Source-linked AI summary
Dynamic Task Offloading and Resource Allocation for Ultra-Reliable Low-Latency Edge Computing
Chen-Feng Liu, Mehdi Bennis, Merouane Debbah, H. Vincent Poor
TL;DR
Average delay and mean queue stability do not capture rare queue-length events important for URLLC. The paper uses extreme value theory, Lyapunov optimization, and matching theory in a two-timescale MEC framework. Simulations show highly reliable task computation and lower delay than several baselines.
Problem
Existing MEC designs mainly use average delay or mean queue stability, leaving rare extreme queue-length events insufficiently represented for URLLC.
Method
The framework combines probabilistic and higher-order queue constraints from extreme value theory with Lyapunov-based resource control and matching-based UE-server association.
Results
The proposed approach guarantees highly reliable task computation and lower delay performance compared with several baselines.
Takeaways & Limitations
Accounting for extreme queue-length statistics supports reliability-aware power minimization and task allocation between local computation and offloading.
Abstract
from arXiv · showhide
To overcome devices' limitations in performing computation-intense applications, mobile edge computing (MEC) enables users to offload tasks to proximal MEC servers for faster task computation. However, current MEC system design is based on average-based metrics, which fails to account for the ultra-reliable low-latency requirements in mission-critical applications. To tackle this, this paper proposes a new system design, where probabilistic and statistical constraints are imposed on task queue lengths, by applying extreme value theory. The aim is to minimize users' power consumption while trading off the allocated resources for local computation and task offloading. Due to wireless channel dynamics, users are re-associated to MEC servers in order to offload tasks using higher rates or accessing proximal servers. In this regard, a user-server association policy is proposed, taking into account the channel quality as well as the servers' computation capabilities and workloads. By marrying tools from Lyapunov optimization and matching theory, a two-timescale mechanism is proposed, where a user-server association is solved in the long timescale while a dynamic task offloading and resource allocation policy is executed in the short timescale. Simulation results corroborate the effectiveness of the proposed approach by guaranteeing highly-reliable task computation and lower delay performance, compared to several baselines.
I. INTRODUCTION
MEC addresses devices’ limited computation capability and energy constraints, but average-based designs do not capture mission-critical URLLC requirements. The paper proposes queue-tail-aware optimization, dynamic task splitting, and adaptive UE-server association.
- MEC lets computation-limited devices offload tasks to proximal servers, but offloading adds latency and consumes communication energy.
- Existing MEC studies primarily use average delay or mean queue stability, overlooking rare extreme queue-length events relevant to URLLC.
- The framework imposes probabilistic threshold-deviation and higher-order queue-statistic constraints using extreme value theory.
- The optimization minimizes network-wide computation and communication power while allocating tasks between local execution and offloading.
- A two-timescale design combines long-timescale UE-server association with short-timescale dynamic offloading and resource allocation.
- The association considers changing UE locations, server computation capability, workload, and wireless conditions.
A. Traffic Model at the UE Side
Each UE splits stochastic task arrivals between local computation and wireless offloading, maintaining separate queues and allocating CPU frequency and transmit power under device constraints.
- Each arrival is divided into disjoint locally computed and remotely offloaded task portions.
- Task arrivals are assumed independent and identically distributed over time with average rate λ_i = E[A_i]/τ.
- Each UE maintains separate local-computation and task-offloading queues for the split tasks.
- Local processing uses CPU-cycle frequency f_i(t), with processing density L_i measured in required cycles per bit.
- Downlink overhead is neglected because computed results are typically smaller than the offloaded tasks.
- The UE uses DVFS to allocate CPU frequency and transmit power for minimizing total resource-allocation power consumption.
B. Traffic Model at the Server Side
MEC servers store offloaded tasks in UE-specific queues and process them with dedicated CPU cores, subject to heterogeneous server capacity constraints.
- Each server maintains distinct queue buffers for the offloaded tasks of different UEs.
- Each server CPU core is dedicated to at most one UE per time slot, and a UE’s tasks at a server use one core at a time.
- Server-side processing allocates CPU-cycle frequency f^j_i(t) to each UE’s offloaded tasks.
- Server capacity is characterized by the total core count N_j and the maximum computation capability f^max_j of one core.
III. LATENCY REQUIREMENTS, RELIABILITY CONSTRAINTS, AND PROBLEM FORMULATION
The paper translates latency and reliability requirements into queue-length constraints, using extreme value theory to control rare excess events and optimize long-term power consumption.
- Latency requirements: End-to-end delay includes queueing and computation locally, or UE offloading queueing, wireless transmission, and server-side processing remotely.
- Reliability constraints: Queue-length bounds use small tolerable violation probabilities because buffer overload can drop incoming tasks and undermine computation reliability.
- Extreme-value modeling: Extreme value theory models rare queue-length exceedances beyond thresholds through their tail distributions.
- Extreme-value modeling: The Pickands–Balkema–de Haan theorem approximates threshold excesses with a generalized Pareto distribution characterized by scale σ and shape ξ.
- Reliability constraints: The framework constrains long-term conditional excess means and second moments for local and offloaded UE queues.
- Reliability constraints: Server offloading queues use thresholds scaled by moving-average transmission rates, linking queue constraints to transmission performance.
- Problem formulation: The resulting problem minimizes long-term UE power consumption subject to association, queue, GPD, and resource constraints.
IV. LATENCY AND RELIABILITY-AWARE TASK OFFLOADING AND RESOURCE ALLOCATION
The framework first performs UE-server association every T0 slots using wireless, computational, workload, and URLLC information. It then handles task offloading and resource allocation through three decomposed optimization problems.
- UE-server association is performed at the beginning of each time frame, every T0 slots.
- Association considers wireless link strength, UE and server computation capabilities, historical workloads, and URLLC constraints.
- A many-to-one matching algorithm assigns multiple UEs to each MEC server before task offloading and resource allocation are optimized.
A. Lyapunov Optimization Framework
The framework converts reliability and latency requirements into queue-stability constraints and minimizes a Lyapunov drift-plus-penalty bound each slot. This produces three decomposed optimization problems for association, task assignment, and resource allocation.
- Virtual queues represent long-term average, probabilistic, and statistical constraints in the Lyapunov optimization framework.
- The conditional Lyapunov drift-plus-penalty is formed using the combined physical and virtual queue vector.
- The parameter V trades off objective optimality against queue-length reduction, with larger V asymptotically approaching the original problem's optimality.
- Minimizing the per-slot upper bound decomposes the problem into P1, P2, and P3.
- In P1, transmit power is coupled with local CPU frequency and depends on channel strength and the offloaded-task queue weight.
B. UE-Server Association using Many-to-One Matching with Externalities
UE-server association is formulated as a many-to-one matching problem with externalities and solved through iterative utility-improving swaps. Matching theory avoids the original NP-hard nonlinear integer program and reduces the search burden relative to exhaustive enumeration.
- P1-1 is an NP-hard nonlinear integer programming problem because its variables are binary and its objective is non-convex.
- The association uses many-to-one matching, assigning each UE to one server while allowing each server to serve multiple UEs.
- UE preferences depend on weighted transmission rates and can change with other UEs' matching states because of interference.
- The algorithm iterates through swap-blocking pairs until two-sided exchange stability is reached.
- A swap is accepted when both involved UEs and servers are no worse off and at least one participant improves.
- Exhaustive search has S^U association choices and grows exponentially with the number of UEs, whereas Algorithm 1 has O(U^2) complexity in the considered setting.
C. Resource Allocation and Task Splitting at the UE Side
The UE-side resource problem locally allocates CPU frequency and transmit power while deciding whether arriving tasks enter local-computation or offloading queues. This decomposition reduces information exchange with a central unit.
- Each UE locally allocates its CPU-cycle frequency and transmit power instead of uploading local information to a central unit every slot.
- When V = 0, the resource problem becomes rate maximization; increasing V places greater emphasis on reducing power cost.
- The optimal solution determines the UE's CPU-cycle frequency, transmit power, and task allocation subject to the decomposed optimization structure.
- The second decomposed problem decides whether each arriving task enters the local-computation queue or the task-offloading queue.
D. Computational Resource Scheduling at the Server Side
At the server side, computational resources are scheduled through a two-timescale mechanism that coordinates UE–server association, task offloading, and resource allocation. The mechanism updates queues and adapts scheduling weights to account for incomplete tasks and delay.
- Server scheduling: The server schedules computational resources with Algorithm 2 by considering UEs whose offloaded-task queue weights are positive.Algorithm 2 initializes U_j using β_ji(t)>0 and iteratively updates selected UEs and allocated frequencies.
- Two-timescale mechanism: The proposed two-timescale mechanism combines UE–server association with dynamic task offloading and resource allocation.Association is performed using Algorithm 1, while UE-side allocation and task splitting follow Lemma 1 and (42).
- Server scheduling: Including every UE’s β_ji(t) in the server objective prevents resource allocation from being over-provisioned.The corresponding queue weight determines whether a UE contributes to the objective even when it is not associated in the current frame.
- Delay-aware scheduling: β_ji(t) increases when ignored incomplete offloaded tasks experience more severe delay, then returns to zero after those tasks are completed.This weighting keeps delayed incomplete tasks in the server objective despite queue lengths no longer growing after reassociation changes.
- Queue and statistic updates: After each slot, UEs and servers update their physical and virtual queues, while transmission-rate observations estimate interference statistics for the next slot.The procedure repeats until the predetermined system lifetime T is reached.
V. NUMERICAL RESULTS
The numerical results evaluate extreme-queue characterization, task splitting, power consumption, delay, queue reliability, and UE-server association under varied network conditions. The proposed approach reduces power and extreme-event severity while improving delay or balancing server workloads, especially in dense or heterogeneous settings.
- Extreme-queue characterization: The Pickands–Balkema–de Haan theorem and generalized Pareto distribution provide a good characterization of task-offloading queue exceedances.The converged exceedance statistics support local estimation of network-wide extreme metrics and proactive handling of extreme events.
- Task splitting: More arrival tasks are offloaded as processing density or task arrival rate increases, while denser networks reduce offloading because of stronger interference.The task split ratio ζ exceeds 1 when λ > 10^9/L, equals 1 when λ = 10^9/L, and is below 1 otherwise.
- Power consumption: Increasing the Lyapunov tradeoff parameter V reduces total power consumption toward its minimum, while weaker local computation capability favors offloading more tasks.For ζ = 10, the gap between local-computation and total power consumption is around 5 dB across different λ values.
- Delay and reliability: Partial offloading can achieve lower queue loading and smaller, more concentrated extreme events, supporting more reliable operation than alternatives in relevant settings.Fully offloading tasks can provide lower delay in sparse networks, whereas partial offloading reduces queue-buffer loading and potential overflow.
- UE-server association: The proposed association approach alleviates server-resource waiting and end-to-end delay versus highest-RSS association when MEC servers have heterogeneous computation capabilities.The advantage is more prominent in dense networks; with homogeneous servers, both association schemes have identical delay performance and a 1 dB gap at the 1st SNR percentile.
VI. CONCLUSIONS
The paper designs a URLLC-oriented MEC system that constrains extreme task-queue behavior while minimizing UE computation and communication power. It combines two-timescale association, offloading, and resource allocation to support reliable, low-latency computation.
- Extreme task-queue deviation probabilities and high-order statistics are incorporated as URLLC constraints for mission-critical applications.
- The optimization minimizes UEs’ computation and communication power subject to the URLLC constraints.
- A two-timescale framework jointly addresses UE-server association, task offloading, and resource allocation.Association is handled over the long timescale, while per-slot computation and communication decisions are made over the short timescale.
- UE-server association is formulated as a many-to-one matching game with externalities and addressed using swap matching.
- Each time slot, UEs split arrivals between local computation and offloading while servers schedule their CPU cores.
APPENDIX A PROOF OF LEMMA 1
The appendix derives optimal local CPU-cycle and transmit-power decisions for the convex subproblem using Lagrangian differentiation and KKT conditions.
- The Lagrangian is differentiated with respect to local CPU frequency and transmit power to obtain optimal resource conditions.
- KKT conditions are applied because the subproblem is convex, yielding the optimal CPU-cycle and transmit-power solution.
- The derivation uses interference, noise, bandwidth, channel gain, and Lagrange multipliers in the transmit-power optimality condition.
- The optimal transmit power is positive and satisfies the UE’s maximum transmit-power constraint.