The Streaming Reservoir Convergence Theorem: A Prospect-Theoretic Framework for Multi-Provider Adaptive Streaming
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| Main Authors: | , , , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866914528168509440 |
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| author | Agyemang, Justice Owusu Kponyo, Jerry John Agyekum, Kwame Opuni-Boachie Obour Somuah, Obed Kwasi Boakye, Sarafina Serwaa Amponsah, Elliot Boakye, Godfred Manu Addo |
| author_facet | Agyemang, Justice Owusu Kponyo, Jerry John Agyekum, Kwame Opuni-Boachie Obour Somuah, Obed Kwasi Boakye, Sarafina Serwaa Amponsah, Elliot Boakye, Godfred Manu Addo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_02761 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Streaming Reservoir Convergence Theorem: A Prospect-Theoretic Framework for Multi-Provider Adaptive Streaming Agyemang, Justice Owusu Kponyo, Jerry John Agyekum, Kwame Opuni-Boachie Obour Somuah, Obed Kwasi Boakye, Sarafina Serwaa Amponsah, Elliot Boakye, Godfred Manu Addo Multimedia Networking and Internet Architecture 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. |
| title | The Streaming Reservoir Convergence Theorem: A Prospect-Theoretic Framework for Multi-Provider Adaptive Streaming |
| topic | Multimedia Networking and Internet Architecture |
| url | https://arxiv.org/abs/2605.02761 |