Examples

Twenty-eight Gaussian random walks of 64 steps, their sample mean in green, and the band of two standard deviations.

Each worked example contains a model module, two tests, a plot.py script that writes PDF files, and a derivation of its results. Every result stated below is verified by the test suite, and each example page shows the figures its script produces.

Stochastic Travelling Salesman

A van serves four customers on roads that are blocked at random. The exact solution equals the best of all 24 tours, with expected cost 17.6227.

tests/stsp

Gaussian Random Walk

A robot moves by discretised Gaussian steps between two absorbing edges. The hitting probability is 0.5 by symmetry and 0.956 under drift, and Monte Carlo estimates agree.

tests/gaussian

Heavy-Tailed Durations

A warehouse robot whose jams follow a truncated power law. The value equals the closed form, the martingale mean is constant, and an incorrect simulator is detected.

tests/heavy_tail

Running the Examples

From the root of a clone of the repository:

pip install -e '.[dev]'
pytest                               # all tests
python tests/stsp/plot.py            # writes route.pdf and overview.pdf into tests/stsp