Abstract

This paper establishes an analytical framework for the upper bound on the average Age-of-Information (AoI) in first-come-first-served (FCFS) wireless communications where a certain level of outage probability is unavoidable. To begin with, we analyze the average AoI and derive a general upper bound for G/G/1 systems with a certain outage probability. Subsequently, for an M/M/1 system with the FCFS scheme, we obtain a concise closed-form expression of the upper bound, and further refine the upper bound after analyzing the relative error. Interestingly, it is found by the analysis that the relative error is independent of the service rate, and the upper bound becomes tighter as the outage probability increases. Based on the refined upper bound, we minimize the average AoI for the communications suffering from block Rayleigh fading. We derive a closed-form expression of the outage probability over a fading channel, and then prove that the refined upper bound is a convex function with respect to the average update generating rate. Consequently, we optimize the AoI performance by solving a convex optimization problem formulated utilizing the refined upper bound expression. The numerical results indicate that the minimum average AoI can be reduced by either increasing the service rate or the transmission power.