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Exploring Multiple Converged States of Network Configurations

Shunyu Yang, Dan Wang, Peng Zhang

TL;DR

It is proved that any network with multiple converged states possesses a specific set of critical links which, when flipped, shifts the network between different stable states, and a tentative theoretical verification method for non-determinism with O(n) complexity, where $n$ is the number of edges in a network.

Abstract

Due to the policy-rich BGP, multiple stable forwarding states might exist for the same network topology and configuration, rendering the network convergence non-deterministic. This paper proves that any network with multiple converged states possesses a specific set of critical links which, when flipped (disconnect then reconnect), shifts the network between different stable states. We establish this result under the Stable Path Problem (SPP) framework, and also examine a real-world corner case where SPP doesn't apply. Building on this theoretical foundation, we propose a tentative theoretical verification method for non-determinism with $O(n)$ complexity, where $n$ is the number of edges in a network. Specifically, we separately flip each link in the network and observe whether new converged states emerge. If no new states are discovered, the network is guaranteed to be free of non-determinism. This approach is proved correct when the set of critical links reduces to a single link -- usually the case in the real-world deployments.

Exploring Multiple Converged States of Network Configurations

TL;DR

It is proved that any network with multiple converged states possesses a specific set of critical links which, when flipped, shifts the network between different stable states, and a tentative theoretical verification method for non-determinism with O(n) complexity, where is the number of edges in a network.

Abstract

Due to the policy-rich BGP, multiple stable forwarding states might exist for the same network topology and configuration, rendering the network convergence non-deterministic. This paper proves that any network with multiple converged states possesses a specific set of critical links which, when flipped (disconnect then reconnect), shifts the network between different stable states. We establish this result under the Stable Path Problem (SPP) framework, and also examine a real-world corner case where SPP doesn't apply. Building on this theoretical foundation, we propose a tentative theoretical verification method for non-determinism with complexity, where is the number of edges in a network. Specifically, we separately flip each link in the network and observe whether new converged states emerge. If no new states are discovered, the network is guaranteed to be free of non-determinism. This approach is proved correct when the set of critical links reduces to a single link -- usually the case in the real-world deployments.
Paper Structure (17 sections, 11 theorems, 1 equation, 5 figures, 1 algorithm)

This paper contains 17 sections, 11 theorems, 1 equation, 5 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Motivation: Network Non-determinism
  3. BGP Wedgie
  4. Insight from Link Flips
  5. Exits and Outgoing Links
  6. Proof Overview
  7. Lemmas
  8. Main Theorem
  9. Non-determinism from Tie-breaking
  10. Time-Based Tie-breaking Routers
  11. Main Theorem
  12. Performing Link Flips
  13. Critical Links Often Reduce to One
  14. Flipping All Links Individually
  15. Discussion on Future Work
  16. ...and 2 more sections

Key Result

Lemma 1

The destination is never part of a dispute wheel.

Figures (5)

  • Figure 1: An example BGP Wedgie. Topology (a) yields 2 states, one intended (b), and the other unintended (c).
  • Figure 2: A dispute wheel where internal routes (green) have higher priority than external routes (red).
  • Figure 3: Within dispute wheel (a), designating 2 as exit eliminates the wheel (b), producing a stable state (c).
  • Figure 4: Designating 2 and 4 as exits eliminates the two wheels.
  • Figure 6: Router 3 tie-breaks between 1 and 2 based on arrival order.

Theorems & Definitions (16)

  • Definition 1: Dispute Wheel
  • Lemma 1
  • Definition 2: Exit
  • Lemma 2
  • Lemma 3
  • Definition 3: Network Exit
  • Lemma 4
  • Definition 4: Solution of an SPP
  • Definition 5: Choice
  • Theorem 1
  • ...and 6 more