The Token Flow Model 22 of 22

Dataflow graphs that are strongly consistent and have finite complete cycles can always be scheduled statically and executed in bounded memory. Some strongly consistent graphs without finite complete cycles can also be executed in bounded memory. We have described a clustering technique that can identify such graphs and construct their schedules. However, some perfectly correct graphs may not fit the models described. To execute these, we must resort to the much more costly methods of dynamic scheduling and memory allocation. Nonetheless, even within such uncooperative graphs, large subgraphs are likely to be consistent and have finite complete cycles. These subgraphs should be statically scheduled and memory should be statically allocated. The cost of dynamic scheduling and memory allocation should be incurred only where absolutely necessary. do { fire ; } while (= TRUE); Treated as a unit, the cluster always consumes and produces exactly one token, so the resulting schedule is. For this purpose, the " state " of a dataflow graph has two components, the number of tokens on each arc, and the value of any Boolean tokens on Boolean arcs. An alternative approach is to construct a schedule with the repetition vector given by (34) with , and observe that two possible states can result from executing this schedule. One of these states is the original state, denoted. The second is a new state, , shown in figure 17. If a schedule with repetition vector (34) is applied to the starting state , then exactly two ending states are possible, and. Consequently, a schedule with repetition vector (34) can be repeated indefinitely with no difficulty. Yet a third alternative approach is to construct a preamble, or initial schedule that transforms the graph into one that has no delays on Boolean arcs. For the graph in figure 16, firing actors 1 and 2 constitute such a preamble. After the preamble has executed, then ordinary scheduling methods can be applied. All three methods fail, however, for the graph in figure 13. The number of states that would need to be considered is unbounded. For this graph, we offer no alternative to dynamic scheduling with dynamic memory allocation. However, the clustering algorithm still finds well-behaved substructures in the graph; by clustering the graph as much as possible, we reduce the amount of dynamic memory allocation and scheduling that is required. Some complex and irregular graphs will not be successfully clustered by …