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

Jixiang Zhang, Han Xu, Daming Cao, Yinfei Xu, Minghao Chen, Chengyu Lin

TL;DR

This work addresses the discrete AoI problem for bufferless status updating systems with general packet interarrival times $Y$ and service times $S$. It develops a probability-generating-function framework to exactly characterize the AoI distribution under preemptive G/G/1/1 and non-preemptive G/Geo/1/1 queues, yielding closed-form AoI PGFs and explicit average AoI formulas. By deriving and validating these expressions, including several special cases (e.g., geometric interarrival/service), the paper provides versatile tools for assessing information freshness in general AoI-enabled networks and IoT settings.

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.

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

TL;DR

This work addresses the discrete AoI problem for bufferless status updating systems with general packet interarrival times and service times . It develops a probability-generating-function framework to exactly characterize the AoI distribution under preemptive G/G/1/1 and non-preemptive G/Geo/1/1 queues, yielding closed-form AoI PGFs and explicit average AoI formulas. By deriving and validating these expressions, including several special cases (e.g., geometric interarrival/service), the paper provides versatile tools for assessing information freshness in general AoI-enabled networks and IoT settings.

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.
Paper Structure (6 sections, 6 theorems, 55 equations, 1 figure, 2 tables)

This paper contains 6 sections, 6 theorems, 55 equations, 1 figure, 2 tables.

Table of Contents

  1. Introduction
  2. System Model and Problem Formulation
  3. Discrete Age of Information of System with G/G/1/1 Queue: Preemptive Case
  4. Discrete Age of Information of System with G/Geo/1/1 Queue: Non-preemptive Case
  5. Average AoI in Several Special Cases
  6. Conclusion

Key Result

Lemma 1

Functions $h_1(z)$ and $h_2(z)$ in (E5) are equal to

Figures (1)

  • Figure 1: Model of a discrete time status updating system with general packet arrival processes.

Theorems & Definitions (6)

  • Lemma 1
  • Theorem 1
  • Lemma 2
  • Theorem 2
  • Corollary 1
  • Corollary 2