Queuing theory is cool, but I'm not 100% sure it actually applies here in a meaningful sense (although, disclaimer: I'm no more experienced here than you). A lot of queuing theory assumes that you must route a request to a handler immediately as you receive it, and that reassigning a request is a very expensive process.
This intuitively explains why queueing theory is very big in router design - imagine that you send a packet through 10 hops and at the last hop experiences a significant delay, does the packet then turn around and go back through another router? Which hop does it pick to look for a different path through? What happens if the packet gets delayed going backwards looking for another route? Does it reverse _again_ looking for a quicker route to another route? Answer: it doesn't, routers deliver messages with the "best effort" (in protocol terminology) they can, and high level latency trends are adapted for through the routing algorithms themselves (read: not adapted for each individual packet). This keeps transport much simpler and therefore faster.
In the case of load balancing, if the "(re)assignment cost" (my terminology) of a request is sufficiently small, then it doesn't make sense to pre-distribute requests until you can be 100% sure a worker is ready. If a request takes 40ms to process and 0.5ms to distribute/assign to a worker, then waiting for feedback (which would also take 0.5ms) from a worker would incur a slowdown of (40 + 0.5 + 0.5)/40 versus if you pre-assigned before a worker was finished. This seems like a no-brainer if it would keep the width of the distribution of your latencies down.
Edit: thinking about this more, if you have an asynchronous worker model, Queueing theory comes back into play. If a worker stops processing Request A to wait for a network response and takes up Request B, and then the network responds while Request B is still working, moving Request A mid-handling to another free machine may be very hard/expensive, if not entirely impossible. As themgt brings up, it sounds like Heroku enabled an asynchronous model in a recent stack and may have dropped the feedback loop that allows for intelligent routing because there's no obvious way to implement it in an asychronous model.
That being said, you could still have a feedback loop when a worker is completely idle. It's certainly very hard to reason about a worker currently executing any task, but it is very easy to reason about a worker that isn't executing anything. Therefore, it should be straightforward (theoretically) to do intelligent routing to empty workers and then keep the random routing for busy workers in such a way that if there is an idle worker no request should ever go to a busy worker. A more advanced version would keep track of the number of open connections to each worker and simply distribute to the worker with the fewest number of active open connections.
I just checked and nginx actually has a directive (least_conn) to do exactly this, but it's not enabled by default! ELB apparently does something similar (see: https://forums.aws.amazon.com/thread.jspa?messageID=135549&#...).