Social Optimal Freshness in Multi-Source, Multi-Channel Systems via MDP

Abstract: Many systems necessitate frequent and consistent updates of a specific information. Often this information is updated regularly, where an old packet becomes completely obsolete in the presence of a new packet. In this context, we consider a system with multiple sources, each equipped with a storage buffer of size one, communicating to a common destination via d orthogonal channels. In each slot, the packets arrive at each source with certain probability and occupy the buffer (by discarding the old packet if any), and each transfer (to the destination) is successful with certain other probability. Thus in any slot, there are two (Age of Information) AoI-measures for each source: one corresponding to the information at the source itself and the other corresponding to the information of the same source available at the destination; some sources may not even have the packet to transmit. The aim of the controller at the destination is to maintain the freshness of information of all the sources, to the best extent possible -- it aims to design an optimal scheduling policy that assigns in each slot, a subset of sources with packets (at maximum d) for transmission. This is achieved using an appropriate Markov Decision Process (MDP) framework, where the objective function is the sum of Average AoIs (AAoI) of all the sources. We derive a very simple stationary policy that is epsilon-optimal -- in any slot, order the sources with packets in the decreasing order of the differences in AoI at the destination and the source and choose the top sources for transmission. With moderate number of sources (less than 30), the AAoI reduces in the range of 30-90%.