🎫 M/M/c Queue

Arrival rate λ 0.8 /s Service rate μ (per server) 1.0 /s Servers c 1 Simulation speed 2× Discipline

FIFO

LIFO

Presets

Stable

Near-saturation

Multi-server bank

Understaffed

Utilisation ρ—

L (in system)—

Lq (in queue)—

W (time in system)—

Wq (time waiting)—

P(wait > 0)—

Servers busy—

Longest wait—

Served / lost—

Customers arrive randomly (Poisson, rate λ) and are served by c servers, each at exponential rate μ. The system is stable only when ρ = λ/(cμ) < 1. As ρ → 1 the waiting line explodes. Yellow = Erlang-C theory, blue = live measurement.