Question

… or how does zmq deal with clients that disconnect? Is there some sort of timeout for a queue where it can continue receiving messages if the client disconnects, but clean up after itself after so many seconds?

Answer 1

See: http://api.zeromq.org/2-1:zmq-setsockopt

ZMQ sockets have a concept of high water mark.

From the docs:

The high water mark is a hard limit on the maximum number of outstanding messages ØMQ shall 
queue in memory for any single peer that the specified socket is communicating with.

If this limit has been reached the socket shall enter an exceptional state and depending on 
the socket type, ØMQ shall take appropriate action such as blocking or dropping sent messages. 

For each type of zmq sockets (REQ, REP, PUB, SUB etc) you can check the document on it’s behavior – if it blocks sending of messages or drops them.

Mostly when the client disconnects, it drops the messages. If that is important to you, you must build message persistence and reliability on top of ZMQ patterns.