  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.
