Effective control of time-sensitive industrial applications depends on the real-time transmission of data from underlying sensors. Quantifying the data freshness through age of information (AoI)

in this paper

we jointly design sampling and non-slot based scheduling policies to minimize the maximum time-average age of information (MAoI) among sensors with the constraints of average energy cost and finite queue stability. To overcome the intractability involving high couplings of such a complex stochastic process

we first focus on the single-sensor time-average AoI optimization problem and convert the constrained Markov decision process (CMDP) into an unconstrained Markov decision process (MDP) by the Lagrangian method. With the infinite-time average energy and AoI expression expended as the Bellman equation

the single-sensor time-average AoI optimization problem can be approached through the steady-state distribution probability. Further

we propose a low-complexity sub-optimal sampling and semi-distributed scheduling scheme for the multi-sensor scenario. The simulation results show that the proposed scheme reduces the MAoI significantly while achieving a balance between the sampling rate and service rate for multiple sensors.