Agrawal and Shukla at NCSU did a good initial analysis and simulation of scheduled routing for arbitrary compile-time streams [60]. Their work focussed on the notion of output consistency, a definition for pipelined computation that requires that data always be received by a node by the time the node is ready to consume it. They contrast traditional dynamic routing, observing that contention may stall messages beyond the time when they are needed by their destination. In particular, they observe that dynamic routing has no sense of changing message priorities: a message from a subsequent iteration of an application might arrive first at a switch and lock out an urgently-needed message from the current iteration of the application.
Their model uses a task flow graph (TFG), a directed acyclic graph whose vertices represent tasks and whose directed edges represent messages between tasks. TFG executions are overlapped as successive problems arrive to be solved. Their algorithm computes schedules for each router by first computing an optimal path assignment for all the messages, then computing which portions of each message are transmitted at what times. Together, this allows the creation of a schedule for each node to transmit the messages.
They simulated their work, comparing it to traditional dynamic routing on both tori and hypercubes. They found that their scheme was able to guarantee consistent message arrival times under most loads, whereas dynamic routing incurred frequent output inconsistency, causing stalling of the entire application.