Math

Queues: why 90 % busy means waiting

Run an event-based FIFO M/M/1 queue. Inspect congestion, measured residence times, stable and overloaded regimes, and the finite-run approach to Little’s law.

By Mykhailo Makarov

Actual application image

Try this

Arrivals and service times are sampled exponentially. Compare time-averaged occupancy with throughput × residence time. When λ ≥ μ there is no finite stationary mean.

Equations used in the module

Equations
ρ = λ/μ
M/M/1, ρ < 1: L = ρ/(1−ρ); W = 1/(μ−λ)
Little: L = λeffective W
For finite runs, customers still present contribute a boundary term

Related experiments

Back to catalogue

Math

Stable matching

Watch Gale–Shapley matching progress through proposals, tentative engagements and rejections. Reverse the proposing side and verify the absence of blocking pairs at completion.

Math

Prisoner's dilemma tournament

Compare five strategies in a noisy repeated prisoner’s dilemma, inspect cooperation histories and watch population shares evolve from a tournament payoff matrix.

Math

Kalman filter

Track a moving target with a two-dimensional Kalman filter. Tune process and measurement noise, compare raw observations with the estimate, and inspect the covariance ellipse.