Queue capacity

Make your prediction before each command, and only then compare. That’s where the learning happens.

Fictional scenario: 100 messages per second, 200 ms of service time, 6,000 messages in the backlog. Open the calculator in the browser or use the terminal.

1. 20 consumers: does the backlog drain? Each consumer processes 5 per second.

   npx -y moretes-builder-workshops queue --arrivals 100 --service-ms 200 --consumers 20 --backlog 6000 --lang en

2. 30 consumers: how long does it take?

   npx -y moretes-builder-workshops queue --arrivals 100 --service-ms 200 --consumers 30 --backlog 6000 --lang en

3. What if the provider accepts only 80 per second?

   npx -y moretes-builder-workshops queue --arrivals 100 --service-ms 200 --consumers 30 --backlog 6000 --dependency-limit 80 --lang en

The answer key

Try to answer before you open it.

See results

Scenario	Capacity	Utilization	Surplus	Drain
20 consumers	100/s	100%	0/s	never
30 consumers	150/s	66.7%	50/s	120 s
30, 80/s ceiling	80/s	125%	-20/s	never

With 20, capacity equals the input: nothing is left to drain. With the 80/s ceiling, adding consumers doesn’t create capacity at the provider, and the backlog grows by 20 messages per second.

The math

consumer capacity  = consumers × concurrency × 1000 ÷ service time (ms)
effective capacity = the lower of consumers and dependency
utilization        = arrivals ÷ effective capacity
drain time         = backlog ÷ (effective capacity − arrivals)

What this math doesn’t say

It uses constant rates and ignores broker limits, batches, retries and failures. It’s not a benchmark or a production setting. It’s there to help you ask the right question before scaling.

To discuss

• What would you measure first in a real system?
• Does more pressure on a saturated provider make things better or worse?
• What would you tell the customer while the queue drains?