THE NUMBERS, EXPLAINED
How to use this calculator.
A deterministic interval model with constant processing time and all arrivals available at each interval start. It does not model random queues, breaks or lane downtime.
Start with your inputs
Enter arrivals by interval, interval length (minutes), measured processing time per guest (seconds), open lanes. Keep amounts in the units shown on each field. The example is a starting point, not a recommended value.
| Input | Example value |
|---|---|
| Arrivals by interval | 100,80,40 |
| Interval length (minutes) | 30 |
| Measured processing time per guest (seconds) | 45 |
| Open lanes | 3 |
A worked example
With the example inputs above, capacity per interval is 120. Change the inputs to explore your own scenario.
| Result | Example answer |
|---|---|
| Capacity per interval | 120 |
| Maximum projected backlog | 0 |
| Final projected backlog | 0 |
| Backlog by interval | 0, 0, 0 |
How this is calculated
Capacity per interval
Lanes × interval seconds ÷ measured seconds per guest.
Maximum projected backlog
Largest backlog reached while applying interval arrivals and capacity in order.
Final projected backlog
Backlog remaining after the final interval.
Backlog by interval
For each interval: max(0, previous backlog + arrivals − interval capacity).
Symbols and units
- a
- Arrivals by interval
- b
- Interval length (minutes)
- c
- Measured processing time per guest (seconds)
- d
- Open lanes
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
A deterministic interval model with constant processing time and all arrivals available at each interval start. It does not model random queues, breaks or lane downtime.
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?
Capacity per interval; Maximum projected backlog; Final projected backlog; Backlog by interval. 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: A deterministic interval model with constant processing time and all arrivals available at each interval start. It does not model random queues, breaks or lane downtime.
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.
Further reading
Background reading; this does not imply endorsement or independent review of SumFizz.
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.
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