The Probability Distribution of the AoI in Queues with Infinitely Many Servers

Abstract

In this paper, we derive an explicit expression for the probability distribution of the age of information (AoI) in the $\mathrm{GI}/\mathrm{GI}/\infty$ queue with loss. Two special cases $\mathrm{M}/\mathrm{GI}/\infty$ and $\mathrm{D}/\mathrm{GI}/\infty$ are discussed, where the distribution function of the AoI is shown to take a simple closed-form. In addition, a comparison result between the $\mathrm{M}/\mathrm{GI}/\infty$ and $\mathrm{D}/\mathrm{GI}/\infty$ queues in terms of the AoI distribution is presented.