Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Information Freshness in Dynamic Gossip Networks

Arunabh Srivastava, Thomas Jacob Maranzatto, Sennur Ulukus

TL;DR

This paper studies information freshness in dynamic gossip networks where topology switches between two fixed configurations according to a continuous-time Markov chain, using the version age of information as the metric. It develops a two-pronged analysis: first, showing that in the fast-switching regime (holding time $h(n)$ with CTMC rates $q_{12},q_{21}=\Theta(1/h(n))$) the average version age scales with the better topology, specifically $v = \Theta(f_1(n))$ when $f_1(n) = o(f_2(n))$ and $h(n) = O(f_1(n))$; and second, introducing the notion of a typical set of nodes to handle non-uniform age distributions in non-vertex-transitive networks, with two regimes: $h(n) = O(f_1(n))$ yielding $\Theta(f_1(n))$ for the typical set and $h(n) = \Omega(n \log n)$ yielding $\Theta(f_2(n))$. These results imply that rapid switching can preserve freshness comparable to the best topology, while slow or intermediate switching can force the typical-set age to track the worse topology, depending on the holding-time scaling. The work also demonstrates that the typical set comprises a linear fraction of nodes, while a vanishingly small fraction can disproportionately influence network freshness. Overall, the paper provides a framework for understanding how time-scale separation in topology dynamics affects version-age performance and introduces a robust concept (typical set) to capture near-sure behavior in heterogeneous networks.

Abstract

We consider a source that shares updates with a network of $n$ gossiping nodes. The network's topology switches between two arbitrary topologies, with switching governed by a two-state continuous time Markov chain (CTMC) process. Information freshness is well-understood for static networks. This work evaluates the impact of time-varying connections on information freshness. In order to quantify the freshness of information, we use the version age of information metric. If the two networks have static long-term average version ages of $f_1(n)$ and $f_2(n)$ with $f_1(n) \ll f_2(n)$, then the version age of the varying-topologies network is related to $f_1(n)$, $f_2(n)$, and the transition rates in the CTMC. If the transition rates in the CTMC are faster than $f_1(n)$, the average version age of the varying-topologies network is $f_1(n)$. Further, we observe that the behavior of a vanishingly small fraction of nodes can severely impact the long-term average version age of a network in a negative way. This motivates the definition of a typical set of nodes in the network. We evaluate the impact of fast and slow CTMC transition rates on the typical set of nodes.

Information Freshness in Dynamic Gossip Networks

TL;DR

This paper studies information freshness in dynamic gossip networks where topology switches between two fixed configurations according to a continuous-time Markov chain, using the version age of information as the metric. It develops a two-pronged analysis: first, showing that in the fast-switching regime (holding time with CTMC rates ) the average version age scales with the better topology, specifically when and ; and second, introducing the notion of a typical set of nodes to handle non-uniform age distributions in non-vertex-transitive networks, with two regimes: yielding for the typical set and yielding . These results imply that rapid switching can preserve freshness comparable to the best topology, while slow or intermediate switching can force the typical-set age to track the worse topology, depending on the holding-time scaling. The work also demonstrates that the typical set comprises a linear fraction of nodes, while a vanishingly small fraction can disproportionately influence network freshness. Overall, the paper provides a framework for understanding how time-scale separation in topology dynamics affects version-age performance and introduces a robust concept (typical set) to capture near-sure behavior in heterogeneous networks.

Abstract

We consider a source that shares updates with a network of gossiping nodes. The network's topology switches between two arbitrary topologies, with switching governed by a two-state continuous time Markov chain (CTMC) process. Information freshness is well-understood for static networks. This work evaluates the impact of time-varying connections on information freshness. In order to quantify the freshness of information, we use the version age of information metric. If the two networks have static long-term average version ages of and with , then the version age of the varying-topologies network is related to , , and the transition rates in the CTMC. If the transition rates in the CTMC are faster than , the average version age of the varying-topologies network is . Further, we observe that the behavior of a vanishingly small fraction of nodes can severely impact the long-term average version age of a network in a negative way. This motivates the definition of a typical set of nodes in the network. We evaluate the impact of fast and slow CTMC transition rates on the typical set of nodes.

Paper Structure

This paper contains 4 sections, 7 theorems, 5 equations, 2 figures.

Table of Contents

  1. Introduction
  2. System Model and the Version Age Metric
  3. Fast Switching
  4. Typical Sets and Varying-Topologies

Key Result

Lemma 1

Let $\{G_n\}_{n=1}^\infty$ be a sequence of networks with $|\mathcal{N}(G_k)| = k$. Suppose $\lim\limits_{t \to \infty} \mathbb{E} [X_1^{G_n}(t)] = \Theta(f(n))$. Then, for large enough $n$ and $t$, with high probability, $X_1^{G_n}(t) = O(f(n))$.

Figures (2)

  • Figure 1: An example of a dynamic network we study. Here, $n=6$, topology 1 is the fully-connected topology, and topology 2 is the ring topology. We have omitted the edge-rates, but these implicitly change as the network switches between topologies 1 and 2.
  • Figure 2: A network formed by combining a fully-connected network with $n-n^{\frac{2}{3}}$ nodes to a line with $n^{\frac{2}{3}}$ nodes. This network poses challenges to the average-case analysis with slow topology switching.

Theorems & Definitions (8)

  • Lemma 1
  • Lemma 2
  • Lemma 3
  • Theorem 1
  • Definition 1
  • Lemma 4
  • Corollary 1
  • Theorem 2