Grades K–2 · Societies
Why does a queue grow or shrink?
A waiting line can grow while a helper is busy. Helping takes time, so people who arrive before their turn must wait in a line called a queue.
At our pretend desk, two people are waiting when four more arrive. Six people now need help. The desk can help three during this round. Those three leave the queue, and three are still waiting for the next round.
The four arrivals join the two already waiting before Desk 1 serves up to three. The people left over carry the waiting line into the next round.
In the diagramArrive first • serve next4 arrivals2 already waitingDesk 1: up to 33 served • 3 wait next round
The line grows when people arrive faster than the desk can help them, and shrinks when more are helped than arrive. A second desk lets two helpers work at once. This picture uses rounds to show that changing balance clearly.
About this explanation
Starting knowledge: Count people and subtract a small group that is served.
Sources
- Massachusetts Institute of Technology — Queueing models: arrivals, servers and service