The Streaming Reservoir Convergence Theorem: A Prospect-Theoretic Framework for Multi-Provider Adaptive Streaming

2026-05-04

AI Summary

This work addresses the high latency and playback interruptions in existing adaptive bitrate streaming systems caused by linear probing, passive switching, and cold standby mechanisms. The authors propose a reservoir model based on concurrent multi-source probing and prefetching of backup streams, formulated as a concurrent reservoir-filling problem. By simultaneously probing all providers and maintaining k pre-validated backup streams, the system achieves sub-second, seamless failover. Theoretical contributions include a harmonic lower bound for reservoir safety, an acceleration ratio for concurrent probing, monotonic quality convergence under lazy loading, and a jitter-resistant switching rule grounded in prospect theory (α=β=0.88, λ=2.25). Experiments across 12 HLS providers demonstrate that with k=3, the mean time to exhaustion improves by 9.15×, and concurrent probing yields a 4.27× speedup under a 40% failure rate, comprehensively validating the theoretical findings.

Abstract

We present the Streaming Reservoir Convergence Theorem (SRCT), a novel mathematical framework for multi-provider adaptive bitrate streaming that addresses three fundamental structural weaknesses in current systems: linear provider probing, reactive failover, and cold standby transitions. SRCT models stream acquisition as a concurrent reservoir filling problem$-$probing all $N$ providers simultaneously rather than in batches$-$and maintains $k$ pre-verified, pre-fetched standby streams alongside the active stream to enable sub-second failover with zero user-visible disruption. We prove four principal results: (1) a harmonic lower bound on reservoir safety showing that $k$ independent streams provide $H_k / \barλ$ expected uptime where $H_k$ is the $k$-th harmonic number; (2) a concurrent acquisition speedup $S(N,b) = (N/b) \cdot (1-F^b)/(1-F^N)$ over batched probing, yielding $3$-$5\times$ practical improvement; (3) monotonic non-decreasing quality under lazy-refill with convergence to the Pareto-optimal frontier; and (4) a prospect-weighted switching rule$-$using Kahneman-Tversky value functions with $α=β=0.88$, $λ=2.25$ $-$ that provably eliminates thrashing between similar-quality streams via a no-thrash bound on the expected switch count. We implement SRCT across two production streaming pipelines: a primary movie/TV system serving 12+ HLS providers with $k=3$ reservoir slots, and a live sports system with multi-format DASH/HLS failover. Empirical verification via Monte Carlo simulation (5000 trials) confirms all four theorems across 22 independent checks. The reservoir of $k=3$ streams achieves $9.15\times$ mean time to depletion versus a single stream, and concurrent probing of 12 providers at 40% failure rate yields a $4.27\times$ speedup over the current batched-by-3 default.

Problem

• adaptive streaming
• multi-provider
• failover
• reservoir
• streaming quality

Innovation

• Streaming Reservoir Convergence Theorem
• concurrent probing
• prospect-theoretic switching
• adaptive bitrate streaming
• sub-second failover