  Totally asymmetric exclusion processes (TASEP) with open boundaries are known
to exhibit moving shocks or delocalised domain walls (DDW) for sufficiently
small equal injection and extraction rates. In contrast
  TASEPs in an inhomogeneous ring have been shown to display pinned shocks or
localised domain walls (LDW) under similar conditions [see, e.g., H. Hinsch and
E. Frey, {\em Phys. Rev. Lett.} {\bf 97}, 095701 (2006)]. By studying periodic
exclusion processes composed of a driven (TASEP) and a diffusive segments, we
uncover smooth transitions between LDW and DDW; the latter mimics DDWs in an
open TASEP, controlled essentially by the fluctuations in the diffusive
segment. Mean-field theory together with Monte Carlo simulations are employed
to characterize the emerging nonequilibrium steady states. Our studies provide
an explicit route to control the degree of shock fluctuations in periodic
systems, and should be relevant in cell biological transport where the
availability of molecular motors is the rate limiting constraint.
