The Token Flow Model

This paper reviews and extends an analytical model for the behavior of dataflow graphs with data-dependent control flow. The number of tokens produced or consumed by each actor is given as a symbolic function of the Booleans in the system. Long-term averages can be analyzed to determine consistency of token flow rates. Short-term behavior can be analyzed to construct an annotated schedule, or a static schedule that annotates each firing of an actor with the Boolean conditions under which that firing occurs. Necessary and sufficient conditions for bounded-length schedules, as well as sufficient conditions for determining that a dataflow graph can be scheduled in bounded memory are given. Annotated schedules can be used to generate efficient implementations of the algorithms described by the dataflow graphs.