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Digital Twin Assisted Task Offloading for Aerial Edge Computing and Networks

Bin Li, Yufeng Liu, Ling Tan, Heng Pan, Yan Zhang

arXiv:2208.00834v1cs.IT

TL;DR

The paper studies energy-efficient task offloading for mobile users in UAV-enabled MEC under dynamic environments and delay constraints. It combines adaptive digital twins with DDQN-based association and trajectory decisions, closed-form power allocation, and iterative computation-capacity allocation. The proposed design reduces system energy consumption relative to benchmark schemes, including reductions of 7%, 11%, and 59% against three named designs.

  • Problem

    The paper addresses energy minimization in mobile UAV-enabled MEC by jointly optimizing MTU association, UAV trajectory, transmission power, and computation capacity under processing-delay constraints.

  • Method

    The approach uses adaptive DTs for dynamic network-state prediction, DDQN for MTU association and UAV trajectory, a closed-form transmission-power solution, and an iterative computation-capacity algorithm.

  • Results

    The proposed design reduces whole MEC-system energy consumption by 7%, 11%, and 59% compared with the DQN design, Without optimize F design, and Greedy design, respectively.

  • Takeaways & Limitations

    Numerical results indicate that DT assistance and the proposed offloading design effectively reduce system energy consumption compared with the evaluated benchmark designs.

Abstract

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Considering the user mobility and unpredictable mobile edge computing (MEC) environments, this paper studies the intelligent task offloading problem in unmanned aerial vehicle (UAV)-enabled MEC with the assistance of digital twin (DT). We aim at minimizing the energy consumption of the entire MEC system by jointly optimizing mobile terminal users (MTUs) association, UAV trajectory, transmission power distribution and computation capacity allocation while respecting the constraints of mission maximum processing delays. Specifically, double deep Q-network (DDQN) algorithm stemming from deep reinforcement learning is first proposed to effectively solve the problem of MTUs association and UAV trajectory. Then, the closed-form expression is employed to handle the problem of transmission power distribution and the computation capacity allocation problem is further addressed via an iterative algorithm. Numerical results show that our proposed scheme is able to converge and significantly reduce the total energy consumption of the MEC system compared to the benchmark schemes.

I. INTRODUCTION

The paper addresses energy-efficient task offloading in a mobile UAV-enabled MEC network assisted by adaptive digital twins. It jointly optimizes user association, UAV trajectory, transmission power, and computation capacity under delay constraints using tractable optimization and learning-based decisions.

  • I. INTRODUCTION: UAVs address the location limitations and deployment costs of static ground base stations, while D2D offloading can reduce latency and help compensate for MEC server shortages.These technologies motivate aerial and device-assisted computing for mobile-edge services.
  • I. INTRODUCTION: Digital twins can monitor network status and provide perceptual data for timely offloading decisions, reducing real-time interaction, energy consumption, and resource use.The DITEN setting still raises challenges involving multiple users, computing platforms, DT placement, and estimation errors.
  • I. INTRODUCTION: The system minimizes overall energy consumption by jointly optimizing MTU association, UAV trajectory, transmission power distribution, and computation capacity allocation under task-delay constraints.The resulting problem is mixed-integer nonlinear and is reformulated to obtain a near-optimal solution with reduced complexity.
  • I. INTRODUCTION: Adaptive digital twins predict dynamic network states while accounting for user mobility, and D2D links assist task offloading and resource assignment.The framework is designed for a UAV-enabled MEC network with mobile users and multiple computing entities.
  • I. INTRODUCTION: The considered DITEN contains mobile users, resource devices, a UAV-mounted MEC server, and a BS, with tasks completed locally or through resource devices, the UAV, or the BS.The UAV acts as a relay when an MTU offloads a task to the BS.

A. A DT Model

The model represents mobile users, resource devices, and a UAV through digital twins that store network-state information while allowing estimation deviations. It then models mobility, task execution, communication, latency, and energy for local and remote computation choices.

  • A. A DT Model: Three DT categories represent MTUs, resource devices, and the UAV, storing raw entity data and monitoring the network’s current operating state at the BS.The MTU DT is updated through interaction with the physical MTU and network topology, but may deviate from the true state.
  • B. Mobility Model of MTUs: MTU mobility is modeled with a Gauss-Markov process, updating each user’s velocity and direction across time slots with persistent and random components.The model uses common average speed, user-specific average directions, and Gaussian random variables.
  • C. Task Computation Model: The task model assigns each independent task to one server choice, including local execution, a resource device, the UAV, or BS offloading assisted by the UAV.Binary decision variables distinguish the available offloading patterns in each time slot.
  • C. Task Computation Model: For local and remote execution, the model calculates transmission or execution latency and energy using task size, required CPU cycles, channel conditions, transmit power, and computing resources.Remote execution includes transmission and processing delays, while downloading results is ignored for resource-device offloading because computation results are much smaller.
  • A. A DT Model: DT estimation deviations are incorporated into the actual latency and computation models for MTUs, resource devices, and the UAV.The framework explicitly distinguishes estimated processing time from the latency gap between DT values and physical values.

T UAV

The section models energy consumption for task offloading across MTUs, UAV, and BS links, including transmission, flying, hovering, and total task energy.

  • UAV Flying Energy Consumption: UAV flying energy depends on the flight distance between successive flight hovering points during each time slot.The model uses flight power Pf and flight speed V.
  • UAV Hovering Energy Consumption: UAV hovering energy accounts for the time spent at a hovering point while completing an offloaded task.Hovering power is denoted by Ph.
  • Offloading Energy Model: The model includes MTU-to-UAV transmission energy and UAV-to-BS unloading energy for tasks forwarded through the UAV.Transmission rates and task durations determine the corresponding link energies.
  • Total Energy Consumption: The total energy for each computing task combines MTU transmission, UAV forwarding, flying, hovering, and associated processing components.The total task cost is represented by Em−j−B[n].

D. Problem Statement

The paper formulates energy-minimizing joint optimization of association, UAV trajectory, transmission power, and computation capacity under delay and energy constraints. The resulting problem is mixed-integer nonlinear and difficult to solve directly.

  • D. Problem Statement: The optimization jointly selects MTU association, UAV trajectory, transmission power distribution, and computation capacity allocation to minimize total system energy.The variable groups are A, U, P, and F.
  • D. Problem Statement: Each task must be assigned to one execution location while CPU frequencies, transmit powers, and energy expenditures remain bounded.The constraints cover association decisions, execution placement, maximum CPU frequencies, transmit powers, and energy limits.
  • D. Problem Statement: Tasks must be completed within their maximum processing delays, and MTUs, resource devices, and UAVs cannot exceed their available energy budgets.These requirements are enforced by delay and energy constraints.
  • D. Problem Statement: The original formulation is a mixed integer nonlinear programming problem that is highly complex for conventional direct optimization.The paper therefore seeks a tractable solution strategy.

IV. PROPOSED SOLUTION

The proposed solution decomposes the nonlinear optimization into sequential subproblems for association and trajectory, transmission power, and computation capacity.

  • IV. PROPOSED SOLUTION: The method first optimizes association and trajectory for fixed power and capacity, then power for fixed association, trajectory, and capacity, and finally capacity.This decomposition provides the solution sequence for the three subproblems.

A. MTUs Association and UAV Trajectory Optimization

The paper uses DT-assisted DDQN to optimize MTU association and UAV trajectory in a dynamic MEC environment. The reinforcement-learning formulation uses system energy as a negatively correlated reward and DDQN to reduce Q-value overestimation.

  • A. MTUs Association and UAV Trajectory Optimization: DDQN optimizes MTU association and UAV trajectory while addressing DQN’s Q-value overestimation problem.The method separates action selection from action evaluation.
  • A. MTUs Association and UAV Trajectory Optimization: The system state represents MTU and UAV locations together with generated task information, while actions include MTU offloading decisions.The state and action design captures mobility and task dynamics.
  • A. MTUs Association and UAV Trajectory Optimization: The reward is defined negatively with total energy consumption so maximizing reward corresponds to minimizing the system objective.A penalty is applied when an MTU exceeds its maximum processing delay.
  • A. MTUs Association and UAV Trajectory Optimization: DT maps MTUs, UAVs, and resource devices into a virtual environment where the DRL agent learns an offloading strategy at lower cost than interacting directly with the real environment.The agent interacts with the DT to obtain the strategy π∗.
  • A. MTUs Association and UAV Trajectory Optimization: The DDQN training uses replay memory, minibatch updates, target-network updates, and decreasing ε-greedy exploration to produce the policy π∗.The target network evaluates the action selected by the predicted network.

B. Transmission Power Distribution Optimization

The transmission power distribution is optimized by exploiting monotonic energy behavior, so each optimal transmit power is obtained in closed form by satisfying the relevant latency constraint.

  • Transmission-power monotonicity: The energy consumption of MTU m associated with resource device j increases with transmit power p_m,j[n], making the latency constraint tight at the optimum.This monotonicity supports the closed-form transmit-power solution for the MTU-to-resource-device link.
  • MTU-to-resource-device transmission: Theorem 1 derives the optimal MTU-to-resource-device transmit power in closed form from the latency constraint.The proof explicitly sets the transmission and execution delay expression equal to the mission deadline before solving for power.
  • MTU-to-UAV transmission: The energy consumption of an MTU associated with UAV j increases with UAV transmit power p^UAV, and Theorem 2 gives the corresponding closed-form optimum.The optimum is obtained by enforcing the latency constraint for the MTU-to-UAV transmission.
  • UAV-to-BS transmission: The energy consumption of UAV j associated with the BS increases with p^BS_j,B[n], and Theorem 3 provides the closed-form optimal transmit power.The derivation again uses the latency constraint and solves the resulting expression for the BS-link transmit power.

C. Computation Capacity Allocation Optimization

Computation capacity allocation is formulated as an optimization subproblem and solved iteratively once the relevant policy and transmission-power distribution are fixed.

  • Capacity-allocation formulation: The computation capacity allocation variable F is optimized through a dedicated subproblem.The section explicitly introduces an optimization problem for F.
  • Iterative solution: With the optimal policy π* and transmission-power distribution P fixed, the capacity-allocation subproblem becomes a standard linear program.The paper states that P1.3 can be solved effectively with optimization tools such as CVX in an iterative way.
  • Policy optimization: The DDQN procedure uses experience replay, ε-greedy action selection, mini-batch updates, and periodic target-network updates to output the optimal policy π*.Algorithm 1 stores transitions, samples mini-batches when memory is full, updates φ1, and periodically sets φ2 = φ1.

D. Joint Algorithm Design

The joint algorithm decomposes the original optimization into association and trajectory decisions, transmission power, and computation capacity, then solves these components through their respective procedures.

  • Joint optimization: The joint method partitions the optimization variables into {A, U}, P, and F and optimizes them through P1.1, Theorems 1–3, and P1.3.MTU association and UAV trajectory use the DRL-based subproblem, transmission powers use closed-form theorems, and computation capacity uses P1.3.

V. COMPLEXITY AND CONVERGENCE ANALYSIS

Algorithm 2 alternates among policy and trajectory optimization, closed-form transmission-power updates, and capacity allocation until the objective improvement falls below a threshold. The analysis establishes convergence, gives a complexity expression, and shows that learning-rate choices trade convergence speed against local-optimum risk.

  • Joint algorithm: Algorithm 2 alternates DDQN-based policy optimization, closed-form power updates, and capacity allocation until the fractional objective increase is below ς.It outputs MTU association A, UAV trajectory U, transmission power P, and computation capacity F.
  • Complexity analysis: The reported complexity of Algorithm 2 is O[NM(K + Q + 2) + EN(M + Q + K)].The expression combines the DDQN-related component and the computation-capacity allocation component, where E denotes the number of external iterations.
  • DDQN convergence: A higher DDQN learning rate accelerates convergence but increases the possibility of reaching a local rather than global optimum.The paper therefore recommends selecting the learning rate according to the specific situation.
  • Convergence analysis: The proposed Algorithm 2 converges because each iteration produces a nonincreasing objective value bounded below by a finite value.This argument applies after alternating updates of the transmission-power and computation-capacity subproblems.

VI. NUMERICAL RESULTS

The proposed DT-assisted design consistently lowers MEC energy consumption across task loads, user populations, DT settings, and benchmark comparisons. Its advantage is attributed to joint offloading and resource optimization, with DT assistance reducing data interaction overhead.

  • Task quantity: The proposed design achieves the lowest total energy consumption across task quantities and increasingly outperforms alternatives as task quantity grows.The comparison is made against DQN, unoptimized-capacity, local-computation, and greedy designs.
  • User number: As user number M increases, total energy consumption rises for every design, while the proposed design remains lower and its gap over benchmarks widens.Greedy design has the highest energy consumption and increases dramatically with M.
  • MTU energy consumption: The proposed design remains superior to greedy and local-computation designs for MTU energy consumption as task bits vary from 50 Mbits to 150 Mbits.UAVs, resource devices, and the BS act as helpers for task computation.
  • DT assistance: DT assistance significantly reduces system energy consumption by storing MTU, UAV, and resource-device states and avoiding additional data interaction when searching for offloading points.The same mechanism also saves data-transmission time.
  • DT deviation: With fixed task quantity, system energy consumption is inversely correlated with DT deviation, and the proposed design outperforms DQN across the examined settings.The passage attributes the relationship to estimation error between DT values and actual system conditions.
  • Computation capacity: Increasing MTUs’ maximum computation capacity decreases system energy consumption because more local computation can satisfy latency requirements without offloading.The trend is reported for varying F_MTU^max.

VII. CONCLUSION

The paper develops a DT-aided task-offloading scheme for mobile users in UAV-enabled edge networks. It combines DDQN, closed-form power allocation, and iterative computation-capacity allocation, reducing energy consumption relative to three benchmark designs.

  • Conclusion: The scheme targets task execution for moving MTUs that generate tasks, using high-performance edge nodes within specified completion times.The system is a DT-aided aerial edge-computing network.
  • Conclusion: DDQN handles intelligent MTU offloading and UAV deployment, while closed-form power allocation and an iterative algorithm allocate computation capacity.Capacity allocation covers multiple MTUs, resource devices, and the UAV.
  • Conclusion: Energy consumption is reduced by 7%, 11%, and 59% versus DQN, unoptimized computation capacity, and greedy designs, respectively.These are the reported numerical comparisons for the proposed design.
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