Lyapunov Optimization with Virtual Queues for adaptive task offloading in multi access edge computing

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Abstract
Multi-access edge computing (MEC) enhances the performance of resource-constrained devices by offloading computation to nearby edge servers, but simultaneously achieving energy efficiency and low latency under dynamic conditions remains challenging. This paper proposes Lyapunov Optimization with Virtual Queues (LOVQ), a task offloading framework based on the Lyapunov Drift Plus Penalty (LDPP) method that jointly optimizes energy consumption and delay while ensuring long-term system stability. The LOVQ framework integrates three complementary algorithms for adaptive task offloading, decay-aware updates to virtual energy queues, and battery-aware task processing under energy-constrained conditions. Simulations with 20 edge devices and 2000 tasks show that LOVQ reduces average energy consumption to 30.0 J, achieving a 33% reduction compared with local execution and a 6% reduction compared with classical Lyapunov-based offloading. LOVQ also achieves the lowest average delay of 0.92 s, reducing delay by 31% relative to local execution and exceeding random and edge-only offloading strategies. These results demonstrate that LOVQ significantly improves the energy–delay trade-off while maintaining system stability, making it a scalable solution for dynamic MEC environments.

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