KBT-TS: Krapivin-Block-Tracker with Tiered Storage

We present KBT-TS v2 (Krapivin-Block-Tracker with Tiered Storage),the complete extension to KBT v2 (Zenodo 10.5281/zenodo.20736937)for multi-tier storage hierarchies (RAM, SSD, HDD). Version 1 introduced the Zipf temperature model, block migrationlogic, and three-tier LRU analysis. Version 2 resolves all fouropen questions from v1 and adds three further contributions: P1 — Optimal decay rate λ*: λ* = p_boundary (analytical formula).Miss rate is determined by n_ram, not λ. Valid range derived. P2 — Adaptive tier boundaries: EMA feedback loop converges towithin ±5% of target RAM hit rate within 50,000 operations. P3 — Write-path analysis: write-back outperforms write-throughfor p_write > 0.01, saving 10–35% at p_write = 0.1–0.4. P4 — Online s-estimation: log-log regression on access countsestimates Zipf exponent with <10% error after 50k warm-up ops. P5 — Optimal migration hysteresis: h* = (2C_thrash/C_mig ·p_boundary/λ)^(1/3), replacing ad hoc thresholds from v1. P6 — Power-of-two block placement: 12× lower fill imbalanceacross all load levels with negligible probe-cost overhead. P7 — Unified cost model: C(λ, n_ram, n_ssd, s, p_write)jointly optimises all parameters in a single expression. The resulting system is fully self-calibrating: given only atarget RAM hit rate and write fraction, all parameters arederived automatically. Includes Python simulation scriptsand analysis charts.