  The freshness of status information is of great importance for time-critical
Internet of Things (IoT) applications. A metric measuring status freshness is
the age-of-information (AoI), which captures the time elapsed from the status
being generated at the source node (e.g., a sensor) to the latest status
update.However, in intelligent IoT applications such as video surveillance, the
status information is revealed after some computation intensive and
time-consuming data processing operations, which would affect the status
freshness. In this paper, we propose a novel metric, age-of-processing (AoP),
to quantify such status freshness, which captures the time elapsed of the
newest received processed status data since it is generated. Compared with AoI,
AoP further takes the data processing time into account. Since an IoT device
has limited computation and energy resource, the device can choose to offload
the data processing to the nearby edge server under constrained status sampling
frequency.We aim to minimize the average AoP in a long-term process by jointly
optimizing the status sampling frequency and processing offloading policy. We
formulate this online problem as an infinite-horizon constrained Markov
decision process (CMDP) with average reward criterion. We then transform the
CMDP problem into an unconstrained Markov decision process (MDP) by leveraging
a Lagrangian method, and propose a Lagrangian transformation framework for the
original CMDP problem. Furthermore, we integrate the framework with
perturbation based refinement for achieving the optimal policy of the CMDP
problem. Extensive numerical evaluations show that the proposed algorithm
outperforms the benchmarks, with an average AoP reduction up to 30%.
