Jenkins parameterized job that only queues one build

Question

Imagine a Jenkins job A which takes 1 minute to run, and job B which takes 5 minutes.

If we configure job A to trigger job B, while job B is running job A may run 5

Answer 1

You could get rid of Parameterized Trigger Plugin, and instead, use the traditional triggering. As you said, this would prevent job B queue from piling up.

How to pass the parameters from A to B then? Make job A to yield the parameters in it's console output. In job B, to get these build parameters, examine the console output of the latest A build (with a Python script, perhaps?).