Spatiotemporal Analysis of Parallelized Computing at the Extreme Edge
This work addresses performance evaluation challenges for EEC systems, which is incremental as it builds on existing edge computing frameworks with a new analytical approach.
The paper tackled the problem of analyzing performance in Extreme Edge Computing (EEC) by developing the first spatiotemporal mathematical model using stochastic geometry and an Absorbing Continuous-Time Markov Chain, which identified an optimal task segmentation to minimize delay and proposed a bias-based collaboration with MEC to reduce congestion.
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.