Universal queue automata
Well, a very similar concept, called Tagsystems is an early universal model developed by Post. Here is the description from wikipedia:


  A tag system is a deterministic computational model published by Emil
  Leon Post in 1943 as a simple form of a Post canonical system. A tag
  system may also be viewed as an abstract machine, called a Post tag
  machine (not to be confused with Post-Turing machines)—briefly, a
  finite state machine whose only tape is a FIFO queue of unbounded
  length, such that in each transition the machine reads the symbol at
  the head of the queue, deletes a constant number of symbols from the
  head, and appends to the tail a symbol-string that depends solely on
  the first symbol read in this transition.


It is explained in the introductory part of a paper by Woods and Neary for FOCS 2006 that small universal TM's are actually built from small universal Tag-systems. Hence there is a big competition in finding small Tag-systems.