Calculator Inputs
Example Data Table
These rows are illustrative examples that show how different settings can affect queue behavior and output measures.
| Scenario | Arrival Dist. | Mean Interarrival | Service Dist. | Mean Service | Servers | Queue Cap. | Horizon | Avg Wait | Utilization | Dropped |
|---|---|---|---|---|---|---|---|---|---|---|
| Balanced Flow | Exponential | 5 | Exponential | 4 | 2 | 8 | 240 | 0.83 | 79.10% | 0 |
| Heavy Traffic | Exponential | 3 | Exponential | 5 | 2 | 6 | 240 | 6.94 | 97.30% | 12 |
| Stable Service | Deterministic | 4 | Deterministic | 4 | 2 | 10 | 240 | 0.18 | 50.00% | 0 |
| Wide Variability | Uniform | 4 | Uniform | 5 | 3 | 12 | 300 | 1.27 | 68.40% | 1 |
Formula Used
λ = 1 / mean interarrival time
μ = 1 / mean service time
ρ = λ / (c × μ), where c is the number of servers
Lq = ∫Q(t)dt / T
L = ∫N(t)dt / T
Wq = total waiting time / served entities
W = total system time / served entities
Utilization = busy server time / (servers × observed time)
Throughput = served entities / observed time
Loss rate = dropped arrivals / total arrivals
This calculator uses event-driven simulation instead of a closed-form shortcut. It tracks each arrival, service start, departure, queue change, and blocked entity through time.
How To Use This Calculator
- Enter the total simulation horizon in your preferred time unit.
- Set a warm-up period if you want to remove early startup distortion.
- Choose the number of servers and waiting capacity.
- Select the arrival and service distributions.
- Enter the mean interarrival and mean service times.
- Use spread percentages when uniform distributions are selected.
- Set an SLA wait threshold to measure service performance.
- Optionally enter a random seed for repeatable results.
- Click Run Simulation to display the result above the form.
- Use the CSV or PDF buttons to export the summary and event sample.
FAQs
1. What does this simulator measure?
It estimates queue length, wait time, throughput, utilization, blocking, service level, and other system measures by processing events in time order.
2. Why use a warm-up period?
Warm-up removes unstable startup behavior. That helps averages reflect steady performance instead of the artificial conditions at time zero.
3. What is the difference between exponential and deterministic inputs?
Exponential timing creates randomness and variable spacing. Deterministic timing uses fixed intervals, which reduces variation and often lowers queue volatility.
4. What does queue capacity control?
It limits how many entities may wait. If all servers are busy and the queue is full, new arrivals are dropped.
5. Why can utilization exceed comfortable levels before reaching 100%?
As utilization gets high, small bursts create longer waits. Systems can become unstable in practice well before full theoretical saturation.
6. What is service level in this calculator?
Service level is the share of served entities whose waiting time stays at or below your chosen SLA threshold.
7. Can I reproduce the same simulation again?
Yes. Enter the same random seed and keep every parameter unchanged. The generated random stream will match the earlier run.
8. Is this calculator exact or estimated?
It is a simulation estimate. Accuracy improves with sensible assumptions, enough runtime, and repeated scenario testing.