Queueing Theory 2D — M/M/c Queue Simulation

Queue length over time — blue = live, yellow dashed = theoretical L

Controls

Arrival rate λ 0.80 /s Service rate μ (per server) 1.00 /s Servers c 1

Live HUD

Utilisation ρ—

Theoretical L—

Theoretical W—

Empirical avg L—

Empirical avg W—

Current queue size—

Servers busy—

Served / lost—

Arrivals follow a Poisson process (exponential inter-arrival times, rate λ). Each of the c servers has an independent exponential service time at rate μ. Stable only when ρ = λ/(cμ) < 1 — Erlang-C theory (yellow) is compared live against the running simulation (blue).

Poisson arrivalsExponential serviceErlang-C