Queue Simulator
How to play
Gameplay
A queue simulator for the M/M/c model: arrivals follow a Poisson process, service times are exponentially distributed, and there are c servers. That model has no simple intuitive answer, which is why simulation earns its keep here — queue length, per-server utilisation and average wait are plotted over time, making it obvious that queues lengthen non-linearly once capacity approaches saturation.
Controls
Set the arrival rate, service rate, server count and total run length, then start. Charts update live with queue length and utilisation, while the side panel reports average wait and maximum queue. Simulation can be sped up or paused, and parameters can be changed to run another comparison.
FAQ
What does the red utilization percentage mean?
Utilization is λ ÷ (servers × μ). Once it exceeds 100% the value turns red: on average customers arrive faster than all servers combined can finish them, so the waiting line keeps growing.
Can I change the parameters while the simulation runs?
Yes - the λ, μ and server-count sliders stay live during a run, and changing servers adjusts the service desks immediately. Start/Pause freezes the tick and Reset clears all stats and the chart.
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