Examples
Examples
Try the starting example
- Arrival rates by equal window (jobs/second)
- 1,5,0
- Window duration (seconds)
- 10
- Service seconds per job per worker
- 1
- Initial workers
- 1
- Minimum workers
- 1
- Maximum workers
- 3
- Scaling delay in whole windows
- 1
- Workers active in each window
- 1, 1, 3
- End-of-window fluid backlog
- 0, 40, 10
- Completed fluid job-equivalents
- 50
- Peak end-of-window backlog
- 40
- Pending final worker target
- None
Try another scenario
- Arrival rates by equal window (jobs/second)
- 1,5,0
- Window duration (seconds)
- 10
- Service seconds per job per worker
- 1
- Initial workers
- 1
- Minimum workers
- 1
- Maximum workers
- 3
- Scaling delay in whole windows
- 0
- Workers active in each window
- 1, 3, 2
- End-of-window fluid backlog
- 0, 20, 0
- Completed fluid job-equivalents
- 60
- Peak end-of-window backlog
- 20
- Pending final worker target
- None
Calculation method
Calculation method
Workers active in each window
Apply due scaling at window start. If no request is pending, request ceil((queue/window + arrival rate) × service seconds), clamped to min/max; delay zero applies immediately.
End-of-window fluid backlog
max(0, previous queue + arrivals×window − active workers×window/service seconds).
Completed fluid job-equivalents
Sum min(available workload, service capacity); fractional job-equivalents are retained.
Peak end-of-window backlog
Maximum backlog sampled at window ends, including initial zero.
Pending final worker target
Target awaiting a future window, or None. Existing pending targets are not overwritten.
Symbols and units
- a
- Arrival rates by equal window (jobs/second)
- b
- Window duration (seconds)
- c
- Service seconds per job per worker
- d
- Initial workers
- e
- Minimum workers
- f
- Maximum workers
- g
- Scaling delay in whole windows
Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.
Assumptions & limits
Assumptions & limits
- A deterministic fluid queue by equal time windows, with integer workers and one pending scaling request. It does not model individual job completion, startup jitter, cold caches or real autoscaler behaviour.
Are these inputs private?
These calculations run in your browser. A shared link contains the values you choose to share. Only questions submitted to the separate AI finder are sent to OpenAI.
Further reading
OpenStax: arithmetic and geometry ↗
Background reading; this does not imply endorsement or independent review of SumFizz.