Figure: two independent constraints on tier traffic. SUSTAINABILITY is the sum over the decode set of R sub KV comma i, less than or equal to B tier: an aggregate rate across all concurrently decoding sequences, not one sequence. HIDING is T transfer of a chunk less than or equal to T compute of the previous chunk plus prefetch slack: per transfer, not on average. An aggregate panel shows four sequences' KV rates stacked inside the tier bandwidth with headroom left over, so sustainability holds. A per-transfer panel then shows four transfers of one 5.00 mebibyte block against a single deadline: 43 microseconds at 121 gigabytes per second is hidden, 82 microseconds at 64 gigabytes per second is hidden, 43 microseconds is hidden again, and 164 microseconds at a contended 32 gigabytes per second misses the deadline and exposes a stall. So hiding fails on one transfer at an entirely satisfactory average bandwidth. Link width and compression act on sustainability; prefetch depth, chunk sizing and traversal order act on hiding. The deadline position is a scenario parameter, not a measurement, and no CXL hardware was measured.

Figure 5.2 · Analytical model

Sustainability and hiding are independent constraints

One is an aggregate rate across the whole decode set. The other is a deadline on every individual transfer. Satisfying the first tells you nothing about the second.

SUSTAINABILITY — an aggregate rate

Σ_{i ∈ decode set} R_KV,i   ≤   B_tier

The summed KV consumption rate across all concurrently decoding sequences, not one sequence. Link width and compression act on this term: they raise B_tier or lower R_KV.

HIDING — a per-transfer deadline

T_transfer(chunk)   ≤   T_compute(previous chunk) + prefetch_slack

Per transfer, not on average. Prefetch depth, chunk sizing and traversal order act on this term. Adding link width does not fix a missed deadline on one transfer.

A case where the average is fine and a transfer still stalls

Aggregate view — across the whole decode setseq 1seq 2seq 3seq 4B_tierheadroomΣ_{i ∈ decode set} R_KV,i  ≤  B_tier✓ SUSTAINABILITY HOLDS — the link is not saturated over this window.Schematic: relative widths only, no rate is claimed.
Per-transfer view — the same window, transfer by transferdeadline = T_compute(prev chunk) + prefetch_slacktransfer 1121 GB/s43 µs — hiddentransfer 264 GB/s82 µs — hiddentransfer 3121 GB/s43 µs — hiddentransfer 432 GB/s, contended164 µs — MISSES the deadline → exposed stall050100150200µs✗ HIDING FAILS — on one transfer, at an entirely satisfactory average bandwidth.
Transfer time inside the deadline — hidden behind computeOverrun — the part that cannot be hidden, and stalls the pipeline

The horizontal scale is set by the three canonical tier-fetch times for one 5.00 MiB block: 43 µs at 121 GB/s, 82 µs at 64 GB/s and 164 µs at 32 GB/s. The deadline position is a scenario parameter, not a measurement — it is drawn long enough to hide an 82 µs transfer and short enough to miss a 164 µs one, which is the only property it needs. No compute time is claimed here, and no CXL hardware was measured.

The two constraints are independent: the first can hold while the second fails.Sustainability is satisfied over the window — the link has headroom — and the pipeline still stalls, because one transfer individually exceeded the compute time available to hide it. Both constraints have to be stated because techniques act on different terms: link width and compression raise or relieve sustainability; prefetch depth, chunk sizing and traversal order address hiding. A stall at satisfactory average bandwidth is the diagnostic signature of the second, and no amount of the first will fix it.

Analytical model — data/formal_core.md §3.3; fetch times from CANONICAL-NUMBERS.md §4. No CXL hardware was measured.