A Bound on Peak Age of Information Distribution

This paper presents a study on peak age of information (AoI), focusing on its distribution that is more important for AoI guarantees than the mean. Specifically, the relation of peak AoI to the underlying information generation and transmission processes is explicitly formulated. Based on this formulation and by exploring the independence information between the information generation and transmission processes, a general bound on the distribution of peak AoI is derived. To showcase the use of the derived bound, it is applied to two representative cases, which are characterized by the M/M/1 and D/M/1 queuing models. Numerical results obtained from the proposed bound analysis are finally introduced and discussed in comparison with exact results, validating the bound.