Age of Computing: A Metric of Computation Freshness in Communication and Computation Cooperative Networks

In communication and computation cooperative networks (3CNs), timely computation is crucial but not always guaranteed. There is a strong demand for a computational task to be completed within a given deadline. The time taken involves processing time, transmission time, and the impact of the deadline. However, a measure of such timeliness in 3CNs is lacking. To address this gap, we propose the novel concept of Age of Computing (AoC) to quantify computation freshness in 3CNs. Built on task timestamps, AoC serves as a practical metric for dynamic and complex real-world 3CNs. We evaluate AoC under two types of deadlines: (i) soft deadline, tasks can be fed back to the source if delayed beyond the deadline, but with additional latency; (ii) hard deadline, tasks delayed beyond the deadline are discarded. We investigate AoC in two distinct networks. In point-to-point, time-continuous networks, tasks are processed sequentially using a first-come, first-served discipline. We derive a general expression for the time-average AoC under both deadlines. Utilizing this expression, we obtain a closed-form solution for M/M/1-M/M/1 systems under soft deadlines and propose an accurate approximation for hard deadlines. These results are further extended to G/G/1-G/G/1 systems. Additionally, we introduce the concept of computation throughput, derive its general expression and an approximation, and explore the trade-off between freshness and throughput. In the multi-source, time-discrete networks, tasks are scheduled for offloading to a computational node. For this scenario, we develop AoC-based Max-Weight policies for real-time scheduling under both deadlines, leveraging a Lyapunov function to minimize its drift.