The Utilization Trap

This simulation is a demonstration of <1>Kingman's Formula</1>, a key equation in queuing theory. The formula states that wait times will explode as a system's utilization approaches 100%, especially in the presence of variability.

This game's primary source of variability is in customer arrivals. Customers don't arrive in a steady, predictable stream; the simulation has both a constant 'drizzle' of orders and random 'mini-rushes', mimicking real-world demand.

When utilization is high (e.g., 3 cooks), there is no spare capacity ('slack') to absorb this variability. A small rush of customers can cause the queue to grow faster than it can be served, leading to system collapse. Adding more cooks provides the slack needed to handle these fluctuations and maintain a stable system.