Model
Statistical multiplexing
Size tenants separately and you buy the sum of the peaks; share and you buy the peak of the sum.
- Tenants
- tenants with independent, bursty demand
- Demand
- mean and standard deviation of one tenant's demand
- Safety factor
- standard deviations of headroom planned for
How it behaves
One input on the horizontal axis, the others held fixed.
separate (sum of peaks)shared (peak of the sum)
Data table
| Tenants n | series | Slots to provision |
|---|---|---|
| 1 | separate (sum of peaks) | 20 |
| 1.06 | separate (sum of peaks) | 21.2 |
| 1.12 | separate (sum of peaks) | 22.4 |
| 1.19 | separate (sum of peaks) | 23.8 |
| 1.26 | separate (sum of peaks) | 25.2 |
| 1.33 | separate (sum of peaks) | 26.7 |
| 1.41 | separate (sum of peaks) | 28.3 |
| 1.5 | separate (sum of peaks) | 29.9 |
| 1.58 | separate (sum of peaks) | 31.7 |
| 1.68 | separate (sum of peaks) | 33.6 |
| 1.78 | separate (sum of peaks) | 35.6 |
| 1.88 | separate (sum of peaks) | 37.7 |
| 2 | separate (sum of peaks) | 39.9 |
| 2.11 | separate (sum of peaks) | 42.3 |
| 2.24 | separate (sum of peaks) | 44.8 |
| 2.37 | separate (sum of peaks) | 47.4 |
| 2.51 | separate (sum of peaks) | 50.2 |
| 2.66 | separate (sum of peaks) | 53.2 |
| 2.82 | separate (sum of peaks) | 56.4 |
| 2.99 | separate (sum of peaks) | 59.7 |
| 3.16 | separate (sum of peaks) | 63.2 |
| 3.35 | separate (sum of peaks) | 67 |
| 3.55 | separate (sum of peaks) | 71 |
| 3.76 | separate (sum of peaks) | 75.2 |
| 3.98 | separate (sum of peaks) | 79.6 |
| 4.22 | separate (sum of peaks) | 84.3 |
| 4.47 | separate (sum of peaks) | 89.3 |
| 4.73 | separate (sum of peaks) | 94.6 |
| 5.01 | separate (sum of peaks) | 100 |
| 5.31 | separate (sum of peaks) | 106 |
| 5.62 | separate (sum of peaks) | 112 |
| 5.96 | separate (sum of peaks) | 119 |
| 6.31 | separate (sum of peaks) | 126 |
| 6.68 | separate (sum of peaks) | 134 |
| 7.08 | separate (sum of peaks) | 142 |
| 7.5 | separate (sum of peaks) | 150 |
| 7.94 | separate (sum of peaks) | 159 |
| 8.41 | separate (sum of peaks) | 168 |
| 8.91 | separate (sum of peaks) | 178 |
| 9.44 | separate (sum of peaks) | 189 |
| 10 | separate (sum of peaks) | 200 |
| 10.6 | separate (sum of peaks) | 212 |
| 11.2 | separate (sum of peaks) | 224 |
| 11.9 | separate (sum of peaks) | 238 |
| 12.6 | separate (sum of peaks) | 252 |
| 13.3 | separate (sum of peaks) | 267 |
| 14.1 | separate (sum of peaks) | 283 |
| 15 | separate (sum of peaks) | 299 |
| 15.8 | separate (sum of peaks) | 317 |
| 16.8 | separate (sum of peaks) | 336 |
| 17.8 | separate (sum of peaks) | 356 |
| 18.8 | separate (sum of peaks) | 377 |
| 20 | separate (sum of peaks) | 399 |
| 21.1 | separate (sum of peaks) | 423 |
| 22.4 | separate (sum of peaks) | 448 |
| 23.7 | separate (sum of peaks) | 474 |
| 25.1 | separate (sum of peaks) | 502 |
| 26.6 | separate (sum of peaks) | 532 |
| 28.2 | separate (sum of peaks) | 564 |
| 29.9 | separate (sum of peaks) | 597 |
| 31.6 | separate (sum of peaks) | 632 |
| 33.5 | separate (sum of peaks) | 670 |
| 35.5 | separate (sum of peaks) | 710 |
| 37.6 | separate (sum of peaks) | 752 |
| 39.8 | separate (sum of peaks) | 796 |
| 42.2 | separate (sum of peaks) | 843 |
| 44.7 | separate (sum of peaks) | 893 |
| 47.3 | separate (sum of peaks) | 946 |
| 50.1 | separate (sum of peaks) | 1K |
| 53.1 | separate (sum of peaks) | 1.06K |
| 56.2 | separate (sum of peaks) | 1.12K |
| 59.6 | separate (sum of peaks) | 1.19K |
| 63.1 | separate (sum of peaks) | 1.26K |
| 66.8 | separate (sum of peaks) | 1.34K |
| 70.8 | separate (sum of peaks) | 1.42K |
| 75 | separate (sum of peaks) | 1.5K |
| 79.4 | separate (sum of peaks) | 1.59K |
| 84.1 | separate (sum of peaks) | 1.68K |
| 89.1 | separate (sum of peaks) | 1.78K |
| 94.4 | separate (sum of peaks) | 1.89K |
| 100 | separate (sum of peaks) | 2K |
| 1 | shared (peak of the sum) | 20 |
| 1.06 | shared (peak of the sum) | 20.9 |
| 1.12 | shared (peak of the sum) | 21.8 |
| 1.19 | shared (peak of the sum) | 22.8 |
| 1.26 | shared (peak of the sum) | 23.8 |
| 1.33 | shared (peak of the sum) | 24.9 |
| 1.41 | shared (peak of the sum) | 26 |
| 1.5 | shared (peak of the sum) | 27.2 |
| 1.58 | shared (peak of the sum) | 28.4 |
| 1.68 | shared (peak of the sum) | 29.7 |
| 1.78 | shared (peak of the sum) | 31.1 |
| 1.88 | shared (peak of the sum) | 32.6 |
| 2 | shared (peak of the sum) | 34.1 |
| 2.11 | shared (peak of the sum) | 35.7 |
| 2.24 | shared (peak of the sum) | 37.3 |
| 2.37 | shared (peak of the sum) | 39.1 |
| 2.51 | shared (peak of the sum) | 41 |
| 2.66 | shared (peak of the sum) | 42.9 |
| 2.82 | shared (peak of the sum) | 45 |
| 2.99 | shared (peak of the sum) | 47.1 |
| 3.16 | shared (peak of the sum) | 49.4 |
| 3.35 | shared (peak of the sum) | 51.8 |
| 3.55 | shared (peak of the sum) | 54.3 |
| 3.76 | shared (peak of the sum) | 57 |
| 3.98 | shared (peak of the sum) | 59.8 |
| 4.22 | shared (peak of the sum) | 62.7 |
| 4.47 | shared (peak of the sum) | 65.8 |
| 4.73 | shared (peak of the sum) | 69.1 |
| 5.01 | shared (peak of the sum) | 72.5 |
| 5.31 | shared (peak of the sum) | 76.1 |
| 5.62 | shared (peak of the sum) | 79.9 |
| 5.96 | shared (peak of the sum) | 84 |
| 6.31 | shared (peak of the sum) | 88.2 |
| 6.68 | shared (peak of the sum) | 92.7 |
| 7.08 | shared (peak of the sum) | 97.4 |
| 7.5 | shared (peak of the sum) | 102 |
| 7.94 | shared (peak of the sum) | 108 |
| 8.41 | shared (peak of the sum) | 113 |
| 8.91 | shared (peak of the sum) | 119 |
| 9.44 | shared (peak of the sum) | 125 |
| 10 | shared (peak of the sum) | 132 |
| 10.6 | shared (peak of the sum) | 138 |
| 11.2 | shared (peak of the sum) | 146 |
| 11.9 | shared (peak of the sum) | 153 |
| 12.6 | shared (peak of the sum) | 161 |
| 13.3 | shared (peak of the sum) | 170 |
| 14.1 | shared (peak of the sum) | 179 |
| 15 | shared (peak of the sum) | 188 |
| 15.8 | shared (peak of the sum) | 198 |
| 16.8 | shared (peak of the sum) | 209 |
| 17.8 | shared (peak of the sum) | 220 |
| 18.8 | shared (peak of the sum) | 232 |
| 20 | shared (peak of the sum) | 244 |
| 21.1 | shared (peak of the sum) | 257 |
| 22.4 | shared (peak of the sum) | 271 |
| 23.7 | shared (peak of the sum) | 286 |
| 25.1 | shared (peak of the sum) | 301 |
| 26.6 | shared (peak of the sum) | 318 |
| 28.2 | shared (peak of the sum) | 335 |
| 29.9 | shared (peak of the sum) | 353 |
| 31.6 | shared (peak of the sum) | 372 |
| 33.5 | shared (peak of the sum) | 393 |
| 35.5 | shared (peak of the sum) | 414 |
| 37.6 | shared (peak of the sum) | 437 |
| 39.8 | shared (peak of the sum) | 461 |
| 42.2 | shared (peak of the sum) | 487 |
| 44.7 | shared (peak of the sum) | 514 |
| 47.3 | shared (peak of the sum) | 542 |
| 50.1 | shared (peak of the sum) | 572 |
| 53.1 | shared (peak of the sum) | 604 |
| 56.2 | shared (peak of the sum) | 637 |
| 59.6 | shared (peak of the sum) | 673 |
| 63.1 | shared (peak of the sum) | 710 |
| 66.8 | shared (peak of the sum) | 750 |
| 70.8 | shared (peak of the sum) | 792 |
| 75 | shared (peak of the sum) | 836 |
| 79.4 | shared (peak of the sum) | 883 |
| 84.1 | shared (peak of the sum) | 933 |
| 89.1 | shared (peak of the sum) | 986 |
| 94.4 | shared (peak of the sum) | 1.04K |
| 100 | shared (peak of the sum) | 1.1K |
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.
- Scheduling & Workload Management
Which work runs now, which work waits, and who pays for the waiting?