1. Stable Phase Theorem - Provided that PR k N-1.  T N,  k  N, the pipeline system assumes a periodic behavior after a finite initial phase. The complete behavior is characterized the unique trace: ρ = t init (inc(i) fq N-1 ? eq N ? c N eq N-1 ! t L fq N ! d(i *T N )) ω. t init – trace recording the initial phase of the system execution. t stable – stable phase: (inc(i) fq N-1 ? eq N ? c N eq N-1 ! t L fq N ! d(i *T N )) ω t L – subtrace recording the interleaved execution of C 1..C N-1. Analysis of a Time-driven Chain of Dependent Components M.A. Weffers-Albu 1, J.J. Lukkien 1, P.D.V. v.d. Stok 1,2 The approach we took was to provide a characterization of streaming applications execution to determine performance attributes and provide insight into best design practices for optimising these attributes. Performance attributes: Number of Context Switches (NCS), Response Time of tasks and chain (RT), Resources utilization (RU) for CPU and memory. 1. Introduction The goal of our work is the prediction and optimization of performance attributes to provide guaranteed and optimized Quality of Service (QoS) for real-time streaming applications. 2. TriMedia Streaming Software Architecture A TSSA media processing application - graph: Nodes: - software components Edges: - finite buffers (queues) that transport the data stream from one component to the next component in the graph.     eq i fq i-1 fq i eq i-1 Component Processing function(c i )  Get Full PacketPut Full Packet Put Empty PacketGet Empty Packet Affiliation 1) Eindhoven University of Technology Department of Mathematics and Computer Science HG 6.57, P.O. Box 513, NL-5600 MB, Eindhoven, The Netherlands 2) Philips Research NatLab Prof. Holstlaan 4, 5656AA Eindhoven, The Netherlands 3. Modeling chain execution About the Author Alina Weffers-Albu received her P.D.Eng. in Software Technology from the Department of Mathematics and Computer Science of the Eindhoven University of Technology (TU/e) in 2003. In July 2003 Alina started a Ph.D. project within the SAN group of the same department, in collaboration with Philips Research Laboratories Eindhoven. Corollaries Given the computation times of components actions, ρ and  eager can be calculated at design time. Hence NCS, task and chain RT, RU for CPU and memory can also be calculated. Minimum Queue Capacity: 1 Minimum NCS at Stable Phase: P(C 1 )<…<P(C N-1 ) and Cap(fq i )=2, i < N-1. The systems we analyse are streaming applications using the TriMedia Streaming Software Architecture (TSSA) and executing on a TriMedia device. 4. Conclusions Results Characterization of streaming applications execution Prediction and optimisation of performance quality attributes. Impose predicates until obtain trace and schedule which specify the system behavior. Unique trace ρ, eager schedule  eager eq 2 eq N-1 fq 1 eq 1 fq N-1 C1C1 C2C2 CNCN fq 2 … Typical program of component C i : j=0; while (true) do { inc(j);  receive( fq i-1, p);  receive( eq i, q);  process_func_c i (p, q);  send( eq i-1, p);  send( fq i, q); delay( j*T N ); } Express behavior as traces: Tr(C i ): { (fq i-1 ?, eq i ?, c i, eq i-1 !, fq i !)  }, Tr(C N ): {j = 0 (inc(j) fq N-1 ? eq N ? c N eq N-1 ! fq N ! d(j *T N )) .}. QoS Requirement – C N executes always strictly at rate T N. First step solution - rate of production higher than rate of consumption for packets in fq N-1 : PR k N-1.  T N,  k  N schedule consistent traces arbitrary interleavings channel consistent traces priority consistent traces Chain RT cannot be optimized C N drives execution in the same way as a minimum priority data- driven component in a chain composed of only data-driven components. Time-driven component Data-driven components enc. hw scaler enc. disk : non-scalable dmux audio dec. sharp enh. main: scalabale DVD mixer mixer : non-scalable scaler digitizer: non-scalable digit audio rend read writer dec enc. scalable task task hierarchical task connection to HW IO buffer data transfer pip: scalable Courtesy of E.F.M. Steffens t init idle time TNTN …