Universal Scalability Law Calculator (Gunther, Amdahl and Beyond)
Relative capacity and throughput of a system with N processors or nodes, from its contention and coherency coefficients, with the number of nodes at which adding more starts to hurt.
Results
The dashed line marks the value you entered.
What this tool does
Amdahl's law says contention for a shared resource caps the speed-up at 1 ÷ α. Neil Gunther's Universal Scalability Law adds a second term, β N (N − 1), for the cost of keeping the nodes consistent with each other, which grows with the square of N and makes capacity peak and then fall: the peak is at √((1 − α) ÷ β) nodes. With α = 0.05 and β = 0.0005 the system tops out at about 10.7× with around 44 nodes, and adds nothing but cost beyond that. α and β are not guessed: they are fitted to measured throughput at several loads, and then the curve predicts the rest.
Formula
C(N) = N ÷ (1 + α(N − 1) + β N (N − 1)) · X(N) = γ C(N) · peak at N* = √((1 − α) ÷ β) (Gunther's Universal Scalability Law)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
n | Number of processors, nodes or threads | — |
al | Contention α (share that is serialised) | — |
be | Coherency delay β (cost of keeping copies in agreement) | — |
ga | Throughput with one node | req/s |
C | Relative capacity C(N) | — |
X | Throughput at N | — |
EF | Efficiency per node | % |
PN | Number of nodes at the peak | — |
PC | Capacity at the peak | — |
AM | Ceiling if there were no coherency delay (Amdahl) | — |
Worked example
- Number of processors, nodes or threads32
- Contention α (share that is serialised)0.05
- Coherency delay β (cost of keeping copies in agreement)0.0005
- Throughput with one node1000 req/s
- Relative capacity C(N)10.51
- Throughput at N10,506
- Efficiency per node32.8 %
- Number of nodes at the peak43.6
- Capacity at the peak10.74
- Ceiling if there were no coherency delay (Amdahl)20.0
Limitations
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.