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Stochastic Joint Radio and Computational Resource Management for Multi-User Mobile-Edge Computing Systems

Yuyi Mao, Jun Zhang, S. H. Song, Khaled B. Letaief

arXiv:1702.00892v1cs.IT

TL;DR

Multi-user MEC must dynamically coordinate radio and computational resources under changing task arrivals and wireless channels while maintaining stable task buffers and limiting long-term weighted power. The paper develops a Lyapunov-based online joint-management algorithm with closed-form CPU and scheduling decisions, Gauss-Seidel offloading allocation, and a delay-improved mechanism. Analysis and simulations characterize an [O(1/V), O(V)] tradeoff between weighted sum power consumption and execution delay.

  • Problem

    Multi-user MEC requires joint radio and computational resource management to minimize long-term average weighted sum power consumption subject to task-buffer stability under stochastic demands and wireless fading.

  • Method

    The paper uses a Lyapunov-optimization online algorithm, closed-form CPU-frequency and MEC-scheduling decisions, Gauss-Seidel offloading allocation, and a delay-improved mechanism.

  • Results

    The weighted sum power consumption and execution delay follow an [O(1/V), O(V)] tradeoff with control parameter V, supported by analysis and simulations.

  • Takeaways & Limitations

    The results characterize power–delay balancing and parameter impacts, supporting joint radio and computational resource management for multi-user MEC deployment.

Abstract

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Mobile-edge computing (MEC) has recently emerged as a prominent technology to liberate mobile devices from computationally intensive workloads, by offloading them to the proximate MEC server. To make offloading effective, the radio and computational resources need to be dynamically managed, to cope with the time-varying computation demands and wireless fading channels. In this paper, we develop an online joint radio and computational resource management algorithm for multi-user MEC systems, with the objective as minimizing the long-term average weighted sum power consumption of the mobile devices and the MEC server, subject to a task buffer stability constraint. Specifically, at each time slot, the optimal CPU-cycle frequencies of the mobile devices are obtained in closed forms, and the optimal transmit power and bandwidth allocation for computation offloading are determined with the Gauss-Seidel method; while for the MEC server, both the optimal frequencies of the CPU cores and the optimal MEC server scheduling decision are derived in closed forms. Besides, a delay-improved mechanism is proposed to reduce the execution delay. Rigorous performance analysis is conducted for the proposed algorithm and its delay-improved version, indicating that the weighted sum power consumption and execution delay obey an $\left[O\left(1\slash V\right),O\left(V\right)\right]$ tradeoff with $V$ as a control parameter. Simulation results are provided to validate the theoretical analysis and demonstrate the impacts of various parameters.

I. INTRODUCTION

MEC addresses resource-limited mobile devices and latency concerns by moving computation toward the radio access network, but multi-user systems require stochastic joint management of shared radio and computational resources. This paper develops an online Lyapunov-based approach that minimizes weighted power while characterizing power–delay tradeoffs.

  • Motivation: Resource-limited mobile devices face stringent computation-quality requirements for intensive applications such as gaming, recognition, and 3D modeling.Limited processing speed, memory, and battery energy constrain mobile execution.
  • Motivation: MEC places computation capability within the radio access network, enabling task offloading that can improve energy consumption and execution latency.Offloading tasks to proximate MEC servers is presented as an alternative to latency-inducing remote public clouds.
  • Research gap: Stochastic task arrivals make long-term system performance relevant for delay-tolerant applications, requiring policies that account for coupled random workloads.Examples include multimedia streaming and file backup.
  • Research gap: Multi-user MEC operations are temporally and spatially coupled because devices share computational and radio resources while supporting parallel local and remote processing.This coupling motivates joint allocation of radio and computational resources.
  • Contributions: The paper formulates weighted sum power minimization subject to task-buffer stability and jointly manages device CPUs, offloading power and bandwidth, and MEC scheduling.The system includes multiple devices and a limited-capability MEC server, extending a prior unlimited-computation-resource setting.
  • Contributions: A Lyapunov-based online algorithm, closed-form resource decisions, and a delay-improved mechanism characterize the power–delay tradeoff and parameter impacts.The reported tradeoff is [O(1/V), O(V)] for weighted sum power consumption and execution delay.

C. Organization

The paper models a multi-device MEC system with stochastic arrivals, local and remote task queues, wireless access, and server execution. Queue evolution tracks local processing, offloading, server scheduling, and newly arriving tasks over slotted time.

  • C. Organization: The paper is organized around system modeling, problem formulation, online joint resource management, performance analysis, simulations, and conclusions.The proposed algorithms and their analysis are developed before simulation validation.
  • System model: The system contains N single-core mobile devices assisted by a physically proximate MEC server accessed through wireless channels.The server may be a small data center deployed at a wireless access point.
  • System model: MEC enables joint radio and computational resource management, and task offloading can improve computation experience and reduce mobile battery energy consumption.The system uses FDMA over total bandwidth ω Hz and operates in slots of length τ.
  • Computation task and queueing models: Each mobile device receives independent fine-grained tasks whose arrivals are i.i.d. over time within bounded ranges and have mean λ_i.Arrived tasks that are not executed or offloaded remain in the mobile task buffer.
  • Computation task and queueing models: The mobile queue evolves from prior backlog after local execution and offloading, plus new arrivals, while the MEC queue stores offloaded tasks awaiting server execution.Only tasks not executed locally are placed in the corresponding server queue.
  • Computation task and queueing models: The MEC server schedules per-device task execution from its queues, with initially empty mobile and server buffers and sufficiently large queue capacities.The queue equations also permit transmission of excess dummy task inputs when departures exceed local backlog.

B. Local Execution Model

The model represents local execution through CPU-cycle frequency and switched-capacitance power, and represents offloading through fading-channel transmission with FDMA bandwidth allocation. The MEC server uses multiple CPU cores with bounded frequencies and shared scheduling constraints.

  • Local execution: Local execution processes Dl,i(t) = τf_i(t)L_i^-1 task-input bits when the mobile CPU frequency f_i(t) is bounded by f_i,max.L_i denotes the CPU cycles required per input bit.
  • Local execution: Mobile CPU power is modeled from dynamic CMOS power and the effective switched capacitance κmob,i associated with the chip architecture.The model relates voltage and CPU-cycle frequency under low-voltage operation.
  • Computation offloading: Offloading delivers task-input bits over i.i.d. frequency-flat block-fading wireless channels characterized by channel gain γ_i(t) and path loss.Transmission uses FDMA, with transmit power ptx,i(t) and bandwidth proportion α_i(t) selected from feasible constraints.
  • MEC server scheduling: The MEC server has an M-core CPU whose core frequencies fC,m(t) are bounded by fCm,max and whose power depends on effective switched capacitance κser,m.Server CPU cycles are allocated among offloaded tasks through a scheduling decision.
  • MEC server scheduling: The server scheduling decision must satisfy CPU-cycle availability constraints when allocating execution capacity across mobile devices.The scheduled amount Ds,n(t) represents tasks from device n executed by the MEC server in slot t.

III. PROBLEM FORMULATION

The paper formulates stochastic joint radio and computational resource management as minimizing long-term average weighted sum power under task-buffer stability. It models local execution, computation offloading, MEC-server processing, and coupled time-slot decisions.

  • A. Performance Metrics: The performance objective is average weighted sum power consumption across mobile devices and the MEC server.Weights allow different emphasis on power consumption at each entity.
  • A. Performance Metrics: The power metric includes local CPU and offloading transmit power while ignoring energy for screens and other basic operations.The model focuses on task-execution processes at mobile devices and the server.
  • A. Performance Metrics: Average task-buffer queue length measures execution delay because Little’s Law makes delay proportional to tasks waiting in the MEC system.The queue includes task buffers at both device and server sides.
  • B. Average Weighted Sum Power Consumption Minimization: P1 imposes bandwidth, mobile CPU-frequency and transmit-power, server CPU-frequency, scheduling, and mean-rate task-buffer stability constraints.Mean-rate stability guarantees finite delay for all arrived computation tasks.
  • B. Average Weighted Sum Power Consumption Minimization: The stochastic optimization jointly determines mobile CPU frequencies, transmit powers, bandwidth allocations, MEC scheduling, and server-core frequencies each time slot.Decisions depend on channel and task-buffer state information and are temporally correlated by random task arrivals.
  • B. Average Weighted Sum Power Consumption Minimization: Spatially coupled bandwidth allocation and its interdependence with computational resources make separate radio or computation optimization inadequate.Over-conservative or over-aggressive offloading can waste available computational resources.
  • B. Average Weighted Sum Power Consumption Minimization: The paper replaces P1 with differentiable P2 by restricting bandwidth allocations away from zero, enabling an efficient online algorithm feasible for P1.The optimal values of P1 and P2 can be made arbitrarily close by choosing ǫA sufficiently small.

IV. ONLINE JOINT RADIO AND COMPUTATIONAL RESOURCE MANAGEMENT ALGORITHM

The paper proposes an online joint radio and computational resource management algorithm based on Lyapunov optimization, together with a mechanism intended to improve delay. The analysis targets asymptotic optimality and the power-delay tradeoff.

  • IV. ONLINE JOINT RADIO AND COMPUTATIONAL RESOURCE MANAGEMENT ALGORITHM: The proposed algorithm uses Lyapunov optimization to manage radio and computational resources online in multi-user MEC systems.The stochastic problem is converted into deterministic per-time-slot optimization with low-complexity solutions.
  • IV. ONLINE JOINT RADIO AND COMPUTATIONAL RESOURCE MANAGEMENT ALGORITHM: A delay-improved mechanism is designed as an extension of the Lyapunov optimization-based algorithm.It is intended to reduce execution delay.
  • IV. ONLINE JOINT RADIO AND COMPUTATIONAL RESOURCE MANAGEMENT ALGORITHM: The proposed algorithm and its delay-improved version achieve asymptotic optimality and reveal a power-delay tradeoff in multi-user MEC systems.These properties are established through the paper’s subsequent performance analysis.

A. The Lyapunov Optimization-Based Online Algorithm

The online algorithm minimizes a Lyapunov drift-plus-penalty upper bound at every time slot. This maintains task queues at a low level while minimizing weighted power consumption through deterministic constrained decisions.

  • A. The Lyapunov Optimization-Based Online Algorithm: The algorithm defines conditional Lyapunov drift as the expected change in a Lyapunov function conditioned on the current queue state.The queue-state vector is Θ(t) = [Q(t), T(t)].
  • A. The Lyapunov Optimization-Based Online Algorithm: The drift-plus-penalty function adds V times conditional weighted power consumption to the Lyapunov drift.V is a positive control parameter that determines the power-versus-queue tradeoff.
  • A. The Lyapunov Optimization-Based Online Algorithm: At each time slot, the algorithm minimizes an upper bound on drift-plus-penalty over feasible system operations.The resulting deterministic problem retains P2’s constraints except task-buffer stability.
  • A. The Lyapunov Optimization-Based Online Algorithm: Algorithm 1 observes queue-related state and arrivals, selects frequencies, transmit power, bandwidth, and scheduling, then updates the task queues.The per-slot objective includes weighted mobile transmit and local-CPU power plus MEC-server power.
  • A. The Lyapunov Optimization-Based Online Algorithm: The drift-based decisions keep waiting tasks at a low level while minimizing weighted sum power consumption of mobile devices and the MEC server.This connects queue control with the paper’s power objective.

B. Optimal Solution For PPTS

The per-slot problem is solved by decomposing local CPU, offloading, bandwidth, and server decisions. Closed-form updates and Gauss-Seidel optimization exploit problem structure while exposing complexity and parameter effects.

  • B. Optimal Solution For PPTS: The per-slot optimization separates local CPU frequencies, offloading power and bandwidth, and MEC-server scheduling and core frequencies.This decomposition enables specialized solutions for the resulting subproblems.
  • B. Optimal Solution For PPTS: Local CPU-frequency optimization decomposes across mobile devices, with each optimum obtained from a stationary point or boundary point.The optimal local frequency is non-decreasing with the local task-buffer backlog.
  • B. Optimal Solution For PPTS: Larger V or device power weight wi lowers the optimal local CPU frequency, while larger Li or κmob,i also lowers it.These parameters increase the relative cost or energy required for local execution.
  • B. Optimal Solution For PPTS: A device offloads only when its local task-buffer amount exceeds the corresponding server-side buffer amount.Otherwise, offloading consumes transmit power and is treated as inferior to local execution for delay.
  • B. Optimal Solution For PPTS: For devices eligible to offload, transmit power and bandwidth are optimized alternately using closed-form power updates and Lagrangian bandwidth allocation.The bandwidth allocation is coupled across mobile devices.
  • B. Optimal Solution For PPTS: The Gauss-Seidel procedure converges to the global optimum of the convex offloading subproblem with a sublinear convergence rate.Its main per-iteration complexity comes from bisection-based Lagrangian bandwidth optimization.
  • B. Optimal Solution For PPTS: Generic convex algorithms have relatively high complexity because they do not fully exploit the problem’s structure.The paper motivates Gauss-Seidel optimization as a structure-aware alternative.
  • B. Optimal Solution For PPTS: The proposed method has low complexity because local and server CPU frequencies are obtained in closed forms, and its performance admits analytical characterization.The analysis supports the claimed asymptotic optimality.

C. A Delay-Improved Mechanism

The delay-improved mechanism reallocates otherwise excessive MEC-server CPU cycles to other devices while preserving Algorithm 1’s power performance and reducing execution delay.

  • Motivation: The mechanism addresses potentially wasted MEC-server CPU cycles by reallocating excessive computational resources to other devices.Only one mobile device is scheduled by the MEC server in each time slot, so available CPU cycles may remain unused.
  • Mechanism: The decision center maintains virtual task buffers and uses their states to compute the optimal per-time-slot solution.The actual implementation modifies the MEC-server scheduling decision from the computed solution.
  • Mechanism: The implementation modifies MEC-server scheduling by sorting devices according to their virtual task-buffer measures and reallocating CPU cycles.Algorithm 3 includes device ordering and CPU-cycle reallocation procedures.
  • Performance: The delay-improved mechanism has the same power consumption as Algorithm 1, while its average execution delay is not increased.The proposition states that power consumption remains the same and average execution delay, measured by average sum queue length, does not increase.
  • Performance: The mechanism preserves Algorithm 1’s benefits while enhancing average execution delay without extra power consumption.The paper explicitly characterizes this as a delay improvement without additional power expenditure.

V. PERFORMANCE ANALYSIS

The performance analysis establishes feasibility relationships and derives bounds for the proposed algorithms’ power consumption and queue lengths. It shows an [O(1/V), O(V)] tradeoff between weighted sum power consumption and execution delay.

  • Feasibility and optimality: P2 is feasible if and only if P3 is feasible, and their optimal objective values are equal.The equivalence is established by relating feasible policies and their induced queue lengths and power consumption.
  • Feasibility and optimality: For any δ > 0, a stationary randomized policy exists that satisfies the instantaneous constraints and operates arbitrarily close to P3’s optimum.This policy provides the basis for the subsequent performance bounds.
  • Theoretical guarantees: Under Algorithm 1 and Algorithm 3, the average weighted sum power consumption, queue stability, and average queue-length bounds are characterized when P2 is feasible.Theorem 1 states these guarantees jointly for both algorithms.
  • Tradeoff: The worst-case average weighted sum power consumption decreases inversely with V, while the upper bound on average sum queue length increases linearly with V.The queue length corresponds to execution delay according to Little’s Law.
  • Tradeoff: The two objectives obey an [O(1/V), O(V)] tradeoff, allowing V to balance power consumption against execution delay.Small V is suggested for delay-sensitive applications, whereas large V is suggested for energy-sensitive or delay-tolerant settings.

VI. SIMULATION RESULTS

Simulations validate the predicted power–delay tradeoff and examine how control parameters, server capacity, weighting factors, and user population affect MEC performance. The delay-improved algorithm preserves power consumption while reducing queue lengths, and task buffers stabilize under tested conditions.

  • Resource allocation: Optimized bandwidth allocation outperforms equal bandwidth allocation in both weighted sum power consumption and task-buffer queue length, supporting joint radio and computational resource management.Equal allocation uses αi(t) = 1/N.
  • Delay improvement: Algorithm 3 achieves the same average weighted sum power consumption as Algorithm 1 while reducing average task-buffer queue length, with the reduction more evident for larger wN+1 and V.The queue-length reduction corresponds to reduced execution delay.
  • Power weighting: Increasing wN+1 shifts power consumption from the MEC server to mobile devices and increases queue lengths by slowing server CPU frequencies.The server’s power decreases while mobile-device power increases, with larger queue lengths at higher weighting factors.
  • Scalability and stability: Task buffers stabilize within approximately 1000 time slots for N = 5, 10, and 20, although larger N produces longer convergence times.The stabilized sum queue lengths are approximately 1 × 10^6, 1.4 × 10^6, and 2 × 10^6 bits, respectively.

VII. CONCLUSIONS

The paper develops stochastic joint radio and computational resource management for multi-user MEC systems and proposes a low-complexity online algorithm with a delay-improved mechanism. Analysis and simulations characterize the power–delay tradeoff and parameter impacts, while identifying directions for extending the work.

  • A low-complexity online algorithm based on Lyapunov optimization is proposed for stochastic joint radio and computational resource management in multi-user MEC systems.
  • A delay-improved mechanism is designed to reduce execution delay.
  • Performance analysis and simulations characterize the tradeoff between average weighted sum power consumption and average execution delay.
  • The study reveals parameter impacts and provides guidelines for practical MEC-system deployment.
  • Future work includes fairness among multiple devices, distributed implementation, mobility-aware management, dynamic access control, and user–server association.

APPENDIX

The appendix derives inequalities for local and MEC-server task-buffer dynamics, analyzes per-slot scheduling structure, and establishes performance and mean-rate-stability results for the algorithms.

  • Drift analysis: Squaring the local task-buffer dynamics and summing the resulting inequalities supports the drift analysis.
  • Drift analysis: Analogous inequalities are derived for MEC-server task-buffer dynamics, including service and task-routing terms.
  • Per-slot optimization: For the per-slot scheduling problem, an optimal solution can schedule only the device with the highest relevant value, with zero scheduling when all CPU-core frequencies are zero.
  • Per-slot optimization: The constructed one-device scheduling solution performs no worse than a solution scheduling multiple devices.
  • Performance bounds: The analysis uses the optimal per-time-slot solution and a stationary randomized policy to derive bounds involving C + V · P opt.
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