# Scheduling Dynamic Dataflow Graphs with Bounded Memory Using the Token Flow Model

### Joseph T. Buck

###
EECS Department

University of California, Berkeley

Technical Report No. UCB/ERL M93/69

1993

### http://www.eecs.berkeley.edu/Pubs/TechRpts/1993/ERL-93-69.pdf

This thesis presents an analytical model of the behavior of dataflow graphs with data-dependent control flow. In this model, the number of tokens produced or consumed by each actor is given as a symbolic function of the Boolean-valued tokens in the system. Several definitions of consistency are discussed and compared. Necessary and sufficient conditions for bounded-length schedules, as well as sufficient conditions for determining whether a dataflow graph can be scheduled in bounded memory are given. These are obtained by analyzing the properties of minimal cyclic schedules, defined as minimal sequences of actor executions that return the dataflow graph to its original state. Additional analysis techniques, including a clustering algorithm that reduces graphs to standard control structures (such as "if-then-else" and "do-while") and a state enumeration procedure, are also described. Relationships between these techniques and those used in Petri net a analysis, as well as in the theory of certain stream languages, are discussed. Finally, an implementation of these techniques using Ptolemy, an object-oriented simulation and software prototyping platform, is described. Given a dynamic dataflow graph, the implementation is capable either of simulating the execution of the graph, or generating efficient code for it (in an assembly language or higher level language).

**Advisor:** Edward A. Lee

BibTeX citation:

@phdthesis{Buck:M93/69, Author = {Buck, Joseph T.}, Title = {Scheduling Dynamic Dataflow Graphs with Bounded Memory Using the Token Flow Model}, School = {EECS Department, University of California, Berkeley}, Year = {1993}, URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/1993/2429.html}, Number = {UCB/ERL M93/69}, Abstract = {This thesis presents an analytical model of the behavior of dataflow graphs with data-dependent control flow. In this model, the number of tokens produced or consumed by each actor is given as a symbolic function of the Boolean-valued tokens in the system. Several definitions of consistency are discussed and compared. Necessary and sufficient conditions for bounded-length schedules, as well as sufficient conditions for determining whether a dataflow graph can be scheduled in bounded memory are given. These are obtained by analyzing the properties of minimal cyclic schedules, defined as minimal sequences of actor executions that return the dataflow graph to its original state. Additional analysis techniques, including a clustering algorithm that reduces graphs to standard control structures (such as "if-then-else" and "do-while") and a state enumeration procedure, are also described. Relationships between these techniques and those used in Petri net a analysis, as well as in the theory of certain stream languages, are discussed. Finally, an implementation of these techniques using Ptolemy, an object-oriented simulation and software prototyping platform, is described. Given a dynamic dataflow graph, the implementation is capable either of simulating the execution of the graph, or generating efficient code for it (in an assembly language or higher level language).} }

EndNote citation:

%0 Thesis %A Buck, Joseph T. %T Scheduling Dynamic Dataflow Graphs with Bounded Memory Using the Token Flow Model %I EECS Department, University of California, Berkeley %D 1993 %@ UCB/ERL M93/69 %U http://www.eecs.berkeley.edu/Pubs/TechRpts/1993/2429.html %F Buck:M93/69