The Sleeping Barber Problem, introduced by Edsger Dijkstra in 1965, captures a coordination challenge that appears throughout computing: how do servers efficiently handle variable client arrivals while avoiding both busy-waiting and missed requests?

Picture a barbershop with one barber, one barber chair, and a waiting room with N chairs. When no customers are present, the barber sleeps. When a customer arrives, they either wake the barber or sit in a waiting chair. If all chairs are full, the customer leaves.

This simple scenario reveals subtle synchronization challenges that mirror connection pooling, thread pools, and bounded queues throughout software systems.

Problem Statement