Real-Time Capacity of Networked Data Fusion University of Illinois at Urbana-ChampaignUniversity of Illinois at Urbana-Champaign

Forrest Iandola (University of Illinois)Fatemeh Saremi (University of Illinois)Tarek Abdelzaher (University of Illinois)Praveen Jayachandran (IBM Research)

Aylin Yener (Pennsylvania State University)

Motivation and Goals Develop a theoretical bound for the

capacity of data fusion systems Enable data fusion systems to run at

full capacity without missing deadlines

Forrest IandolaIllustration of a data fusion system with merging

Outline Introduce data fusion system model Scheduling theory background: Feasible

Region Calculus Derive a capacity utilization bound for

data fusion pipelines Extend this bound to capture merging

pipelines Performance evaluation

Forrest Iandola

“Data Fusion System” refers to… Distributed sensor networks Control systems that receive one or

more data feeds “Real-Time Capacity” = data

packets transmitted within time constraints

Forrest Iandola

Data Fusion System Model (1/3)

Data Fusion System Model (2/3) Workflow i is denoted as Fi

Invocation of Fi is a “job” q Di = deadline of Fi

Pi = period of Fi

Ri = 1/Pi = “Rate” Ci,j = computation of Fi on stage j

Forrest Iandola

Data Fusion System Model (3/3) System constraints reflect a

realistic data fusion system Non-preemptive earliest deadline first

(EDF) scheduling Workflows are periodic. Di >> Pi (in other words, many

invocations of Fi may be active simultaneously.)

Forrest Iandola

Scheduling Theory Background: Feasible Region Calculus (FRC) A pipeline task set can be reduced

to a uniprocessor equivalent: Assume qN is the lowest-priority

workflow

Forrest Iandola

For simplicity, let us refer to the “modified” equivalent of the lowest-priority task as q

Forrest Iandola

Scheduling Theory Background: Feasible Region Calculus (FRC)

Deriving Capacity Bound from FRC Testing schedulability of equivalent

uniprocessor from as defined by FRC Remember: we assume non-

preemptive EDF scheduling

Forrest Iandola

Testing schedulability of equivalent uniprocessor from as defined by FRC Remember: we assume non-

preemptive EDF scheduling

Forrest Iandola

Deriving Capacity Bound from FRC

Basic utilization formula:

Combining utilization formula with FRC definitions:

To avoid deadline misses,utilization must be less than 1.

Simplifying the Capacity Bound to Reduce Computation Overhead

Stage-additive component is very small when Di >> Pi

Can approximate the utilization even if we ignore stage-additive component

Forrest Iandola

Reduce computation time bydropping lowest-priority invocation:

Replace ceiling function with (DiRi+1):

Handling Merging Flows

Forrest Iandola

Forrest Iandola

Handling Merging Flows

Let’s discuss the intuition behind this.

Step 1: Reduce child pipelines to equivalent uniprocessor workflow sets

Step 2: Obtain two-stage pipeline Ignore all but the largest equivalent

pipeline per workflow Step 3: Calculate equivalent

uniprocessor for two-stage pipelineForrest Iandola

Handling Merging Flows

Fundamental Results

Forrest Iandola

Evaluation of Capacity Bound Comparing predicted useful work of a data fusion tree to actual useful

work (just before onset of deadline misses) Note: Utilization due to jobs/flows that miss deadlines is not counted as useful

work.

Forrest Iandola

Observations: Capacity bound

accurately predicts ability to do useful work

Evaluation of Overload Behavior

Comparing overload behavior of a data fusion tree with admission control (based on new capacity result) to one without Note: Utilization due to jobs/flows that miss deadlines is not counted as useful

work.

Forrest Iandola

Observations: Capacity bound

accurately predicts ability to do useful work

At high load, significant degradation is observed in the absence of admission control due to excessive deadline misses

Conclusions Derived a capacity utilization bound

for data fusion systems Simplified the bound into an easy-

to-use approximation Extended this result for merging

workflows Evaluation demonstrates accuracy

of bound

Forrest Iandola