Does Craft have a server-side queuing system?
Not so much true queues, but Craft does have the (completely undocumented) concept of Tasks, which are meant to be used for potentially long running tasks that don't need to execute immediately.  Plugins can create and register tasks to run.

Here are some questions discussing them:

My tasks don&#39;t seem to be running as a background process

How to add a subTask to an already running Task?

Triggering the start of a task from a CRON job

You can view the TaskService in craft/app/services/TaskService.php and you can see examples of Craft's own tasks in craft/app/tasks.

Also worth noting that proper support for queues at the framework level looks like it's on the roadmap for Yii 2.1.