Concept

Temporal resolution — where it appears

How finely a windowed structure can place an event in time, as opposed to in arrivals. A window counted in arrivals has none it can state: its blocks cover whatever duration the stream took to supply them, which ran from half a second to fifteen on a stream whose rate rose and fell.

Named by 4 essays across 3 fields — each of them below, with the objects they name alongside it.

0%25%50%75%100%1.5×shareheadroom over the mean occupancyoverflowingstanding idledrifting · 4.0 s window · 100 Hz47% overflow at the mean

Sized for a rate that does not hold still

A four-second window on a stream at a hundred arrivals a second holds four hundred items on average and between 105 and 2,169 when the rate moves. An allocation set at that average overflows at 47 per cent of instants while 35 per cent of it stands empty, which is the same decision failing in both directions at once.

practice · Window
even5.1 s – 5.1 s1.00× · dispersion 0.00Poisson4.7 s – 5.5 s1.16× · dispersion 0.70bursty4.5 s – 4.5 s1.00× · dispersion 0.57drifting565 ms – 14.8 s26.14× · dispersion 849.57duration one block covered4,096 arrivals in 8 blocks · 100 Hz · 1 ms clock26.1× on the drifting stream

The window that is even in the wrong currency

A window of four thousand arrivals in eight blocks retires a block every 5.1 seconds on a steady stream and anywhere between 0.57 and 14.8 seconds on a stream whose rate moves. The structure cannot tell, because it is counting arrivals, and the alert written against it is in seconds.

streaming · Window
1.821251.951.431752.731.302253.521.292503.911.183755.861.005128.00longest block ÷ shortestarrivals per block, and bursts per blockpart of a bursta whole numberbursts of 64 · 8 blocks · 20,000 arrivalsdispersion 0.57 and a ratio of 1.00

The boundary that hides the burst

A window whose blocks hold five hundred and twelve arrivals reports a perfectly even stream — every block the same duration to the tick — while the arrivals it is retiring have an index of dispersion of 0.57. Move the block to a hundred and twenty-five and the same stream varies by 1.8 times.

wrong · Window
1 — no differencethe whole array reviewed1.03×only this batch reviewed1.22×a block window, which does alias1.48×20,000 arrivals · period 50 · cyclethe instrument reads 1.48 where an alias is known to be

The sampler that cannot alias

A block window's boundary fires on an arrival count, and a stream whose burst repeats every sixty-four arrivals is reported as perfectly even by a block of five hundred and twelve. A quantile summary compresses on an update count, which is the same arrangement. Swept against three periodic value processes and their shuffles, it does not alias — and the reason is one line of arithmetic rather than a lucky sweep.

wrong · Window

Named alongside it

The objects these essays reach for when they reach for this one.

Arrival processBurstinessMeasurementSliding windowAliasingExpiryOccupancyTime windowClock resolutionCommensurabilityExponential histogramFailure mode

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