University of North Carolina at Chapel Hill

Department of Computer Science

Chapel Hill, NC

August, 1998

Complex digital signal processing systems are commonly developed using directed
graphs called *processing graphs.* Processing graphs are large grain
dataflow graphs in which nodes represent processing functions and graph edges
depict the flow of data from one node to the next. When sufficient data
arrives, a node executes its function from start to finish without
synchronization with other nodes, and appends data to the edge connecting it
to a consumer node.

We combine software engineering techniques with real-time scheduling theory to solve the problem of transforming a processing graph into a predictable real-time system in which latency can be managed. For signal processing graphs, real-time execution means processing signal samples as they arrive without losing data. Latency is defined as the time between when a sample of sensor data is produced and when the graph outputs the processed signal.

We study a processing graph method, called PGM, developed by the U.S. Navy for
embedded signal processing applications. We present formulae for computing node
execution rates, techniques for mapping nodes to tasks in the
rate-based-execution (RBE) task model, and conditions to verify the
schedulability of the resulting task set under a rate-based,
earliest-deadline-first scheduling algorithm. Furthermore, we prove upper and
lower bounds for the total latency any sample will encounter in the system. We
show that there are two sources of latency in real-time systems created from
processing graphs: inherent and imposed latency. * Inherent latency*
is the
latency defined by the dataflow attributes and topology of the processing
graph. * Imposed latency* is the latency imposed by the scheduling and
execution of nodes in the graph.

We demonstrate our synthesis method, and the management of latency using three applications from the literature and industry: a synthetic aperture radar application, an INMARSAT mobile satellite receiver application, and an acoustic signal processing application from the ALFS anti-submarine warfare system.

This research is the first to model the execution of processing graphs with the real-time RBE model, and appears to be the first to identify and quantify inherent latency in processing graphs.

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Last revised Tue Jan 5 19:34:44 EST 1999 by jeffay at cs.unc.edu.