Abstract: Triplet-based interconnection network (THIN), which is a novel topology of network-on-chip, is redefined using graph theory. The ergodic property of THIN is proved, and several kinds of streaming models of THIN are induced. The streaming models conclude the streaming features of data in the triplet-based architecture. The parallel sorting by regular sampling (PSRS) algorithm is used to explain the course of applying streaming models. The simulation shows that the performance effected by the topology and the running patterns can be well evaluated by using cited streaming models.