Max-Plus Algebraic Throughput Analysis of Synchronous Dataflow Graphs

In this paper we present a novel approach to throughput analysis of synchronous dataflow (SDF) graphs. Our approach is based on describing the evolution of actor firing times as a linear time-invariant system in max-plus algebra. Experimental results indicate that our approach is faster than state-of-the-art approaches to throughput analysis of SDF graphs. The efficiency of our approach is due to an exploitation of the regular structure of the max-plus system's graphical representation, the properties of which we thoroughly prove.

[1]  Marc Geilen,et al.  Reduction techniques for Synchronous Dataflow graphs , 2009, 2009 46th ACM/IEEE Design Automation Conference.

[2]  Geert Jan Olsder,et al.  Max Plus at Work: Modeling and Analysis of Synchronized Systems: A Course on Max-Plus Algebra and Its Applications , 2005 .

[3]  Keshab K. Parhi,et al.  Determining the minimum iteration period of an algorithm , 1995, J. VLSI Signal Process..

[4]  Jean A. Peperstraete,et al.  Cycle-static dataflow , 1996, IEEE Trans. Signal Process..

[5]  Shuvra S. Bhattacharyya,et al.  Embedded Multiprocessors: Scheduling and Synchronization , 2000 .

[6]  E.A. Lee,et al.  Synchronous data flow , 1987, Proceedings of the IEEE.

[7]  C. Leake.  Synchronization and Linearity: An Algebra for Discrete Event Systems , 1994 .

[8]  Robert E. Tarjan,et al.  Faster parametric shortest path and minimum-balance algorithms , 1991, Networks.

[9]  Ali Dasdan,et al.  Experimental analysis of the fastest optimum cycle ratio and mean algorithms , 2004, TODE.

[10]  J. Quadrat,et al.  Numerical Computation of Spectral Elements in Max-Plus Algebra☆ , 1998 .

[11]  Manuel Silva Suárez,et al.  On Weighted T-Systems , 1992, Application and Theory of Petri Nets.

[12]  J. Quadrat,et al.  Max-Plus Algebra and System Theory: Where We Are and Where to Go Now , 1999 .

[13]  Manuel Silva,et al.  Cycle time computation in deterministically timed weighted marked graphs , 1999, 1999 7th IEEE International Conference on Emerging Technologies and Factory Automation. Proceedings ETFA '99 (Cat. No.99TH8467).

[14]  Sander Stuijk,et al.  Throughput Analysis of Synchronous Data Flow Graphs , 2006, Sixth International Conference on Application of Concurrency to System Design (ACSD'06).

[15]  Sander Stuijk,et al.  SDF^3: SDF For Free , 2006, Sixth International Conference on Application of Concurrency to System Design (ACSD'06).

[16]  Sander Stuijk,et al.  Liveness and Boundedness of Synchronous Data Flow Graphs , 2006, 2006 Formal Methods in Computer Aided Design.