Math

Queueing Theory Calculator (M/M/1)

M/M/1 mean wait and utilization from arrival rate λ and service rate μ.

Free to use — no sign-up or login.

Utilization ρ

Mean wait in queue

This free Queueing Theory Calculator (M/M/1) covers M/M/1 mean wait and utilization from arrival rate λ and service rate μ.

Utilization ρ = λ/μ; mean queue wait λ/(μ(μ−λ)) for ρ < 1. Related math tools sit beside How it works, with no account required.

Using the Queueing Theory Calculator (M/M/1)

M/M/1 mean wait and utilization from arrival rate λ and service rate μ. Typical inputs are Arrival rate λ and Service rate μ. How it works beside the form states the identity the Queueing Theory Calculator (M/M/1) applies.

FAQ

How do I use the Queueing Theory Calculator (M/M/1)?

Open the Queueing Theory Calculator (M/M/1), fill Arrival rate λ and Service rate μ, and read the result. Utilization ρ = λ/μ; mean queue wait λ/(μ(μ−λ)) for ρ < 1.

What formula does the Queueing Theory Calculator (M/M/1) use?

The Queueing Theory Calculator (M/M/1) uses the identity in How it works. In words: Utilization ρ = λ/μ; mean queue wait λ/(μ(μ−λ)) for ρ < 1.