NCDS| = P_N preserves feasibility while improving the objective when the constraint is slack.
- For consecutive CDS slots, the proof establishes Δ_φk = 0 for every k ∈ {1, . . . , |NCDS| − 1}, completing the stated optimality structure.
- The constructed allocation satisfies the energy-causality constraints, and the argument concludes by verifying Theorem 2.