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Joint Computation and Communication Cooperation for Energy-Efficient Mobile Edge Computing

Xiaowen Cao, Feng Wang, Jie Xu, Rui Zhang, Shuguang Cui

arXiv:1805.05906v2cs.IT

TL;DR

Resource-limited wireless devices need energy-efficient execution of latency-constrained, computation-intensive tasks in MEC. The paper jointly designs computation and communication cooperation for partial and binary offloading in a coordinated three-node system, and reports higher computation capacity and lower energy consumption than benchmark schemes. Its practical scope assumes a helper sharing the user’s objective, motivating future incentive and distributed designs.

  • Problem

    Wireless devices face latency-critical computation demands despite limited communication, computation, and storage resources, while prior studies considered computation and communication cooperation separately.

  • Method

    The paper jointly allocates task partitions, CPU frequencies, offloading times, and transmit powers in a three-node MEC system using a four-slot cooperation protocol for partial and binary offloading.

  • Results

    The proposed joint cooperation achieves higher computation capacity and lower energy consumption than benchmark schemes without joint design.

  • Takeaways & Limitations

    Jointly exploiting computation and communication cooperation improves computation capacity and energy efficiency at the user and helper nodes.

  • Takeaways & Limitations

    The centralized design assumes the user and helper share a common interest in improving MEC system energy efficiency; self-interested helpers require incentive mechanisms and distributed algorithms.

Abstract

from arXiv · show

This paper proposes a novel user cooperation approach in both computation and communication for mobile edge computing (MEC) systems to improve the energy efficiency for latency-constrained computation. We consider a basic three-node MEC system consisting of a user node, a helper node, and an access point (AP) node attached with an MEC server, in which the user has latency-constrained and computation-intensive tasks to be executed. We consider two different computation offloading models, namely the partial and binary offloading, respectively. Under this setup, we focus on a particular finite time block and develop an efficient four-slot transmission protocol to enable the joint computation and communication cooperation. Besides the local task computing over the whole block, the user can offload some computation tasks to the helper in the first slot, and the helper cooperatively computes these tasks in the remaining time; while in the second and third slots, the helper works as a cooperative relay to help the user offload some other tasks to the AP for remote execution in the fourth slot. For both cases with partial and binary offloading, we jointly optimize the computation and communication resources allocation at both the user and the helper (i.e., the time and transmit power allocations for offloading, and the CPU frequencies for computing), so as to minimize their total energy consumption while satisfying the user's computation latency constraint. Although the two problems are non-convex in general, we propose efficient algorithms to solve them optimally. Numerical results show that the proposed joint computation and communication cooperation approach significantly improves the computation capacity and energy efficiency at the user and helper nodes, as compared to other benchmark schemes without such a joint design.

I. INTRODUCTION

The paper addresses latency-constrained, computation-intensive tasks on resource-limited wireless devices by jointly using computation and communication cooperation in MEC. It develops resource-allocation methods for partial and binary offloading and reports gains in computation capacity and energy efficiency.

  • Motivation: Latency-critical 5G applications require substantial computation and communication, while wireless devices have limited resources.MEC brings cloud-like computing closer to devices to address latency requirements, but resource sharing and channel conditions remain challenging.
  • System and protocol: The system uses a user, helper, and AP with an attached MEC server, coordinated over a finite block divided into four cooperation slots.The helper computes tasks offloaded in the first slot and relays other tasks to the AP in later slots.
  • Partial offloading: For partial offloading, tasks are divided among local computing, helper computation cooperation, and AP offloading through jointly optimized resources.The optimization includes task partitioning, CPU frequencies, offloading time, and transmit powers under a latency constraint.
  • Binary offloading: For binary offloading, the user selects local computing, computation cooperation, or communication cooperation, then optimizes the corresponding resources.The resulting latency-constrained energy minimization problem is solved by first selecting the computation mode and then optimizing resource allocation.
  • Results: The proposed joint cooperation achieves higher computation capacity and lower energy consumption than benchmark schemes without joint design.The computation-capacity advantage is attributed to exploiting both computation and communication cooperation benefits.
  • Related work: Prior work studied communication cooperation and computation cooperation separately, whereas this paper combines them in one MEC design.The paper positions joint cooperation as distinct from existing relaying and cooperative-computing studies.

1) Computation Offloading to Helper:

The user offloads task bits to the helper through a wireless link, with transmission modeled by achievable rate and transmit-energy constraints. Local computing is modeled through CPU-cycle requirements, latency, frequency limits, and energy consumption.

  • Computation Offloading to Helper:: The user’s first-slot offloading energy is modeled as dominant transmission energy while circuit and baseband energy are ignored.The user’s transmit power is bounded by Pu,max.
  • Computation Offloading to Helper:: In the second and third slots, the helper relays the user’s data toward the AP, with separate user-to-helper and helper-to-AP transmission rates.The helper forwards decoded data in the third slot under its transmit-power limit.
  • Computation Offloading to Helper:: The user’s local workload requires CPU cycles proportional to input bits and must finish within the block under a maximum CPU-frequency constraint.The per-bit cycle coefficient is cu.
  • Computation Offloading to Helper:: For latency-constrained local computing, identical CPU frequencies across cycles and a tight latency constraint minimize the user’s computation energy.The resulting energy expression is obtained by substituting the optimal common frequency.

2) Cooperative Computing at Helper:

The helper computes user-offloaded bits during the time remaining after the first slot, while AP execution occupies a fourth slot. The paper formulates partial and binary offloading as latency-constrained total-energy minimization problems over computation and communication resources.

  • Cooperative Computing at Helper:: After receiving lh bits, the helper computes them during T − τ1 using a common CPU frequency bounded by fh,max.The helper’s required cycles are chlh.
  • Cooperative Computing at Helper:: The helper’s cooperative-computation energy depends on its effective capacitance coefficient κh and the chosen workload and execution duration.The model assigns ch CPU cycles per helper-computed input bit.
  • Cooperative Computing at Helper:: In the fourth slot, the AP executes AP-offloaded bits at its maximum CPU frequency, determining the remote-execution duration.The duration depends on the AP cycle requirement ca.
  • Problem Formulation:: The objective minimizes total user-and-helper energy subject to the user’s latency constraint by optimizing slot times, task partitions, and transmit powers.The design variables include τ, l, and P.
  • Problem Formulation:: Partial offloading is non-convex because time and transmit power are coupled, whereas binary offloading forms a mixed-integer nonlinear program over three computation modes.The paper develops separate solution procedures for the two models.

A. Feasibility of (P1) and (P2)

Feasibility is checked by comparing the task workload L with the maximum input bits supportable within the time block under each offloading model. Partial offloading can support at least as many bits as binary offloading.

  • A. Feasibility of (P1) and (P2):: A partial-offloading instance is feasible when its maximum supported workload satisfies L(1)_max ≥ L.Otherwise, the corresponding latency-constrained problem is infeasible.
  • A. Feasibility of (P1) and (P2):: For partial offloading, the maximum supportable bits are obtained by fully using available communication and computation resources and solving a linear program.The resource settings use maximum transmit powers and tight CPU, timing, and offloading constraints.
  • A. Feasibility of (P1) and (P2):: Binary offloading evaluates local computing, computation cooperation, and communication cooperation as the three possible execution modes.Each mode imposes a different zero-task assignment and resource configuration.
  • A. Feasibility of (P1) and (P2):: Binary feasibility is determined by comparing L with the maximum workload supported across the three modes.The communication-cooperation mode’s maximum is obtained from a linear program.
  • A. Feasibility of (P1) and (P2):: Partial offloading supports at least as many task input-bits as binary offloading because it can better use distributed computation resources.Every feasible binary solution is feasible for the partial-offloading formulation, but not conversely in general.

IV. OPTIMAL SOLUTION TO (P1)

The partial-offloading problem is transformed into a convex formulation and solved optimally through interior-point or Lagrange-duality methods. The dual decomposition yields structured subproblems and requires an additional step to recover a primal-optimal slot allocation in non-unique cases.

  • IV. OPTIMAL SOLUTION TO (P1):: Introducing Ei = Piτi replaces coupled transmit power and slot duration variables with energy variables, enabling reformulation of the partial-offloading problem.Power is recovered as Ei/τi when τi > 0.
  • IV. OPTIMAL SOLUTION TO (P1):: The reformulated problem is convex because rate perspective functions are jointly concave and the computing-energy terms are jointly convex.These properties establish convexity of the constraints and objective.
  • IV. OPTIMAL SOLUTION TO (P1):: Standard interior-point optimization can solve the convex reformulation optimally, while Lagrange duality provides additional engineering insight.The paper uses strong duality under Slater’s condition.
  • IV. OPTIMAL SOLUTION TO (P1):: The partial Lagrangian uses dual variables for offloading, timing, and task-partition constraints, then decomposes dual-function evaluation into five subproblems.The feasible dual set includes nonnegative inequality multipliers and coupling conditions.
  • IV. OPTIMAL SOLUTION TO (P1):: When certain coefficients vanish, the dual-derived slot solution may be non-unique or infeasible, so an additional procedure finds the primal-optimal τa.The selected dual-function evaluation point is not necessarily feasible or optimal for the primal problem.

B. Obtaining (λopt1, µopt1) to Maximize g(λ, µ)

The dual problem is solved by maximizing a concave, generally nondifferentiable dual function over nonnegative multipliers using subgradient-based methods.

  • The algorithm searches over (λ, µ) ∈ X to maximize the concave dual function g(λ, µ).Because g is generally nondifferentiable, an ellipsoid method can obtain optimal multipliers.
  • The subgradient of the objective with respect to (λ, µ) is used to guide the dual search.
  • Nonnegative constraints on µ1 and λi contribute unit-vector subgradients e4 and ei, respectively.Here, ei has one in the i-th position and zeros elsewhere in R5.

C. Optimal Primal Solution to (P1)

After obtaining the optimal dual multipliers, the method reconstructs the optimal primal allocation for partial offloading and derives qualitative relationships between resources, channels, and block duration.

  • C. Optimal Primal Solution to (P1): Substituting λopt1 and µopt1 into Lemmas 4.3–4.7 yields the corresponding optimal primal variables for (P1.1) and (P1).
  • C. Optimal Primal Solution to (P1): Because τ∗a is nonunique, an additional step constructs the remaining optimal variables for problem (P1).
  • C. Optimal Primal Solution to (P1): The remaining time and task allocations are obtained by solving a linear program, which can be efficiently handled by an interior-point method.
  • C. Optimal Primal Solution to (P1): Algorithm 1 combines the recovered allocations to optimally solve (P1) under partial offloading.
  • Insights on optimal cooperation: As T becomes large, the optimal number of locally computed task input-bits generally increases.This indicates a preference for local computing when the computation latency constraint becomes looser.
  • Insights on optimal cooperation: A stronger user-helper channel gain h01 increases the first-slot offloading power because the marginal offloading energy consumption decreases.
  • Insights on optimal cooperation: The second-slot cooperative-communication power depends on h01 and h0, whereas third-slot power increases as h1 becomes large.

V. OPTIMAL SOLUTION TO (P2)

For binary offloading, the paper solves (P2) by evaluating the energy consumption of three computation modes and selecting the minimum-energy mode.

  • An efficient algorithm optimally solves problem (P2) for binary offloading.
  • The user’s task can execute through local computing, computation cooperation, or communication cooperation.These modes correspond respectively to lu = L, lh = L, and la = L, with the other task portions set to zero.
  • The optimal solution evaluates energy consumption under all three modes and chooses the mode with minimum energy consumption.

A. Computation Modes for Binary Offloading Case

The binary-offloading solution compares feasible local, helper-computation, and AP-communication modes, deriving each mode’s minimum energy before selecting the best one.

  • Computation modes: The local mode assigns all L input-bits to the user, with lh = la = 0, and uses zero transmit power and time.It is feasible only when the user’s maximum locally executable input-bits condition is satisfied.
  • Computation modes: The computation-cooperation mode assigns all L input-bits to the helper, with lu = la = 0, and sets P2 = P3 = 0 and τ2 = τ3 = 0.This mode is feasible only under the helper’s corresponding maximum-computation condition.
  • Computation modes: At optimality, constraint (51b) is tight, reducing the computation-cooperation problem to a univariable convex optimization problem.The remaining scalar optimization can be solved efficiently by bisectional search.
  • Computation modes: The algorithm computes the minimum energy for each feasible mode and selects the mode with the lowest total energy consumption.

3) Communication Cooperation Mode:

The communication cooperation mode is reduced to a special case with all tasks offloaded to the AP through the helper relay, and its energy is obtained from the optimized formulation.

  • Communication Cooperation Mode: Communication cooperation sets l_a = L, l_u = l_h = 0, so all task input-bits are offloaded to the AP.Under this setting, P_1 = 0 and τ_1 = 0, and problem (P2) is re-expressed accordingly.
  • Communication Cooperation Mode: The resulting communication-cooperation problem is optimally solved using Algorithm 1 with l_u = 0, l_h = 0, l_a = L, and τ_1 = 0.The optimal solution is denoted by (τ opt_2), and the mode’s energy consumption is then obtained.

B. Computation Mode Selection

The paper selects the minimum-energy computation mode for binary offloading and evaluates joint cooperation against separate cooperation and local-computing benchmarks. Results show joint cooperation provides the strongest capacity and energy benefits, subject to the paper’s single-user, single-helper and common-interest assumptions.

  • Computation Mode Selection: For binary offloading, the optimal computation mode is selected among local computing, computation cooperation, and communication cooperation by minimum energy.The corresponding joint computation and communication resource allocation becomes the optimal solution after mode selection.
  • Benchmark Schemes: The benchmarks include local computing, computation cooperation, and communication cooperation under both partial and binary offloading.Partial offloading partitions tasks between local computing and either the helper or AP; binary cooperation offloads all tasks to the helper or AP.
  • Numerical Results: The proposed joint cooperation achieves the highest computation capacity across the evaluated local, computation-cooperation, and communication-cooperation schemes.This result is reported for both partial and binary offloading as block duration increases, with D = 20 m.
  • Numerical Results: The proposed joint cooperation achieves minimum average energy consumption for both partial and binary offloading cases.Figure 4 evaluates average energy versus block length with L = 0.02 Mbits and D = 120 m.
  • Numerical Results: Task partitioning yields more significant energy reduction under partial offloading than under binary offloading, while all schemes consume less energy as block length increases.In binary offloading, the preferred separate cooperation mode changes with block length; in partial offloading, communication cooperation is better at small T and computation cooperation at large T.
  • Numerical Results: As the user-helper distance increases, communication-cooperation energy first decreases then increases, computation-cooperation energy rises monotonically, and joint cooperation gains remain significant.The reported explanation is that user-helper channel gain decreases while helper-AP channel gain strengthens with distance.
  • Optimization Framework: The paper jointly optimizes task partitioning, CPU frequencies, offloading times, and transmit powers to minimize total user-helper energy under a latency constraint.The non-convex formulation is reformulated as a convex problem and solved optimally for partial offloading, while binary offloading uses computation-mode selection.

APPENDIX

The appendix establishes optimality conditions for a convex reformulation using strong duality and KKT conditions. It derives multiplier constraints, complementary slackness, stationarity relations, and the optimal time allocation.

  • The dual function is bounded below only when λ1 − µ2 ≥ 0 and λ2 + λ3 + µ1ca/fa,max − µ2 ≥ 0.
  • Convexity and Slater’s condition establish strong duality between problem (31) and its dual, enabling a KKT-based solution.
  • The Lagrangian multipliers correspond to energy, transmission-time, CPU-frequency, and helper-computation constraints.
  • KKT conditions include complementary slackness and first-order derivative conditions with respect to E1, τ1, and lh.
  • Substitution into the stationarity condition yields ρ1 and the optimal τ1* given in the cited equations.
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