Queueing Theory API
Queueing-theory maths as an API, computed locally and deterministically. The littles-law endpoint applies Little's law, L = λ·W — the average number in a system equals the arrival rate times the average time in the system — and solves for whichever of the three you leave out; it holds for any stable system, from a checkout line to a request pipeline. The mm1 endpoint gives the full steady-state metrics of a single-server M/M/1 queue from the arrival rate λ and the service rate μ: the utilization ρ = λ/μ, the average number in the system and in the queue, the average time in the system and waiting, and the probability the system is empty — and it flags an unstable queue when ρ ≥ 1. The mmc endpoint extends this to a multi-server M/M/c queue with the Erlang-C waiting probability, returning the offered load in erlangs, the per-server utilization, the chance an arrival has to wait, and the same length and time metrics. Rates must share a time unit, and the times come out in that unit. Everything is computed locally and deterministically, so it is instant and private. Ideal for capacity-planning and operations tools, call-centre and staffing apps, server and throughput sizing, and operations-research education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is queueing theory; for descriptive statistics on a list of numbers use a statistics API.
api.oanor.com/queue-api
