Alpha-beta (α-β) model: definition

Beginner

A simple rule for how long sending data takes. There is a fixed delay to get started, plus a time that grows with the amount of data.

Novice

A cost model in which sending $n$ bytes takes $\alpha + n/B$ : $\alpha$ is a fixed per-message latency and $B$ is the link bandwidth ( $\beta = 1/B$ is the time per byte). A collective’s time is the sum over its steps.

Expert

Hockney-style linear model $T = \alpha + n\beta$ ( $+\, n\gamma$ for reduction arithmetic). Ignores contention, protocol switching, pipelining granularity and congestion, but captures the latency-bound vs bandwidth-bound trade-off that drives algorithm selection.