Optimizing Age of Information in Wireless Uplink Networks With Partial Observations

This paper considers a wireless uplink network consisting of multiple end devices and an access point (AP). Each device monitors a physical process with randomly generated status updates and sends these update packets to the AP in the uplink. The AP aims to schedule the transmissions of these devices to optimize the network-wide information freshness, quantified by the age of information (AoI) metric. Due to the stochastic arrival of the status updates at end devices, the AP only has
partial observations
of system times of the latest status update packets at end devices when making scheduling decisions. Such a decision-making problem can be naturally formulated as a partially observable Markov decision process (POMDP). We reformulate the POMDP into an equivalent belief Markov decision process (belief-MDP), by defining fully observable belief states of the POMDP as the states of the belief-MDP. The belief-MDP in its original form is difficult to solve as the dimension of its states can go to infinity and its belief space is uncountable. Fortunately, by carefully leveraging the properties of the status update arrival processes (i.e., Bernoulli processes), we manage to simplify the belief-MDP substantially, where every feasible state is characterized by a two-dimensional vector. Based on the simplified belief-MDP, we devise a low-complexity scheduling policy, termed Partially Observing Max-Weight (POMW) policy, for the formulated AoI-oriented scheduling problem. We derive upper bounds for the time-average AoI performance of the proposed POMW policy. We analyze the performance guarantee for the POMW policy by comparing its performance with a universal lower bound available in the literature. Numerical results validate our analyses and demonstrate that the performance gap between the POMW policy and its fully observable counterpart is proportional to the inverse of the lowest arrival rate of all end devices.