DiffLyap-MEC: Diffusion-Guided Lyapunov Optimization for Joint Offloading, Semantic Compression, and Resource Allocation in ISAC-Enabled 6G Edge Computing
- 1Department of Computer Science and Information, The Applied College, Taibah University, Madinah 42353, Saudi Arabia
- 2Department of Computer Engineering, Faculty of Computers and Information Technology, University of Tabuk, Tabuk 71421, Saudi Arabia
Abstract
Integrated sensing and communication (ISAC), semantic communication, and mobile edge computing (MEC) jointly create a high-dimensional, non-convex, and time-coupled resource allocation problem in sixth-generation (6G) networks that existing heuristics and deep reinforcement learning (DRL) methods solve either slowly or without stability guarantees. This study proposes DiffLyap-MEC, a framework that couples generative diffusion models with Lyapunov drift-plus-penalty optimization for online decision-making in ISAC-enabled multi-user, multi-server MEC systems. A mixed-integer non-linear program jointly optimizes task offloading ratios, semantic compression levels, ISAC beamforming, and edge CPU and bandwidth allocation under long-term energy-queue stability and sensing-accuracy constraints. Lyapunov theory decouples the long-term problem into per-slot subproblems with a provable O(1/V) optimality versus backlog trade-off, and a conditional denoising diffusion policy generates near-optimal offloading and beamforming decisions in a fixed number of reverse steps, with a closed-form water-filling solution embedded as a differentiable layer. Bounds on queue stability, policy convergence, and the distortion versus latency trade-off are derived. Simulations with 3GPP-compliant channel models show that DiffLyap-MEC reduces average end-to-end latency by 27.3% to 33.9% and energy consumption by 22.2% to 27.1% relative to proximal policy optimization (PPO), soft actor–critic (SAC), and Lyapunov-only baselines while maintaining 97.3% sensing accuracy at 0.74 ms inference time per slot on an NVIDIA RTX A6000 GPU with a batch size of one.
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BibTeX
@article{alhazmi2026difflyapmec,
title = {{DiffLyap-MEC: Diffusion-Guided Lyapunov Optimization for Joint Offloading, Semantic Compression, and Resource Allocation in ISAC-Enabled 6G Edge Computing}},
author = {Abrar S. Alhazmi and Mohammed M. Alenazi},
journal = {Mathematics},
year = {2026},
month = oct,
doi = {10.3390/math14203737},
url = {https://www.mdpi.com/2227-7390/14/20/3737},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - DiffLyap-MEC: Diffusion-Guided Lyapunov Optimization for Joint Offloading, Semantic Compression, and Resource Allocation in ISAC-Enabled 6G Edge Computing
AU - Abrar S. Alhazmi
AU - Mohammed M. Alenazi
PY - 2026
DA - 2026/10/14
JO - Mathematics
DO - 10.3390/math14203737
UR - https://www.mdpi.com/2227-7390/14/20/3737
AB - Integrated sensing and communication (ISAC), semantic communication, and mobile edge computing (MEC) jointly create a high-dimensional, non-convex, and time-coupled resource allocation problem in sixth-generation (6G) networks that existing heuristics and deep reinforcement learning (DRL) methods solve either slowly or without stability guarantees. This study proposes DiffLyap-MEC, a framework that couples generative diffusion models with Lyapunov drift-plus-penalty optimization for online decision-making in ISAC-enabled multi-user, multi-server MEC systems. A mixed-integer non-linear program jointly optimizes task offloading ratios, semantic compression levels, ISAC beamforming, and edge CPU and bandwidth allocation under long-term energy-queue stability and sensing-accuracy constraints. Lyapunov theory decouples the long-term problem into per-slot subproblems with a provable O(1/V) optimality versus backlog trade-off, and a conditional denoising diffusion policy generates near-optimal offloading and beamforming decisions in a fixed number of reverse steps, with a closed-form water-filling solution embedded as a differentiable layer. Bounds on queue stability, policy convergence, and the distortion versus latency trade-off are derived. Simulations with 3GPP-compliant channel models show that DiffLyap-MEC reduces average end-to-end latency by 27.3% to 33.9% and energy consumption by 22.2% to 27.1% relative to proximal policy optimization (PPO), soft actor–critic (SAC), and Lyapunov-only baselines while maintaining 97.3% sensing accuracy at 0.74 ms inference time per slot on an NVIDIA RTX A6000 GPU with a batch size of one.
SN - 2227-7390
ER -