Writers arrive uniformly at rate λ = writers/min ÷ 60. A commit attempt succeeds iff no other writer commits
during the build window Tb.
Retries (max K, mean wait W) are truncated geometric. Cascading interference emerges under higher load.
Expected average commit duration
—
Commit failure probability (all retries exhausted)
—
Per-attempt success / conflict
— • —
Expected attempts per success
— • E[R] = —
Commit failure probability (all retries
exhausted)
Failure = (1 − p)K+1
Expected average commit duration (s)
E[T] = E[A] · Tb + (E[A] − 1) · W
Formulas
Open system (uniform arrivals)
λ = writers_per_minute / 60
q = 1 − p
s = 1 − q^(K+1)
r = λ · s
ρ = r · T_b
L(ρ) = 1 / (1 + exp(−β (ρ − ρ₀)))
r_eff = r · (1 + α · L(ρ) · (E[A] − 1))
p = exp(− r_eff · T_b)
E[A] = Σ_{i=1}^{K+1} i · p · q^{i−1} / s
E[T] = E[A] · T_b + (E[A] − 1) · W
Failure probability (all retries exhausted) = q^(K+1)
References:
H.T. Kung, J.T. Robinson, "On Optimistic Methods for Concurrency Control," ACM TODS, 1981.
R. Agrawal, M.J. Carey, M. Livny, "Concurrency Control Performance Modeling: Alternatives and Implications," ACM TODS, 1987.