THE NUMBERS, EXPLAINED
How to use this calculator.
Utilisation alone does not determine waiting time. Arrival and service processes require a more specific queueing model.
Start with your inputs
Enter arrival rate per second, service rate per server per second, servers. Keep amounts in the units shown on each field. The example is a starting point, not a recommended value.
| Input | Example value |
|---|---|
| Arrival rate per second | 5 |
| Service rate per server per second | 10 |
| Servers | 1 |
A worked example
With the example inputs above, utilisation (%) is 50. Change the inputs to explore your own scenario.
| Result | Example answer |
|---|---|
| Utilisation (%) | 50 |
| Steady-state capacity status | Below nominal capacity |
How this is calculated
Utilisation (%)
a/(b × c) × 100
Steady-state capacity status
Compare arrivals a with nominal capacity b × c. Report below nominal capacity only when a is strictly smaller. This classification does not estimate waiting times.
Symbols and units
- a
- Arrival rate per second
- b
- Service rate per server per second
- c
- Servers
Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.
Assumptions and limits
Utilisation alone does not determine waiting time. Arrival and service processes require a more specific queueing model.
Calculations use the values you enter. Blank or invalid inputs show an error instead of silently substituting zero. Results are displayed to useful precision; calculations retain the underlying numeric precision.
Questions about this tool
What does the result tell me?
Utilisation (%); Steady-state capacity status. The result applies to the method and inputs described above. Check the units and assumptions before using it in a decision.
Why might another calculator differ?
Differences in units, rounding, timing or model definitions can produce different answers. Compare the input definitions and the method, rather than only the final number. For this tool: Utilisation alone does not determine waiting time. Arrival and service processes require a more specific queueing model.
Are my inputs stored or sent to AI?
Calculations on this page happen in your browser. The separate AI question finder sends its submitted conversation to OpenAI; these calculator fields are not sent. Favourites and recent tool names are stored locally. A shared link contains the inputs you choose to include.
Review status
Software example and browser checks are recorded in our quality report. No external expert review is claimed. Created with coding assistance; calculations run as ordinary browser code.
Read the quality report →