Joint Sampling and Transmission Policies for Minimizing Cost Under Age of Information Constraints

In this work, we consider the problem of jointly minimizing the average cost of sampling and transmitting status updates by users over a wireless channel subject to average Age of Information (AoI) constraints. Errors in the transmission may occur and a policy has to decide if the users sample a new packet or attempt to retransmission the packet sampled previously. The cost consists of both sampling and transmission costs. The sampling of a new packet after a failure imposes an additional cost on the system. We formulate a stochastic optimization problem with the average cost in the objective under average AoI constraints. To solve this problem, we propose three scheduling policies: (a) a dynamic policy, which is centralized and requires full knowledge of the state of the system and (b) two stationary randomized policies that require no knowledge of the state of the system. We utilize tools from Lyapunov optimization theory and Discrete-Time Markov Chain (DTMC) to provide the dynamic policy and the randomized ones, respectively. Simulation results show the importance of providing the option to transmit an old packet in order to minimize the total average cost.