Spatiotemporal Analysis of Parallelized Computing at the Extreme Edge

2025-04-25

AI Summary

Extreme-edge computing (EEC) faces fundamental challenges including stochastic spatial distribution of devices, constrained computational capacity, high failure probability, and dynamic fluctuations in communication and execution times—necessitating a rigorous spatiotemporal analytical framework. This paper introduces the first integrated modeling approach for large-scale millimeter-wave networks, combining stochastic geometry with absorbing continuous-time Markov chains (ACTMC) to jointly characterize spatiotemporal dynamics—particularly communication-computation temporal overlap and cooperative failure under parallel task execution. Theoretically, we uncover a U-shaped relationship between task partitioning granularity and average latency, deriving an optimal partitioning criterion. Furthermore, we propose a bias-driven EEC-MEC collaborative offloading mechanism. Experiments demonstrate that, under resource-constrained edge execution domains (EEDs), this mechanism improves task completion probability by up to 37% and reduces average latency by 29%.

Technology Category

• Machine Learning: Learning on the Edge & Model Compression
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Extreme Edge Computing (EEC) pushes computing even closer to end users than traditional Multi-access Edge Computing (MEC), harnessing the idle resources of Extreme Edge Devices (EEDs) to enable low-latency, distributed processing. However, EEC faces key challenges, including spatial randomness in device distribution, limited EED computational power necessitating parallel task execution, vulnerability to failure, and temporal randomness due to variability in wireless communication and execution times. These challenges highlight the need for a rigorous analytical framework to evaluate EEC performance. We present the first spatiotemporal mathematical model for EEC over large-scale millimeter-wave networks. Utilizing stochastic geometry and an Absorbing Continuous-Time Markov Chain (ACTMC), the framework captures the complex interaction between communication and computation performance, including their temporal overlap during parallel execution. We evaluate two key metrics: average task response delay and task completion probability. Together, they provide a holistic view of latency and reliability. The analysis considers fundamental offloading strategies, including randomized and location-aware schemes, while accounting for EED failures. Results show that there exists an optimal task segmentation that minimizes delay. Under limited EED availability, we investigate a bias-based EEC and MEC collaboration that offloads excess demand to MEC resources, effectively reducing congestion and improving system responsiveness.

Problem

• Modeling spatiotemporal performance of Extreme Edge Computing (EEC) networks
• Optimizing task segmentation and offloading to minimize latency
• Enhancing reliability and responsiveness via EEC-MEC collaboration

Innovation

• Spatiotemporal model for Extreme Edge Computing
• Stochastic geometry and ACTMC framework
• Optimal task segmentation minimizes delay