Concept

Clock resolution — where it appears

The smallest interval a system's timestamps can distinguish, which sets a stamp's width and caps the burstiness anything can observe. It arrives with the timestamp format rather than being chosen, and refining it by a factor costs the logarithm of that factor in bits per stamp.

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

16326412825610244096window length W, in arrivals (D = W × the mean gap)share of the counts they disagree onevenPoissonburstydrifting1 ms clock · mean gap 10 ticks · 30,000 arrivalseven: 0% at every length

A window that is a duration

Nobody asks for the error rate over the last four thousand and ninety-six requests. They ask for the last five minutes. The two are the same question exactly when the arrivals are evenly spaced, and on a stream whose rate drifts they disagree about fifty-seven per cent of the counts.

streaming · Window
71 s60 ticks11100 ms600 ticks1410 ms6,000 ticks171 ms60,000 ticks270.001 ms60,000,000 ticksclock resolutionbits per stamp⌈log₂ 2D/r⌉no arrival rateappears in itD = 60 s · key 32 bitscomputed, not measured

The clock that cannot see the burst

A stream generator asked for a burst ten times faster than its mean rate, on a clock whose resolution was the mean gap, produced a perfectly even stream — index of dispersion 0.00, for something called bursty. Nothing had gone wrong except that the instrument could not represent what it was being asked to measure.

space · 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

Named alongside it

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

Arrival processBurstinessOccupancyTime windowMeasurementSliding windowTimestampAliasingExpiryExponential histogramState bitsStreaming model

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