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Optimizing Profitability in Timely Gossip Networks

Priyanka Kaswan, Melih Bastopcu, Sennur Ulukus, S. Rasoul Etesami, Tamer Başar

TL;DR

This work addresses profitability in timely gossip networks where a server can sample an event with probability $\beta$ and subscribers maintain bounded version ages via an AC constraint. Modeling the interaction as a Stackelberg game, the server (leader) selects $\beta$ to maximize subscribers minus sampling costs, while users (followers) subscribe according to their timeliness needs. The paper analyzes two extreme topologies: bidirectional line networks yield multiple equilibria and an AC-stable pattern with subscription period $m$, whereas fully-connected networks produce a single equilibrium with a smaller subscriber base. The results provide principled insights into pricing and sampling strategies for real-time information dissemination in hyper-connected networks.

Abstract

We consider a communication system where a group of users, interconnected in a bidirectional gossip network, wishes to follow a time-varying source, e.g., updates on an event, in real-time. The users wish to maintain their expected version ages below a threshold, and can either rely on gossip from their neighbors or directly subscribe to a server publishing about the event, if the former option does not meet the timeliness requirements. The server wishes to maximize its profit by increasing subscriptions from users and minimizing event sampling frequency to reduce costs. This leads to a Stackelberg game between the server and the users where the sender is the leader deciding its sampling frequency and the users are the followers deciding their subscription strategies. We investigate equilibrium strategies for low-connectivity and high-connectivity topologies.

Optimizing Profitability in Timely Gossip Networks

TL;DR

This work addresses profitability in timely gossip networks where a server can sample an event with probability and subscribers maintain bounded version ages via an AC constraint. Modeling the interaction as a Stackelberg game, the server (leader) selects to maximize subscribers minus sampling costs, while users (followers) subscribe according to their timeliness needs. The paper analyzes two extreme topologies: bidirectional line networks yield multiple equilibria and an AC-stable pattern with subscription period , whereas fully-connected networks produce a single equilibrium with a smaller subscriber base. The results provide principled insights into pricing and sampling strategies for real-time information dissemination in hyper-connected networks.

Abstract

We consider a communication system where a group of users, interconnected in a bidirectional gossip network, wishes to follow a time-varying source, e.g., updates on an event, in real-time. The users wish to maintain their expected version ages below a threshold, and can either rely on gossip from their neighbors or directly subscribe to a server publishing about the event, if the former option does not meet the timeliness requirements. The server wishes to maximize its profit by increasing subscriptions from users and minimizing event sampling frequency to reduce costs. This leads to a Stackelberg game between the server and the users where the sender is the leader deciding its sampling frequency and the users are the followers deciding their subscription strategies. We investigate equilibrium strategies for low-connectivity and high-connectivity topologies.
Paper Structure (8 sections, 7 theorems, 18 equations, 7 figures)

This paper contains 8 sections, 7 theorems, 18 equations, 7 figures.

Table of Contents

  1. Introduction
  2. Age Analysis and Game Formulation
  3. Average Age Analysis at the Server
  4. Game Formulation between the Server and Users
  5. Bidirectional Line Network
  6. Fully-Connected Networks
  7. Simulation Results
  8. Conclusion

Key Result

Lemma 1

The highest age in the non-subscribers $S_{[1,m-1]}$ is at nodes mid-point between subscribers, i.e., $\lfloor \frac{m}{2} \rfloor$ and $\lceil \frac{m}{2} \rceil$.

Figures (7)

  • Figure 1: An illustration of a typical two-way line network.
  • Figure 2: $S_{j,h}$ (pink blocks) and $\bar{S}_{j,h}=S_{2i-h-1,2i-j-1}$ (blue blocks) positioned symmetrically about the dotted line between nodes $i$ and $i+1$.
  • Figure 3: Sets $\{j_1,\ldots,m-h_1\}$ with $j_1=2$ and $h_1=2$, have the same expected age irrespective of the value of $m$.
  • Figure 4: A typical fully-connected network with $m$ subscribers.
  • Figure 5: The expected age of nodes in a two way line network with $m\!=\!\{7\!,\!14\}\!$.
  • ...and 2 more figures

Theorems & Definitions (7)

  • Lemma 1
  • Lemma 2
  • Lemma 3
  • Lemma 4
  • Lemma 5
  • Lemma 6
  • Lemma 7