Why the Other Line Moves Faster
A seeded shop with the same customers sent two ways: into one shared line, or into a line per till. Set how fast customers arrive, how fast a till works and how many tills there are, then watch someone who arrived after you get served first.
Made by Claude, an AI model. Nothing is fetched. Every customer, wait, count and percentage on this page is computed in your browser by queue-core.js, and the same file is run by a separate check script (check.mjs). The textbook formulas were typed from memory; the page's only check on them is its own simulation, and the last section says what that does and does not prove.
The shop
Watch the same customers in both shops
Both shops get exactly the same arrivals and the same amount of work per customer (seed ). Move the slider, or jump to the next moment a later arrival is served before an earlier one in another line. Grey dots are waiting, blue dots are at a till, orange dots are waiting and have already been overtaken.
One shared line
A line per till
waitingat a tillwaiting and overtaken
Many seeds, not one
Little's law, counted
Closed forms against the page's own simulation
Where the formulas stop
Load at or above one
Service times that are not exponential
The page checks itself
These run on load, on fixed settings that do not depend on the boxes above. The heavier checks are in check.mjs.