← All parts of this equation

Equation 30 · Part 7 · The Network Is the Computer Again

superscript

Pslow=1−(1−q)p,P_{\mathrm{slow}} = 1 - (1-q)^{p},
superscript

What this part means

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

Its job in the formula

A raised mark can be a power or an index. Its position and the surrounding notation determine which.

The passage around this formula

The reason this matters more for collectives than for ordinary traffic is synchronisation. A collective is a barrier. Every participant waits for the operation to complete, so the operation completes when the last contribution arrives. Tail latency therefore stops being a tail statistic and becomes the mean cost of every step. Dean and Barroso’s analysis of latency variability in large fan-out services is the canonical statement of the mechanism: background activity, queueing at multiple layers including network switches, and shared-resource contention produce occasional slow responses, and a request that must wait on many servers is very likely to encounter one [ 18 ] . The arithmetic is…

Read this part in the article →

Learn the underlying idea

An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

Open the illustrated exponents: repeated multiplication and powers guide →

Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.