Minimum Achievable Peak Age of Information Under Service Preemptions and Request Delay

There is a growing interest in analysing freshness of data in networked systems. Age of Information (AoI) has emerged as a relevant metric to quantify this freshness at a receiver, and minimizing this metric for different system models has received significant research attention. However, a fundamental question remains: what is the minimum achievable AoI in any single-server-single-source queuing system for a given service-time distribution? We address this question for the average peak AoI (PAoI) statistic by considering generate-at-will source model, service preemptions, and request delays. Our main result is on the characterization of the minimum achievable average PAoI, and we show that it is achieved by a fixed-threshold policy among the set of all causal policies. We use the characterization to provide necessary and sufficient condition for preemptions to be beneficial for a given service-time distribution. Our numerical results, obtained using well-known distributions, demonstrate that the heavier the tail of a distribution the higher the performance gains of using preemptions.