Message Query to HTTP and vice versa, via Tomcat, how?

Question

Java

Actually, there is a need to engage in such a perversion:
We connect to the MQ broker, stand in line, upon the arrival of a message, transform it into an HTTP request,
wait for a response, make an MQ message from the response and push it back to the broker.

From ideas:
Write something in java, run it in parallel on an existing/new tomcat instance, and actually it will deal with this case i.e. listen to the queue, broadcast everything to the web, then back to the queue.
Moreover, sitting in line is a permanent connection, does the cat support it?

Where more specifically to poke? Didn't write serverlets, didn't work with jms (??).

How can I do that?