M/M/1 Queue Calculator

Poisson arrivals (λ), exponential service (μ), 1 server. Client-side only.

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Inputs

Tip: if you know average service time S (seconds/request), then μ = 1/S.

Model assumes a single server and no finite queue limits. For multi-server, use M/M/c (not here).

Outputs

Utilization ρ = λ/μ
Stability requires ρ < 1
P0 (system empty)
L (mean in system)
Lq (mean in queue)
W (mean time in system)
Wq (mean wait time)
Formulas
  • ρ = λ/μ
  • P0 = 1 − ρ
  • L = ρ/(1−ρ)
  • Lq = ρ²/(1−ρ)
  • W = 1/(μ−λ)
  • Wq = ρ/(μ−λ)
Notes for SREs
As ρ approaches 1, wait times blow up non-linearly. If you want p95/p99 you need a distributional model (this only gives means).