For Educators · M/M/1 Queue
M/M/1 Queue for a cutting-stock plan
Built for educators teaching it to a class. Drop a live demo into a lecture or assign it as a shareable link — no lab installs. Simulate a cutting-stock plan live below — adjust the inputs and watch it respond, right in your browser.
M/M/1 QueueLive
queueing theory
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The M/M/1 queue models a single server with random arrivals and service — a checkout, help desk, or router. The utilization ρ = λ/μ decides everything: as it approaches 1, the average wait and queue length explode toward infinity. This nonlinear blow-up is why systems run at, say, 80% and not 99% capacity.
Data Inspector
Utilization ρ0.70
Avg in system L2.33
Avg in queue Lq1.63
Avg wait W3.33
Live count0
Governing equation
Reading this result: Moderate load: ρ=0.70. On average L≈2.3 in the system waiting W≈3.3. You are on the steep part of the curve — pushing ρ toward 1 makes waits climb far faster than the extra traffic would suggest.
Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.
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Frequently asked questions
- Is this good for educators?
- Yes — this version of "M/M/1 Queue for a cutting-stock plan" is framed for educators teaching it to a class. Drop a live demo into a lecture or assign it as a shareable link — no lab installs.
- Do I need to install anything?
- No. It runs in any modern browser, free, with no account required.