The Counterintuitive Math of Waiting

If you arrive at a bus stop at a random time, you will likely wait longer than half the total interval between buses. This phenomenon is known as the inspection paradox, where average wait times defy basic intuition.

This happens because random arrivals are more likely to fall within longer gaps than shorter ones. Even if buses arrive on a perfect schedule, a random observer experiences a bias toward the longer periods. It is a mathematical quirk that explains why lines often seem to move slower than they should. Understanding this helps engineers optimize everything from transit systems to computer server traffic.