Performance Analysis of Dynamic Equilibria in Joint Path Selection and Congestion Control in Path-Aware Networks

TL;DR

This work analyzes the stability of joint path selection and congestion control in path-aware networks by extending a discrete-time axiomatic framework to many parallel paths. It shows that a high-midelity trade-off exists: increasing migration responsiveness improves fairness but can harm efficiency and convergence, while a lossless operating point can simultaneously optimize efficiency, convergence, and loss avoidance. A key insight is that path diversity can desynchronize traffic and suppress coherent temporal oscillations, yet realistic limited-visibility conditions reintroduce persistent spatial load imbalance at scale. The results offer principled guidelines for designing multipath protocols over future path-aware Internet architectures, balancing agility, stability, and throughput where path diversity is extensive.

Abstract

Path-aware networking (PAN) architectures, such as SCION and emerging LEO constellations, expose tens to hundreds of verifiable paths to endpoints. When multipath protocols like MPTCP and MPQUIC greedily exploit this diversity, uncoordinated migration can induce persistent, high-amplitude load oscillations. Although this instability is well-known, its quantitative performance impact remains poorly understood. In this paper, we apply a discrete-time axiomatic framework to the joint dynamics of loss-based congestion control and greedy path selection. By deriving the system's dynamic equilibria (stable periodic oscillations), we prove a fundamental trade-off: high Responsiveness improves Fairness but necessarily degrades Efficiency and Convergence. Conversely, we demonstrate that Efficiency, Convergence, and Loss Avoidance are simultaneously achievable at a critical lossless operating point. Furthermore, we find that while migration de-synchronizes traffic in high-diversity environments, realistic limited-visibility constraints transform coherent oscillations into persistent spatial load imbalance, rather than eliminating instability entirely. These results yield concrete design guidelines for robust multipath transport over the future path-aware Internet.

Figures (13)

• Figure 1: The probability distribution of agent continuity times for a system with $P=4$ paths, conditioned on a path's rank ($p=0, 1, 2, 3$). The periodic influx of new agents to the Rank 0 path (blue) creates a heterogeneous distribution with significant mass at $\tau=0$. As the path shifts to higher ranks (orange, green, red) in subsequent steps, this mass shifts to higher $\tau$ values.
• Figure 2: Logical consistency of the $P$-step oscillation. The (small) shaded regions represent the parameter space where the assumption is inconsistent. The vast unshaded majority confirms this pattern is a robust, fundamental emergent property of the system.
• Figure 3: Visual proof of convergence to the lossless dynamic equilibrium. The system's state variables converge exponentially fast to the unique, stable periodic orbit predicted by our analytical model.
• Figure 4: Structural patterns of lossy dynamic equilibria. (a) High Responsiveness ($\rho=0.45$): loss is absorbed into the regular $P$-step cycle. (b) Low Responsiveness ($\rho=0.1$): multiplicative decrease temporarily disrupts rank ordering, but the $P$-step cycle immediately resumes after one step.
• Figure 5: Sensitivity to path diversity: Equilibrium oscillation amplitude as a function of $P$. Higher $P$ (mimicking path-aware networks) improves stability via de-synchronization.

Theorems & Definitions (1)

• Definition 1: $P$-step Oscillation