01 / THE QUESTION

Why does the queue keep growing?

A simplified model · start with an empty queue

The worker is busy. The line still gets longer.

02 / THE MISMATCH

One request stays behind.

Add arrivals first, then process requests each tick

Each second: 3 arrive, 2 finish, 1 waits.

03 / TEN SECONDS LATER

Small gaps become a backlog.

30 + (−20) = 10 requests in the queue

30 arrived. 20 finished. 10 are still waiting.

04 / CHANGE ONE THING

Give the worker spare capacity.

The 10-request backlog clears after 10 more ticks

Keep arrivals at 3/sec. Raise capacity to 4/sec.

05 / KEEP THIS DISTINCTION

Match to hold. Exceed to clear.

In this fixed-rate model · real arrivals can vary

Matching arrivals stops growth. Spare capacity clears the line.