Estimating Age of Information in Wireless Systems With Unknown Distributions of Inter-Arrival/Service Time

In this paper, we estimate the average age of information (AoI) of the status updating over a wireless channel with an unknown fading model. Different from most related works which take the distributions of the inter-arrival time and transmission time of updates as known information, we approximate the average AoI of the system by using their first and second-order moments. Note that these distributions are often not accessible or known with inevitable errors while their moments are much easier to obtain, e.g., by using counting and statistics. We model the communications over the fading channel with a continuous transmission model and a discrete transmission model, which use the variable-rate scheme and the fixed-rate scheme, respectively. We assume that the arrival of the continuous transmission model is a Bernoulli process and make no assumptions about the arrival process of the discrete transmission model. Based on these information, we present two pairs of tight lower and upper bounds for the AoI of the two models. We show that obtained bounds are the tightest when the inter-arrival time (or transmission time) follows the degenerate distribution and are the loosest when it follows the two-point distribution, which randomly takes value from two possible outcomes. We also show that tighter bounds can be obtained by using higher order moments.