On Discrete Age of Information of Status Updating System With General Packet Arrival Processes

TL;DR

This paper characterizes the probability generating functions of discrete Age of Information in G/G/1/1 queues with preemption and G/Geo/1/1 queues without preemption, providing new theoretical insights into discrete AoI analysis.

Contribution

It provides the first complete characterization of discrete AoI PGFs for G/G/1/1 queues with preemption and extends results to G/Geo/1/1 queues without preemption.

Findings

Derived PGFs of discrete AoI for G/G/1/1 with preemption

Extended results to G/Geo/1/1 queues without preemption

Calculated average discrete AoI based on new theoretical models

Abstract

Characterizing Age of Information (AoI) in status updating systems with general arrival and service processes has great significance considering that the interarrival and service time of updates can possibly be arbitrary in a real world. While expressions of average continuous AoI under G/G/1/1 queues have been derived in the paper by Soysal and Ulukus, the discrete case remained unsolved. To address it, this paper gives a fully characterization of probability generation functions (PGF) of discrete AoI under G/G/1/1 settings when preemption is allowed. In the non-preemptive case, this paper gives the expressions of PGF of discrete AoI under G/Geo/1/1 settings, which also extends the former results. The average discrete AoI is derived and discussed based on these new theoretical findings.