  We investigate the monoid of transformations that are induced by sequences of
writing to and reading from a queue storage. We describe this monoid by means
of a confluent and terminating semi-Thue system and study some of its basic
algebraic properties, e.g., conjugacy. Moreover, we show that while several
properties concerning its rational subsets are undecidable, their uniform
membership problem is NL-complete. Furthermore, we present an algebraic
characterization of this monoid's recognizable subsets. Finally, we prove that
it is not Thurston-automatic.
