Queueing Theory Calculator (M/M/1, M/M/c)
Computes the standard steady-state metrics for M/M/1 and multi-server M/M/c queues: utilization, average queue length, waiting time, probability of an empty system and the Erlang C probability of having to wait. Built on Little’s law L = λW, the deceptively simple identity that holds for any stable queue.
Read the full guide to this tool
Results
Notes
- Stability requires ρ = λ/(cμ) < 1 — otherwise the queue grows without bound.
- Waiting time explodes as ρ → 1: at 90% utilization the M/M/1 queue is 9 customers long on average.
- Little’s law L = λW needs no assumptions about distributions — it is bookkeeping, not statistics.
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