Examples
Examples
Try the starting example
- Independent source updates per hour
- 1
- Fixed refresh interval / TTL (seconds)
- 3600
- Independent requests per second
- 2
- Expected stale-time share (%)
- 36.787944
- Expected fresh-time share (%)
- 63.212056
- Expected stale requests per refresh interval
- 2,648.731976
- Mean cache age across interval (seconds)
- 1800
Try another scenario
- Independent source updates per hour
- 0
- Fixed refresh interval / TTL (seconds)
- 3600
- Independent requests per second
- 2
- Expected stale-time share (%)
- 0
- Expected fresh-time share (%)
- 100
- Expected stale requests per refresh interval
- 0
- Mean cache age across interval (seconds)
- 1800
Calculation method
Calculation method
Expected stale-time share (%)
For Poisson updates with rate λ per second and fixed refresh T, stale share = 1 − (1 − exp(−λT))/(λT). At λT=0 use zero; use a series near zero.
Expected fresh-time share (%)
100% − stale-time share.
Expected stale requests per refresh interval
Request rate × refresh interval × stale-time share, assuming requests are independent and uniformly exposed to cache age.
Mean cache age across interval (seconds)
A proactive fixed refresh gives uniformly distributed age from 0 to T, whose mean is T/2.
Symbols and units
- a
- Independent source updates per hour
- b
- Fixed refresh interval / TTL (seconds)
- c
- Independent requests per second
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
- Simplified proactive refresh at fixed TTL, instantaneous successful refresh, independent Poisson source updates and independent requests. This is not lazy expiry-on-request, cache hit ratio, a freshness guarantee or a model of correlated traffic.
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.