Joint asymptotic limit for mixed audience segments

Characterize the joint large-rendition asymptotic limit of the optimal quality gap for mixed web audiences whose segments have different window-height caps and share a common adaptive-bitrate ladder.

Background

For mixed audiences, viewers with different window heights impose different resolution caps on the same ladder. The paper derives upper and lower asymptotic brackets based respectively on shared-rung and private-rung designs, but the exact joint behavior of the shared optimization is not determined.

Numerical experiments indicate that the normalized gap can continue growing through ten renditions and that the effective decay exponent is slower than the one-dimensional 1/n law. The unresolved issue is therefore to determine the limiting interaction among audience segments, caps, and ladder size.

References

The joint limit---segments, caps, and $n$ interacting---is the principal open problem.

— A Quantization Problem Posed by Adaptive Streaming  (2609.03745 - Reznik, 3 Sep 2026) in Section 7.2, final paragraph of the subsection “Two-dimensional adaptation: player size”

The open problems we find most inviting are the Zador-general version of the law, including the atoms that rate-capped service tiers produce; converses under richer client models; and the joint multi-segment limit.

— A Quantization Problem Posed by Adaptive Streaming  (2609.03745 - Reznik, 3 Sep 2026) in Conclusion