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Age of Gossip with the Push-Pull Protocol

Arunabh Srivastava, Thomas Jacob Maranzatto, Sennur Ulukus

TL;DR

This paper uses the stochastic hybrid systems (SHS) framework to obtain recursive equations for the expected version age of sets of nodes in the time limit, and shows that the pull and push-pull protocols can achieve constant version age.

Abstract

We consider a wireless network where a source generates packets and forwards them to a network containing $n$ nodes. The nodes in the network use the asynchronous push, pull or push-pull gossip communication protocols to maintain the most recent updates from the source. We use the version age of information metric to quantify the freshness of information in the network. Prior to this work, only the push gossiping protocol has been studied for age of information analysis. In this paper, we use the stochastic hybrid systems (SHS) framework to obtain recursive equations for the expected version age of sets of nodes in the time limit. We then show that the pull and push-pull protocols can achieve constant version age, while it is already known that the push protocol can only achieve logarithmic version age. We then show that the push-pull protocol performs better than the push and the pull protocol. Finally, we carry out numerical simulations to evaluate these results.

Age of Gossip with the Push-Pull Protocol

TL;DR

This paper uses the stochastic hybrid systems (SHS) framework to obtain recursive equations for the expected version age of sets of nodes in the time limit, and shows that the pull and push-pull protocols can achieve constant version age.

Abstract

We consider a wireless network where a source generates packets and forwards them to a network containing nodes. The nodes in the network use the asynchronous push, pull or push-pull gossip communication protocols to maintain the most recent updates from the source. We use the version age of information metric to quantify the freshness of information in the network. Prior to this work, only the push gossiping protocol has been studied for age of information analysis. In this paper, we use the stochastic hybrid systems (SHS) framework to obtain recursive equations for the expected version age of sets of nodes in the time limit. We then show that the pull and push-pull protocols can achieve constant version age, while it is already known that the push protocol can only achieve logarithmic version age. We then show that the push-pull protocol performs better than the push and the pull protocol. Finally, we carry out numerical simulations to evaluate these results.
Paper Structure (7 sections, 1 theorem, 16 equations, 4 figures)

This paper contains 7 sections, 1 theorem, 16 equations, 4 figures.

Table of Contents

  1. Introduction
  2. System Model and the Version Age Metric
  3. Recursive Equations and Bounds
  4. A Comparison of the Gossip Protocols
  5. Comparison between Push-Pull Protocol and Push-Only/Pull-Only Protocols
  6. Numerical Results
  7. Conclusion

Key Result

Lemma 1

For any gossip network $G$, for any $S \subseteq \mathcal{N}$, where $v_S^{\text{push}}$ is the limiting average version age of $S$ under the push-only protocol, and likewise for $v_S^{\text{push-pull}}$ and $v_S^{\text{pull}}$.

Figures (4)

  • Figure 1: A gossiping network following the push-pull protocol. Each node can push or pull information from neighboring nodes. Arrows denote the flow of information, with red arrows denoting push updates and blue arrows denoting pull updates.
  • Figure 2: A star network where only one node receives updates directly from the source node. In the left network, the central node receives the updates and in the right network, a non-central node receives the updates. In this example, $n=7$.
  • Figure 3: A comparison of the push, pull and push-pull protocols for the star networks, explained in Section \ref{['sec: numerical results']}.
  • Figure 4: Version age of a single node in the ring and fully connected network with the push-pull protocol when compared to the respective theoretical values under the push protocol found in buyukates22ClusterGossip and yates21gossip.

Theorems & Definitions (1)

  • Lemma 1