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Latency and Reliability-Aware Task Offloading and Resource Allocation for Mobile Edge Computing

Chen-Feng Liu, Mehdi Bennis, H. Vincent Poor

arXiv:1710.00590v1cs.NI

TL;DR

The paper addresses the extra latency of MEC offloading and the inadequacy of average queue metrics for latency and reliability guarantees. It imposes probabilistic queue-length constraints, uses extreme value theory and Lyapunov stochastic optimization, and evaluates the resulting power-delay tradeoff and resource requirements.

  • Problem

    Average queue length and latency metrics do not capture low-probability queueing violations, while server-side waiting can matter when many users offload tasks.

  • Method

    The paper formulates computation and transmit power minimization with latency and reliability constraints, using extreme value theory and Lyapunov stochastic optimization for dynamic control.

  • Results

    The proposed MEC network achieves a better power-delay tradeoff while satisfying probabilistic queueing constraints and examining server-resource requirements across computation intensities.

  • Takeaways & Limitations

    Latency and reliability-aware control can evaluate both average delay and rare queueing violations in multi-user MEC offloading.

Abstract

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While mobile edge computing (MEC) alleviates the computation and power limitations of mobile devices, additional latency is incurred when offloading tasks to remote MEC servers. In this work, the power-delay tradeoff in the context of task offloading is studied in a multi-user MEC scenario. In contrast with current system designs relying on average metrics (e.g., the average queue length and average latency), a novel network design is proposed in which latency and reliability constraints are taken into account. This is done by imposing a probabilistic constraint on users' task queue lengths and invoking results from extreme value theory to characterize the occurrence of low-probability events in terms of queue length (or queuing delay) violation. The problem is formulated as a computation and transmit power minimization subject to latency and reliability constraints, and solved using tools from Lyapunov stochastic optimization. Simulation results demonstrate the effectiveness of the proposed approach, while examining the power-delay tradeoff and required computational resources for various computation intensities.

I. INTRODUCTION

The paper addresses latency and reliability limitations in MEC designs that rely on average queueing metrics. It proposes probabilistic queue-length constraints, extreme value theory, and Lyapunov optimization for latency- and reliability-aware task offloading and resource allocation.

  • MEC reduces mobile devices’ computation and energy burdens, but offloading introduces additional latency that must be included in system design.
  • Prior MEC studies ensured finite average queue length, which is insufficient for URLLC reliability requirements and ignores server-side waiting when many users offload tasks.
  • The proposed design models higher-order queue-length statistics and imposes probabilistic constraints on delay or queue-length violations.
  • Extreme value theory is used to characterize low-probability queue-length deviations, while Lyapunov stochastic optimization produces a dynamic policy for computation, offloading, and resource allocation.
  • Numerical results examine the power-delay tradeoff and how server computational resources scale with computation intensity.

II. SYSTEM MODEL

The system model contains UEs with local computation capabilities and multi-core MEC servers that assist by computing offloaded tasks. UEs dynamically access servers selected according to expected channel strength over block-fading wireless links.

  • The MEC network consists of UEs with local computation capability and MEC servers with N-core CPUs for offloaded task computation.
  • Each UE accesses servers whose expected channel gains exceed a threshold and dynamically offloads tasks to those servers.
  • The channel gain between UE i and server j includes path loss and fading, with wireless channels modeled as block fading over unit-length coherence blocks.

A. Traffic Model at the UE Side

Tasks arrive stochastically at each UE and may be computed locally or offloaded to one server. UE task completion combines local CPU execution with wireless transmission, under bandwidth, noise, and device-resource constraints.

  • Tasks arrive according to an arbitrary probability distribution, and large tasks are divided into subtasks that can be computed in one time slot.
  • Each task is computed either at its UE or at one assigned MEC server, while each UE maintains a queue for arriving tasks.
  • UE task completion consists of local computation and offloading transmission, with local rate determined by CPU frequency and processing density.
  • Offloading transmission uses transmit power over shared server bands, with reception modeled in additive white Gaussian noise.
  • Local computation power follows κ[f_i(t)]^3, and DVFS adapts CPU frequency subject to local-computation and transmit-power limits.

B. Traffic Model at the Server Side

Each MEC server maintains separate buffers for users’ offloaded tasks and allocates CPU resources to process them. Server scheduling limits each CPU core to at most one UE per time slot and assigns each UE’s tasks to one core.

  • Each server maintains a parallel offloaded-task buffer for every associated UE, with queue length measured in bits.
  • Server j allocates CPU-cycle frequency f_ji(t) to process UE i’s offloaded tasks.
  • Each CPU core serves at most one UE per time slot, and a UE’s offloaded tasks are computed by only one core at a given server.

III. LATENCY REQUIREMENTS AND RELIABILITY CONSTRAINTS

The paper treats low-probability queue-length violations as reliability risks that average queue metrics cannot capture. It uses extreme value theory to model queue exceedances and impose probabilistic latency constraints while accounting for computation and transmission delays.

  • Average queue length alone cannot represent low-probability latency and reliability violations.End-to-end delay includes UE/server queuing, computation, and wireless transmission delays.
  • The framework constrains UE queue-length violations using a bound d_i and tolerable probability ϵ_i ≪ 1.Queue overflow can drop incoming tasks and undermine computing reliability.
  • Extreme value theory characterizes the tail behavior of queue lengths and the probability of extreme latency events.The queue-length CCDF reflects the latency profile: faster decay indicates lower probability of extreme latency.
  • For sufficiently high thresholds, the conditional excess queue value is approximated by a generalized Pareto distribution.The excess is defined as X_i(t)=Q_i(t)−d_i conditioned on Q_i(t)>d_i.
  • The GPD is controlled by scale σ_i and shape ξ_i parameters, whose thresholds constrain the mean and variance of queue exceedances.Smaller σ_i and ξ_i correspond to smaller GPD mean and variance; the analysis assumes ξ<1/2.
  • Server-side offloaded-task queues receive analogous exceedance constraints based on latency bounds and moving average offloading rates.This extends the reliability treatment beyond UE queues to server queuing latency.
  • Higher local CPU frequency or transmit power reduces computation, transmission, and implicitly queueing delays but depletes battery energy faster.

IV. LATENCY AND RELIABILITY-AWARE TASK OFFLOADING AND RESOURCE ALLOCATION

The paper formulates network-wide power minimization for local computation, task offloading, and server resource allocation under resource, latency-violation, and reliability constraints. Long-term power and the associated offloading and computational decisions are optimized using Lyapunov stochastic optimization.

  • The optimization minimizes network-wide power over transmit power and UE/server computational resource allocations.
  • Resource-allocation constraints and delay-bound violation constraints jointly define the optimization problem.
  • The objective includes each UE’s long-term time-average power consumption.
  • Lyapunov stochastic optimization is used to obtain the task-offloading and computational-resource allocation policy.

A. Lyapunov Optimization Framework

The Lyapunov framework converts time-averaged latency, reliability, and resource constraints into virtual queues and minimizes an upper bound on drift-plus-penalty each slot. The parameter V controls the power–latency tradeoff.

  • The paper rewrites queue-violation constraints using indicator functions before introducing virtual queues.
  • Corresponding virtual queues enforce the time-averaged constraints for conditional-excess moments, delays, reliability, and resource allocation.
  • The conditional Lyapunov drift-plus-penalty combines queue evolution with the power penalty for each time slot.
  • V is a nonnegative parameter that trades off power consumption against end-to-end latency.
  • The original problem is solved by minimizing the drift-plus-penalty upper bound, producing three per-slot optimization problems.Two concern UE local computation and offloading; one concerns server resource allocation.

B. Task Computation and Offloading at the UE Side

At each slot, UEs and servers solve resource-allocation subproblems for local computation, task offloading, and transmission. The design decomposes UE offloading decisions to avoid requiring other users’ channel and queue information.

  • Local computation: UE local computation allocates CPU-cycle frequency through a dedicated optimization problem.
  • Task offloading: UE-side task offloading is formulated as a joint decision over all users’ offloading policies.
  • Task offloading: Decomposing the aggregate objective into |U| subproblems enables each UE to decide transmit power without other UEs’ CSI or QSI.The decomposition addresses the overhead and impracticality of centralized information exchange in dense networks.
  • Task offloading: Each UE’s optimal positive offloading power is obtained by applying KKT conditions to its convex subproblem.
  • Simulation setup: Simulation parameters are listed in Table I.

C. Computational Resource Allocation at the Server Side

The server allocates computational resources through an optimization problem and updates system queues and empirical offloading statistics across time slots.

  • Server-side resource allocation is formulated as an optimization problem for each MEC server.
  • The server equally dedicates its N CPU cores to the UEs with the N largest values of bji(t)/Li.
  • Algorithm 1 details the solution to the server resource-allocation problem.
  • After each slot, UEs and MEC servers update their queues and related state variables for the next slot.
  • The UE empirically estimates offloading-interruption statistics from the transmission rate for the next slot.

V. NUMERICAL RESULTS

Numerical experiments examine the power-delay tradeoff, delay and reliability under different offloading configurations, and queue-tail behavior under probabilistic constraints. Results show that offloading is most beneficial for intense computation or high task arrival rates, while extreme-value modeling tracks queue exceedances.

  • Experimental setup: Four MEC servers with 9 CPU cores each serve 36 UEs randomly distributed in a 100 × 100 m2 indoor area.
  • Experimental setup: The processing densities correspond to applications ranging from the English Wikipedia main page to 7-queen puzzle workloads.
  • Power-delay tradeoff: Small V yields lower end-to-end delay at higher power, whereas large V asymptotically minimizes power at higher latency.
  • Power-delay tradeoff: For L = 737.5 cycle/bit and λ = 0.3 Mbps, local computation is sufficient and offloading worsens delay performance.
  • Offloading performance: Higher processing density or task arrival rates make offloading beneficial because servers provide faster computation and increase task completion rates.
  • Reliability: The MEC architecture achieves better reliability than local computation in settings where it also improves average end-to-end delay.
  • Reliability: For L = 8250 cycles/bit, reliability enhancement is more prominent while average end-to-end delay is reduced.
  • Queue-tail analysis: At λi = 1.3 Mbps and Li = 737.5 cycle/bit, Pr(Q > 2.6 × 10^5) = 3 × 10^-4, while the excess distribution and approximated GPD coincide.

VI. CONCLUSIONS

The paper develops a latency- and reliability-aware MEC design for multi-user task computation and offloading. It combines probabilistic queue constraints, extreme value theory, and Lyapunov optimization, with numerical results showing improved power-delay tradeoffs for demanding workloads.

  • The study considers an URLLC-enabled MEC architecture with multiple users and servers using high-order latency and reliability statistics.
  • Probabilistic queue-length or queuing-delay violation constraints and extreme value theory address low-probability extreme events.
  • The optimization minimizes computation and transmit power subject to latency requirements and reliability constraints.
  • Lyapunov stochastic optimization produces a dynamic policy for task computation, offloading, and resource allocation.
  • Numerical results show a better power-delay tradeoff for intense computation requirements and higher task arrival rates.
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