Enter Queue Inputs
Example Data Table
| Scenario | λ | μ | Ca | Cs | ρ | Wq | W |
|---|---|---|---|---|---|---|---|
| Morning approvals | 6 | 10 | 0.8 | 0.7 | 0.6 | 0.0848 | 0.1848 |
| Support queue | 8 | 11 | 1.3 | 1.1 | 0.7273 | 0.3515 | 0.4424 |
| Peak dispatch | 9 | 12 | 1.5 | 1.2 | 0.75 | 0.4613 | 0.5446 |
These sample rows show how higher variability and utilization can stretch queue wait and total system time.
Formula Used
This calculator uses the Kingman approximation for a stable G/G/1 queue. It estimates average delay for one server with general arrival and service distributions.
The queue is stable only when λ is less than μ. If utilization reaches 1 or more, waiting time can grow without bound.
How to Use This Calculator
- Enter the average arrival rate for tasks, callers, or jobs.
- Enter the average service rate for the same time unit.
- Provide the arrival and service coefficients of variation.
- Optionally enter a target queue wait and delay cost.
- Choose the time unit that matches your rates.
- Click the calculate button to view delay and utilization metrics.
- Use the chart to see how delay changes as load rises.
- Download CSV or PDF copies for reporting and planning.
Frequently Asked Questions
1. What does G/G/1 mean?
It means one server, general arrival timing, and general service timing. The model handles variable real-world patterns better than memoryless assumptions, making it useful for support desks, review queues, and approval workflows.
2. Why are coefficients of variation important?
They show how unpredictable arrivals and service times are. Greater variability usually increases waiting, even when average rates stay unchanged. That makes variability a major driver of congestion and schedule risk.
3. Is this an exact G/G/1 solution?
No. This calculator uses Kingman’s approximation for average waiting time. It is widely used because exact closed forms are rare for general distributions, yet the estimate is practical and informative.
4. What happens when utilization reaches 100%?
Once arrival rate reaches or exceeds service rate, the queue becomes unstable. Backlog can grow indefinitely, so the calculator flags that condition instead of reporting normal steady-state delay metrics.
5. When should I use Ca and Cs equal to 1?
Use 1 when arrivals or service times roughly follow exponential-style randomness. It is a common baseline. Values below 1 mean smoother flows, while values above 1 reflect burstier, less predictable behavior.
6. Can this help with time management decisions?
Yes. It helps estimate waiting, backlog, and pressure in single-channel workflows. That supports staffing, scheduling, batching, SLA checks, and better timing for approvals, calls, and task handling.
7. What does the queue delay cost represent?
It estimates the cost of time lost in the queue per selected time unit. The calculation multiplies average queued work by the waiting cost you provide, giving a simple planning indicator.
8. Why does the graph curve rise sharply near capacity?
As utilization approaches 1, the server has less spare time to absorb randomness. Even small bursts then create larger waiting effects, so mean queue delay rises quickly near saturation.