Exploring Multiple Converged States of Network Configurations

2026-03-03

AI Summary

This work addresses the non-deterministic behavior of BGP networks, which—under identical topologies and configurations—may converge to multiple stable forwarding states. Building upon the Stable Paths Problem (SPP) framework, the paper establishes for the first time that if a network admits multiple convergence outcomes, there necessarily exists a set of critical links whose state toggling can trigger transitions between distinct stable solutions. Leveraging this insight, the authors propose a linear-time (O(n)) verification method that combines link-flipping experiments with formal verification to efficiently determine whether a network exhibits multistability, particularly in scenarios involving a single critical link. The approach achieves both theoretical rigor and practical scalability, offering a novel and efficient means to analyze BGP convergence non-determinism.

Technology Category

Planning, Routing, and Scheduling: Deterministic PlanningMultiagent Systems: Other Foundations of Multi Agent SystemsReasoning under Uncertainty: Stochastic Optimization

Application Category

Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphsSystems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterizationWeb Mining and Content Analysis: Models for Web evolution

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.

Problem

• BGP
• network convergence
• non-determinism
• multiple stable states
• Stable Path Problem

Innovation

• BGP convergence
• non-determinism
• critical links
• Stable Path Problem
• network verification