Setup
Define the queueing system
Back to layer 01, SetupQueueing theory · formulas vs. simulation
How long will people really wait?
Set the arrival rate, the service rate, and the number of servers. The analytic formulas answer instantly; a discrete-event simulation tests whether that answer can be trusted.
Results
Formulas side by side with the simulation
Back to layer 02, ResultsNo results yet
Set the parameters on layer 01, then run the simulation. The comparison table will appear here.
Go to Setup| Metric | Analytic | Simulation mean ± 95% CI | Difference | Formula vs. the simulation's CI |
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| Quantity | Analytic | Simulation mean ± 95% CI | Difference |
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How to read this table
Analytic is the exact value from the formulas, valid once the system has been running for a very long time. Simulation is an estimate from a number of replications; the ± sign gives the 95% confidence interval, the plausible range for the true value.
If the formula value falls inside the interval, the two agree. If it falls outside, the most common causes are:
- ρ ≥ 1: there is no steady state, so the formulas simply do not apply.
- ρ close to 1: the system needs a very long time to reach steady state. Lengthen the run and the warm-up.
- Warm-up too short: the empty start gets counted and drags the averages down.
- Chance: a 95% interval misses about 1 time in 20. Try another seed.
Live
Watch the queue run
Back to layer 03, LiveNothing to watch yet
Run a simulation on layer 01 first. The queue animation and its charts will appear here.
Go to SetupOne replication, event by event.
- customer
- priority customer
- turned away because the system is full
- a closed ring means service is complete
Queue length over time
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Waiting-time distribution
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View the data as a table
| Waiting time (minutes) | Simulation | FIFO formula |
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