| Interval | Length | Arrivals | Running Total | Rate in Interval |
|---|---|---|---|---|
| 1 | 10 minutes | 6 | 6 | 0.60 per minute |
| 2 | 10 minutes | 8 | 14 | 0.80 per minute |
| 3 | 10 minutes | 7 | 21 | 0.70 per minute |
| 4 | 10 minutes | 9 | 30 | 0.90 per minute |
| 5 | 10 minutes | 10 | 40 | 1.00 per minute |
In this example, total arrivals are 40 over 50 minutes. The mean arrival rate is 40 ÷ 50 = 0.80 arrivals per minute.
Mean arrival rate is widely used in queueing models, event flow analysis, call forecasting, reliability studies, network traffic review, and workload planning. When arrivals follow a Poisson-style assumption, λ represents the expected number of arrivals per time unit.
- Select whether you want to use total observations or interval data.
- Enter total arrivals and total time for summary mode.
- Or enter a sequence of arrival counts and interval length for dataset mode.
- Choose the time unit that matches your observation window.
- Set a peak multiplier if you want a planning buffer.
- Pick the decimal precision for reported values.
- Press the calculate button to show results above the form.
- Use the CSV or PDF buttons to export your calculation summary.
1. What is mean arrival rate?
Mean arrival rate is the average number of events entering a system during one unit of time. It is often written as λ and used in queueing and probability models.
2. How is mean arrival rate calculated?
Divide the total number of arrivals by the total observation time. If 120 customers arrive in 4 hours, the mean arrival rate is 30 customers per hour.
3. What does interarrival time mean?
Interarrival time is the average gap between consecutive arrivals. It is the inverse-style timing view of the arrival rate and helps estimate waiting behavior.
4. When should I use interval data?
Use interval data when arrivals are recorded in equal blocks, such as every minute or every hour. This helps inspect consistency, variance, and clustering patterns.
5. Why include a peak multiplier?
A peak multiplier builds a planning margin above the observed average. It is useful for staffing, server sizing, call handling, and other capacity decisions.
6. Can this calculator help with Poisson models?
Yes. In many Poisson-based analyses, λ is the expected event count per time unit. This calculator provides the core estimate needed for those models.
7. What is the dispersion index?
Dispersion index is variance divided by mean for interval counts. Values near one can indicate Poisson-like spread, while larger values may show overdispersion.
8. Which fields should I ignore in summary mode?
Ignore interval arrivals, interval length, and interval unit when using total arrivals and total time. Those fields matter only for the interval dataset method.