Calculator Inputs
Example Data Table
| Scenario | λ | μ | c | Offered Load (a) | Traffic Intensity (ρ) | Status |
|---|---|---|---|---|---|---|
| Support Desk | 12.00 | 5.00 | 3 | 2.4000 | 0.8000 | Stable |
| Checkout Area | 18.00 | 6.00 | 4 | 3.0000 | 0.7500 | Stable |
| Batch Processor | 32.00 | 8.00 | 5 | 4.0000 | 0.8000 | Stable |
These rows show how larger capacity lowers utilization and reduces instability risk.
Formula Used
This calculator treats arrivals as Poisson, service times as exponential, and servers as identical. Those assumptions match the classic M/M/c queue.
When you enter average service time instead of service rate, the calculator converts it using μ = 1 / service time.
Queue length, waiting time, and time in system are displayed only for stable systems, because unstable queues grow without a finite long-run average.
How to Use This Calculator
- Enter the average arrival rate for your queue.
- Enter the number of active servers.
- Choose whether you know service rate or service time.
- Fill the matching service input field.
- Set a target utilization percentage for capacity planning.
- Optionally label the time period, such as hour or minute.
- Press the calculate button.
- Review traffic intensity, utilization, waiting risk, and recommended servers.
- Use the export buttons to save the result table as CSV or PDF.
Frequently Asked Questions
1) What does traffic intensity mean?
Traffic intensity shows how heavily a service system is loaded. It compares incoming work with total service capacity. Higher values mean greater congestion risk.
2) What happens when ρ is above 1?
A value above 1 means arrivals exceed total capacity. In long-run terms, the queue becomes unstable, waiting grows, and average queue metrics stop having finite steady-state values.
3) Why is offered load different from traffic intensity?
Offered load uses λ/μ and measures total demand in erlangs. Traffic intensity divides that load across all servers by using λ/(cμ).
4) When should I enter service time instead of service rate?
Use service time when you know how long one job takes. Use service rate when you know how many jobs one server completes per period.
5) What is a good utilization target?
It depends on your tolerance for delay. Many systems aim below 80% to 90%, because wait times often rise sharply as utilization approaches full capacity.
6) Does this calculator work for single and multi-server queues?
Yes. Set c = 1 for a single-server queue. Set c above 1 for multi-server systems, and the calculator applies the M/M/c formulas.
7) Why are some waiting outputs shown as N/A?
Queue metrics like steady-state waiting time are only reliable when the queue is stable. If ρ is 1 or more, the calculator marks them unavailable.
8) Can I use this for staffing and capacity planning?
Yes. The calculator estimates spare capacity, minimum stable servers, and recommended servers for your target utilization, making it useful for sizing service systems.