The Waiting-Time Paradox

TL;DR

The paper explains the waiting-time paradox, a counterintuitive phenomenon where the expected waiting time for a bus is longer than the schedule suggests, due to the mathematical properties of variable bus intervals.

Contribution

It provides a detailed explanation of the waiting-time paradox, its mathematical origin, and explores its implications beyond everyday scenarios.

Findings

Waiting-time is longer than expected due to bus interval variability.

Mathematical analysis reveals the paradox's origin.

Implications extend to various fields beyond transportation.

Abstract

Suppose that you're going to school and arrive at a bus stop. How long do you have to wait before the next bus arrives? Surprisingly, it is longer - possibly much longer - than what the bus schedule suggests intuitively. This phenomenon, which is called the waiting-time paradox, has a purely mathematical origin. Different buses arrive with different intervals, leading to this paradox. In this article, we explore the waiting-time paradox, explain why it happens, and discuss some of its implications (beyond the possibility of being late for school).