How long will they wait - and how sure are you?
Describe a queue: servers, waiting room, arrival and service times. Your browser runs the SimPy skill's replication study exactly - same seeds, same numbers - with intervals, a textbook benchmark and a what-if, free, nothing uploaded. A paid run then interprets the study or writes the SimPy script that reproduces it.
Each example has a saved model run, so you can see the whole page for free.
Your recent runs
What this does, and what it does not
The model is the one the SimPy agent skill bundles: customers arrive with exponential gaps,
wait first-come first-served for one of c identical servers, take an exponential
service time, and are turned away when the servers and the waiting room are full. Arrivals stop
at the horizon; a steady-state study drops the customers who arrived before the warm-up. The
page runs its own port of the skill's basic_simulation_template.py,
resource_monitor.py and replication_runner.py on a small copy of the
SimPy 4.1.2 event loop, with Python's Mersenne Twister and the skill's BLAKE2b seed rule, so a
configuration gives the counts and the event totals the skill gives and the same floating-point
values to about twelve significant digits. It was checked against SimPy 4.1.2 on 560 random
configurations and 40 invalid ones.
An interval is Monte Carlo uncertainty under this model - how precisely the replications pin down its mean - not evidence that the model matches the real queue. The M/M/c/K values are the exact long-run answer for this model, so they are a check on a steady-state study and only a reference for a terminating one. The paid run reads only what the browser computed and your notes; it is told never to compute a new number, and the page checks every number it writes. Derived from the agent skill @k-dense-ai/simpy (k-dense-ai/scientific-agent-skills, K-Dense Inc., MIT; see the notice).