Model

Recovery time from the checkpoint interval

Recovery costs write_rate / replay_rate seconds of downtime for each second of checkpoint interval.

t_{recovery} \approx τ \cdot \frac{write rate}{replay rate}

$τ$: Checkpoint interval; time between checkpoints
$write rate$: Log write rate; bytes of log written per second
$replay rate$: Replay rate; bytes of log replayed per second on a cold pool

Recurring principle: Costs are conserved

How it behaves

One input on the horizontal axis, the others held fixed.

log 20 MB/s, replay 10 MB/slog 28 MB/s, replay 14 MB/slog 10 MB/s, replay 40 MB/s

Data table

Worst-case recovery time by checkpoint interval
Checkpoint interval τ (seconds)	series	Recovery time
30 s	log 20 MB/s, replay 10 MB/s	60 s
52.1 s	log 20 MB/s, replay 10 MB/s	104 s
74.3 s	log 20 MB/s, replay 10 MB/s	149 s
96.4 s	log 20 MB/s, replay 10 MB/s	193 s
119 s	log 20 MB/s, replay 10 MB/s	237 s
141 s	log 20 MB/s, replay 10 MB/s	281 s
163 s	log 20 MB/s, replay 10 MB/s	326 s
185 s	log 20 MB/s, replay 10 MB/s	370 s
207 s	log 20 MB/s, replay 10 MB/s	414 s
229 s	log 20 MB/s, replay 10 MB/s	458 s
251 s	log 20 MB/s, replay 10 MB/s	503 s
273 s	log 20 MB/s, replay 10 MB/s	547 s
296 s	log 20 MB/s, replay 10 MB/s	591 s
318 s	log 20 MB/s, replay 10 MB/s	635 s
340 s	log 20 MB/s, replay 10 MB/s	680 s
362 s	log 20 MB/s, replay 10 MB/s	724 s
384 s	log 20 MB/s, replay 10 MB/s	768 s
406 s	log 20 MB/s, replay 10 MB/s	812 s
428 s	log 20 MB/s, replay 10 MB/s	857 s
450 s	log 20 MB/s, replay 10 MB/s	901 s
473 s	log 20 MB/s, replay 10 MB/s	945 s
495 s	log 20 MB/s, replay 10 MB/s	989 s
517 s	log 20 MB/s, replay 10 MB/s	1,030 s
539 s	log 20 MB/s, replay 10 MB/s	1,080 s
561 s	log 20 MB/s, replay 10 MB/s	1,120 s
583 s	log 20 MB/s, replay 10 MB/s	1,170 s
605 s	log 20 MB/s, replay 10 MB/s	1,210 s
627 s	log 20 MB/s, replay 10 MB/s	1,250 s
650 s	log 20 MB/s, replay 10 MB/s	1,300 s
672 s	log 20 MB/s, replay 10 MB/s	1,340 s
694 s	log 20 MB/s, replay 10 MB/s	1,390 s
716 s	log 20 MB/s, replay 10 MB/s	1,430 s
738 s	log 20 MB/s, replay 10 MB/s	1,480 s
760 s	log 20 MB/s, replay 10 MB/s	1,520 s
782 s	log 20 MB/s, replay 10 MB/s	1,560 s
804 s	log 20 MB/s, replay 10 MB/s	1,610 s
827 s	log 20 MB/s, replay 10 MB/s	1,650 s
849 s	log 20 MB/s, replay 10 MB/s	1,700 s
871 s	log 20 MB/s, replay 10 MB/s	1,740 s
893 s	log 20 MB/s, replay 10 MB/s	1,790 s
915 s	log 20 MB/s, replay 10 MB/s	1,830 s
937 s	log 20 MB/s, replay 10 MB/s	1,870 s
959 s	log 20 MB/s, replay 10 MB/s	1,920 s
981 s	log 20 MB/s, replay 10 MB/s	1,960 s
1,000 s	log 20 MB/s, replay 10 MB/s	2,010 s
1,030 s	log 20 MB/s, replay 10 MB/s	2,050 s
1,050 s	log 20 MB/s, replay 10 MB/s	2,100 s
1,070 s	log 20 MB/s, replay 10 MB/s	2,140 s
1,090 s	log 20 MB/s, replay 10 MB/s	2,180 s
1,110 s	log 20 MB/s, replay 10 MB/s	2,230 s
1,140 s	log 20 MB/s, replay 10 MB/s	2,270 s
1,160 s	log 20 MB/s, replay 10 MB/s	2,320 s
1,180 s	log 20 MB/s, replay 10 MB/s	2,360 s
1,200 s	log 20 MB/s, replay 10 MB/s	2,410 s
1,220 s	log 20 MB/s, replay 10 MB/s	2,450 s
1,250 s	log 20 MB/s, replay 10 MB/s	2,490 s
1,270 s	log 20 MB/s, replay 10 MB/s	2,540 s
1,290 s	log 20 MB/s, replay 10 MB/s	2,580 s
1,310 s	log 20 MB/s, replay 10 MB/s	2,630 s
1,340 s	log 20 MB/s, replay 10 MB/s	2,670 s
1,360 s	log 20 MB/s, replay 10 MB/s	2,720 s
1,380 s	log 20 MB/s, replay 10 MB/s	2,760 s
1,400 s	log 20 MB/s, replay 10 MB/s	2,800 s
1,420 s	log 20 MB/s, replay 10 MB/s	2,850 s
1,450 s	log 20 MB/s, replay 10 MB/s	2,890 s
1,470 s	log 20 MB/s, replay 10 MB/s	2,940 s
1,490 s	log 20 MB/s, replay 10 MB/s	2,980 s
1,510 s	log 20 MB/s, replay 10 MB/s	3,020 s
1,530 s	log 20 MB/s, replay 10 MB/s	3,070 s
1,560 s	log 20 MB/s, replay 10 MB/s	3,110 s
1,580 s	log 20 MB/s, replay 10 MB/s	3,160 s
1,600 s	log 20 MB/s, replay 10 MB/s	3,200 s
1,620 s	log 20 MB/s, replay 10 MB/s	3,250 s
1,650 s	log 20 MB/s, replay 10 MB/s	3,290 s
1,670 s	log 20 MB/s, replay 10 MB/s	3,330 s
1,690 s	log 20 MB/s, replay 10 MB/s	3,380 s
1,710 s	log 20 MB/s, replay 10 MB/s	3,420 s
1,730 s	log 20 MB/s, replay 10 MB/s	3,470 s
1,760 s	log 20 MB/s, replay 10 MB/s	3,510 s
1,780 s	log 20 MB/s, replay 10 MB/s	3,560 s
1,800 s	log 20 MB/s, replay 10 MB/s	3,600 s
30 s	log 28 MB/s, replay 14 MB/s	60 s
52.1 s	log 28 MB/s, replay 14 MB/s	104 s
74.3 s	log 28 MB/s, replay 14 MB/s	149 s
96.4 s	log 28 MB/s, replay 14 MB/s	193 s
119 s	log 28 MB/s, replay 14 MB/s	237 s
141 s	log 28 MB/s, replay 14 MB/s	281 s
163 s	log 28 MB/s, replay 14 MB/s	326 s
185 s	log 28 MB/s, replay 14 MB/s	370 s
207 s	log 28 MB/s, replay 14 MB/s	414 s
229 s	log 28 MB/s, replay 14 MB/s	458 s
251 s	log 28 MB/s, replay 14 MB/s	503 s
273 s	log 28 MB/s, replay 14 MB/s	547 s
296 s	log 28 MB/s, replay 14 MB/s	591 s
318 s	log 28 MB/s, replay 14 MB/s	635 s
340 s	log 28 MB/s, replay 14 MB/s	680 s
362 s	log 28 MB/s, replay 14 MB/s	724 s
384 s	log 28 MB/s, replay 14 MB/s	768 s
406 s	log 28 MB/s, replay 14 MB/s	812 s
428 s	log 28 MB/s, replay 14 MB/s	857 s
450 s	log 28 MB/s, replay 14 MB/s	901 s
473 s	log 28 MB/s, replay 14 MB/s	945 s
495 s	log 28 MB/s, replay 14 MB/s	989 s
517 s	log 28 MB/s, replay 14 MB/s	1,030 s
539 s	log 28 MB/s, replay 14 MB/s	1,080 s
561 s	log 28 MB/s, replay 14 MB/s	1,120 s
583 s	log 28 MB/s, replay 14 MB/s	1,170 s
605 s	log 28 MB/s, replay 14 MB/s	1,210 s
627 s	log 28 MB/s, replay 14 MB/s	1,250 s
650 s	log 28 MB/s, replay 14 MB/s	1,300 s
672 s	log 28 MB/s, replay 14 MB/s	1,340 s
694 s	log 28 MB/s, replay 14 MB/s	1,390 s
716 s	log 28 MB/s, replay 14 MB/s	1,430 s
738 s	log 28 MB/s, replay 14 MB/s	1,480 s
760 s	log 28 MB/s, replay 14 MB/s	1,520 s
782 s	log 28 MB/s, replay 14 MB/s	1,560 s
804 s	log 28 MB/s, replay 14 MB/s	1,610 s
827 s	log 28 MB/s, replay 14 MB/s	1,650 s
849 s	log 28 MB/s, replay 14 MB/s	1,700 s
871 s	log 28 MB/s, replay 14 MB/s	1,740 s
893 s	log 28 MB/s, replay 14 MB/s	1,790 s
915 s	log 28 MB/s, replay 14 MB/s	1,830 s
937 s	log 28 MB/s, replay 14 MB/s	1,870 s
959 s	log 28 MB/s, replay 14 MB/s	1,920 s
981 s	log 28 MB/s, replay 14 MB/s	1,960 s
1,000 s	log 28 MB/s, replay 14 MB/s	2,010 s
1,030 s	log 28 MB/s, replay 14 MB/s	2,050 s
1,050 s	log 28 MB/s, replay 14 MB/s	2,100 s
1,070 s	log 28 MB/s, replay 14 MB/s	2,140 s
1,090 s	log 28 MB/s, replay 14 MB/s	2,180 s
1,110 s	log 28 MB/s, replay 14 MB/s	2,230 s
1,140 s	log 28 MB/s, replay 14 MB/s	2,270 s
1,160 s	log 28 MB/s, replay 14 MB/s	2,320 s
1,180 s	log 28 MB/s, replay 14 MB/s	2,360 s
1,200 s	log 28 MB/s, replay 14 MB/s	2,410 s
1,220 s	log 28 MB/s, replay 14 MB/s	2,450 s
1,250 s	log 28 MB/s, replay 14 MB/s	2,490 s
1,270 s	log 28 MB/s, replay 14 MB/s	2,540 s
1,290 s	log 28 MB/s, replay 14 MB/s	2,580 s
1,310 s	log 28 MB/s, replay 14 MB/s	2,630 s
1,340 s	log 28 MB/s, replay 14 MB/s	2,670 s
1,360 s	log 28 MB/s, replay 14 MB/s	2,720 s
1,380 s	log 28 MB/s, replay 14 MB/s	2,760 s
1,400 s	log 28 MB/s, replay 14 MB/s	2,800 s
1,420 s	log 28 MB/s, replay 14 MB/s	2,850 s
1,450 s	log 28 MB/s, replay 14 MB/s	2,890 s
1,470 s	log 28 MB/s, replay 14 MB/s	2,940 s
1,490 s	log 28 MB/s, replay 14 MB/s	2,980 s
1,510 s	log 28 MB/s, replay 14 MB/s	3,020 s
1,530 s	log 28 MB/s, replay 14 MB/s	3,070 s
1,560 s	log 28 MB/s, replay 14 MB/s	3,110 s
1,580 s	log 28 MB/s, replay 14 MB/s	3,160 s
1,600 s	log 28 MB/s, replay 14 MB/s	3,200 s
1,620 s	log 28 MB/s, replay 14 MB/s	3,250 s
1,650 s	log 28 MB/s, replay 14 MB/s	3,290 s
1,670 s	log 28 MB/s, replay 14 MB/s	3,330 s
1,690 s	log 28 MB/s, replay 14 MB/s	3,380 s
1,710 s	log 28 MB/s, replay 14 MB/s	3,420 s
1,730 s	log 28 MB/s, replay 14 MB/s	3,470 s
1,760 s	log 28 MB/s, replay 14 MB/s	3,510 s
1,780 s	log 28 MB/s, replay 14 MB/s	3,560 s
1,800 s	log 28 MB/s, replay 14 MB/s	3,600 s
30 s	log 10 MB/s, replay 40 MB/s	7.5 s
52.1 s	log 10 MB/s, replay 40 MB/s	13 s
74.3 s	log 10 MB/s, replay 40 MB/s	18.6 s
96.4 s	log 10 MB/s, replay 40 MB/s	24.1 s
119 s	log 10 MB/s, replay 40 MB/s	29.6 s
141 s	log 10 MB/s, replay 40 MB/s	35.2 s
163 s	log 10 MB/s, replay 40 MB/s	40.7 s
185 s	log 10 MB/s, replay 40 MB/s	46.2 s
207 s	log 10 MB/s, replay 40 MB/s	51.8 s
229 s	log 10 MB/s, replay 40 MB/s	57.3 s
251 s	log 10 MB/s, replay 40 MB/s	62.8 s
273 s	log 10 MB/s, replay 40 MB/s	68.3 s
296 s	log 10 MB/s, replay 40 MB/s	73.9 s
318 s	log 10 MB/s, replay 40 MB/s	79.4 s
340 s	log 10 MB/s, replay 40 MB/s	84.9 s
362 s	log 10 MB/s, replay 40 MB/s	90.5 s
384 s	log 10 MB/s, replay 40 MB/s	96 s
406 s	log 10 MB/s, replay 40 MB/s	102 s
428 s	log 10 MB/s, replay 40 MB/s	107 s
450 s	log 10 MB/s, replay 40 MB/s	113 s
473 s	log 10 MB/s, replay 40 MB/s	118 s
495 s	log 10 MB/s, replay 40 MB/s	124 s
517 s	log 10 MB/s, replay 40 MB/s	129 s
539 s	log 10 MB/s, replay 40 MB/s	135 s
561 s	log 10 MB/s, replay 40 MB/s	140 s
583 s	log 10 MB/s, replay 40 MB/s	146 s
605 s	log 10 MB/s, replay 40 MB/s	151 s
627 s	log 10 MB/s, replay 40 MB/s	157 s
650 s	log 10 MB/s, replay 40 MB/s	162 s
672 s	log 10 MB/s, replay 40 MB/s	168 s
694 s	log 10 MB/s, replay 40 MB/s	173 s
716 s	log 10 MB/s, replay 40 MB/s	179 s
738 s	log 10 MB/s, replay 40 MB/s	185 s
760 s	log 10 MB/s, replay 40 MB/s	190 s
782 s	log 10 MB/s, replay 40 MB/s	196 s
804 s	log 10 MB/s, replay 40 MB/s	201 s
827 s	log 10 MB/s, replay 40 MB/s	207 s
849 s	log 10 MB/s, replay 40 MB/s	212 s
871 s	log 10 MB/s, replay 40 MB/s	218 s
893 s	log 10 MB/s, replay 40 MB/s	223 s
915 s	log 10 MB/s, replay 40 MB/s	229 s
937 s	log 10 MB/s, replay 40 MB/s	234 s
959 s	log 10 MB/s, replay 40 MB/s	240 s
981 s	log 10 MB/s, replay 40 MB/s	245 s
1,000 s	log 10 MB/s, replay 40 MB/s	251 s
1,030 s	log 10 MB/s, replay 40 MB/s	256 s
1,050 s	log 10 MB/s, replay 40 MB/s	262 s
1,070 s	log 10 MB/s, replay 40 MB/s	267 s
1,090 s	log 10 MB/s, replay 40 MB/s	273 s
1,110 s	log 10 MB/s, replay 40 MB/s	279 s
1,140 s	log 10 MB/s, replay 40 MB/s	284 s
1,160 s	log 10 MB/s, replay 40 MB/s	290 s
1,180 s	log 10 MB/s, replay 40 MB/s	295 s
1,200 s	log 10 MB/s, replay 40 MB/s	301 s
1,220 s	log 10 MB/s, replay 40 MB/s	306 s
1,250 s	log 10 MB/s, replay 40 MB/s	312 s
1,270 s	log 10 MB/s, replay 40 MB/s	317 s
1,290 s	log 10 MB/s, replay 40 MB/s	323 s
1,310 s	log 10 MB/s, replay 40 MB/s	328 s
1,340 s	log 10 MB/s, replay 40 MB/s	334 s
1,360 s	log 10 MB/s, replay 40 MB/s	339 s
1,380 s	log 10 MB/s, replay 40 MB/s	345 s
1,400 s	log 10 MB/s, replay 40 MB/s	350 s
1,420 s	log 10 MB/s, replay 40 MB/s	356 s
1,450 s	log 10 MB/s, replay 40 MB/s	362 s
1,470 s	log 10 MB/s, replay 40 MB/s	367 s
1,490 s	log 10 MB/s, replay 40 MB/s	373 s
1,510 s	log 10 MB/s, replay 40 MB/s	378 s
1,530 s	log 10 MB/s, replay 40 MB/s	384 s
1,560 s	log 10 MB/s, replay 40 MB/s	389 s
1,580 s	log 10 MB/s, replay 40 MB/s	395 s
1,600 s	log 10 MB/s, replay 40 MB/s	400 s
1,620 s	log 10 MB/s, replay 40 MB/s	406 s
1,650 s	log 10 MB/s, replay 40 MB/s	411 s
1,670 s	log 10 MB/s, replay 40 MB/s	417 s
1,690 s	log 10 MB/s, replay 40 MB/s	422 s
1,710 s	log 10 MB/s, replay 40 MB/s	428 s
1,730 s	log 10 MB/s, replay 40 MB/s	433 s
1,760 s	log 10 MB/s, replay 40 MB/s	439 s
1,780 s	log 10 MB/s, replay 40 MB/s	444 s
1,800 s	log 10 MB/s, replay 40 MB/s	450 s

Worked examples, recomputed

Every number the mechanisms quote for this relationship is recomputed from it, so none of them disagrees with it.

Where it appears

Each mechanism states it in its own names. The general symbol each name stands for is shown with it.

Persistence & Durability
When a system says "yes, your data is safe", what exactly has it promised, and what did it have to do to keep that promise?
$\frac{write rate}{replay rate} seconds of downtime per second of checkpoint interval$
Read it in place →