Wait in Line — Queueing Theory Simulator

Visualization

Queue

Gates

Over time

Avg wait · ETA —

— 0 s

time — last 60 s →

Time a typical customer waits in line. It climbs steeply as utilization rises — and never settles if the system is unstable.

Utilization · Load —

100%50%0%

time — last 60 s →

Share of server capacity in use. Waits blow up as this nears 100% — the queueing “hockey stick.”

measured (6-second average) theory (long-run average)

Controls

Arrival rate (λ) 1.0 / sec

Service time (S) 0.25 sec

Number of servers (m)

Try:

Metrics

—

Model: M/M/1

Metric	Measured	Theoretical
Queue length (L_q)	—	—
Service rate (μ)	—	—
Utilization (ρ)	—	—
Concurrency (L)	—	—

Measured values update every 5s and converge toward theory. They restart whenever you Start, Pause/Resume, or change a control. Changing a control adjusts the running system without clearing the queue — so you can watch an unstable system recover.

Arrival rate (λ) 4.0 / sec

Service time (S) 0.25 sec

Servers 2 (fixed)

—

Try:

Same arrival stream and job sizes feed both configurations — only the queue structure differs.

One combined queue M/M/2 ρ —

Queue

Gates

Avg wait (W_q) · ETA —

Queue length (L_q) —

Separate queues 2 × M/M/1 ρ —

Line 1

Line 2

Random line assignment: one line backs up while the other server sits idle — wasted capacity, so the wait runs longer.

Avg wait (W_q) · ETA —

Queue length (L_q) —

Avg wait · ETA — · —

— 0 s

time — last 60 s →

The same customers wait longer in separate lines than in one combined queue — at the same utilization.

Utilization · Load — · —

100%50%0%

time — last 60 s →

Both setups run at the same utilization — the whole difference is in the wait.

combined separate