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

Pinned or moving: states of a single shock in a ring