Bus-Bunching Effect

Wait forty minutes for a bus and two arrive together. It feels like a conspiracy of transit authorities; it is actually mathematics. A bus that falls slightly behind picks up more passengers at each stop, which slows it further; the bus behind, finding empty stops, speeds up — until they meet.

The general principle is worth more than the commute: in any loop where delay increases the load and speed decreases it, small gaps self-destruct and equality is unstable. Queues, cash flow, laundry, email — all bunch.

Notice the personal version: you fall behind on messages one week, and the backlog makes each reply heavier, which delays you further — while the empty days stay empty. Bunching is how small lateness becomes a landslide.

The fix used by good transit systems is the fix for you: sacrifice to restore the gap. The lead bus drops passengers and runs empty past stops; you must skip, declare, batch, or delete — anything that breaks the loop. Equality never restores itself. Someone has to drive the empty bus.