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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 both processing time, communication time, and the impact of the deadline. However, a measure of such timeliness in 3CNs is lacking. In this paper, we introduce the novel concept, Age of Computing (AoC), to capture computation freshness in 3CNs. We analyze AoC in a line topology consisting of a source, a transmitter, a receiver, and a computational node. Tasks generated by the source are immediately available at the transmitter, where they enter a communication queue. These tasks then pass to the receiver and subsequently to a computation queue at the computational node for processing. Each task has a deadline, requiring completion within this timeframe. AoC is evaluated 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. Under both deadlines, we derive the AoC formula and a general expression for the time-average AoC. For the first-come, first-serve discipline, we obtain a closed-form expression for the average AoC under the soft deadline and an approximation for the hard deadline. In addition to freshness, we define computation throughput, providing a general expression and an approximation. To explore the relationship between freshness and throughput, we construct an optimization problem and prove that the objective pair is a weakly Pareto-optimal point. Numerical results validate all the theoretical findings. Additionally, they reveal that under the hard deadline, the computation throughput serves as a reliable proxy for the average AoC. |
