Impact of Channel Memory on the Data Freshness

Abstract

In this letter, we investigate the impact of channel memory on the average age of information (AoI) for networks with various packet arrival models under the first-come-first-served (FCFS) and the preemptive last-generated-first-served (pLGFS) policies over the Gilbert-Elliott (GE) erasure channel. For networks with Bernoulli and generate-at-will arrival models, the AoI performances under the FCFS and pLGFS policies are derived explicitly as functions of the channel state transition probabilities. For networks with periodic arrival model, we derive the closed-form expression for the average AoI under pLGFS and propose a numerical algorithm for efficient evaluation of the AoI under FCFS. It is revealed that for pLGFS policy, the average AoI increases monotonically with channel memory <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\eta $ </tex-math></inline-formula> at <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\frac {\eta }{1-\eta }$ </tex-math></inline-formula> over the symmetric GE channel. For FCFS, the average AoI increases even faster due to the queuing delay, with an additional term related to the packet arrival rate.