Age of information using Markov-renewal methods

When designing a message transmission system, from the point of view of making sure that the information transmitted is as fresh as possible, two rules of thumb seem reasonable: use small buffers and adopt a last-in-first-out policy. In this paper, the freshness of information is interpreted as the recently studied “age of information” performance measure. Considering it as a stochastic process operating in a stationary regime, we compute the whole marginal distribution of the age of information for some well-performing systems. We assume that the arrival process is Poisson and that the messages have independent service times with common distribution, i.e., the M/GI model. We demonstrate the usefulness of Palm and Markov-renewal theory to derive results for Laplace transforms. Our numerical studies address some aspects of open questions regarding the optimality of previously proposed scheduling policies, and a policy newly considered herein, for AoI management.