  Given an irreducible, end-periodic homeomorphism f of a surface S with
finitely many ends, all accumulated by genus, the mapping torus is the interior
of a compact, irreducible, atoroidal 3-manifold with incompressible boundary.
Our main result is an upper bound on the infimal hyperbolic volume of the
compactified mapping torus in terms of the translation length of f on the pants
graph of S. This builds on work of Brock and Agol in the finite-type setting.
We also construct a broad class of examples of irreducible, end-periodic
homeomorphisms and use them to show that our bound is asymptotically sharp.
