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.

翻译：极端边缘计算（EEC）将计算资源推至比传统多接入边缘计算（MEC）更接近终端用户的位置，通过利用极端边缘设备（EED）的闲置资源实现低延迟分布式处理。然而，EEC面临若干关键挑战，包括设备分布的空间随机性、EED计算能力有限导致任务需并行执行、系统易受故障影响，以及无线通信与执行时间波动引起的时间随机性。这些挑战凸显了建立严格分析框架以评估EEC性能的必要性。我们首次提出了面向大规模毫米波网络的EEC时空数学模型。该框架运用随机几何与吸收连续时间马尔可夫链（ACTMC），刻画了通信与计算性能间的复杂交互作用，包括并行执行期间二者在时间上的重叠。我们评估了两个关键指标：平均任务响应延迟与任务完成概率。二者共同提供了延迟与可靠性的整体视图。分析考虑了包括随机化与位置感知策略在内的基本卸载机制，同时计入了EED故障的影响。结果表明，存在可最小化延迟的最优任务分割方案。在EED可用性受限的情况下，我们研究了一种基于偏置的EEC与MEC协同机制，将超额负载卸载至MEC资源，从而有效缓解拥塞并提升系统响应能力。