On Schedulability andTime Composability of

Data Aggregation Networks

Fatemeh Saremi*, Praveen Jayachandran†, Forrest Iandola*, Md Yusuf Sarwar Uddin*,

Tarek Abdelzaher*, and Aylin Yener‡

* Department of Computer Science, University of Illinois, Urbana, IL† IBM Research, India

‡ Department of Electrical Engineering, Pennsylvania State University, University Park, PA

Email: saremi1@illinois.edu, prjayach@in.ibm.com, {iandola1, mduddin2, zaher}@illinois.edu, yener@ee.psu.edu

Motivation

2F. Saremi et al., On Schedulability and Time Composability of Data Aggregation Networks7/11/2012

Aircraft radardetects presenceof the submarine

Ship receives observation dataand fuses it with a reference database to identify submarine

Coordination of input from multiple sonars is used to track the submarine

Related Work

3F. Saremi et al., On Schedulability and Time Composability of Data Aggregation Networks7/11/2012

CWS[Li et al.]

2008

[Xue et al.]Constructing the

complete schedule1993

[Kao et al.]Per-stage deadlines

1997

Holistic Analysis[Pellizzoni et al.]

2005

Real-time Calculus[Thiele et al.]

2000

Delay CompositionAlgebra

[Jayachndran et al.]2009

[Fohler et al.]Constructing the

complete schedule1997

[Zhang et al.]Per-stage deadlines

2005

Holistic Analysis[Tindell et al.]

1994

Real-time Calculus[Jonsson et al.]

2008

[Koubaa et al.]Comparing

Real-time Calculus & Holistic2004

Aggregation Model• Each job of every workflow is

assigned a priority • "i<=k" means

Priority(i)<=Priority(k)• Low number == high priority

• The relative priority of each job remains the same across all the stages on which it executes

• MERGE Semantics: A job does not become eligible to execute on the merge-stage until all pipelines have finished processing it.

7/11/2012 F. Saremi et al., On Schedulability and Time Composability of Data Aggregation Networks 4

• Offi: the (maximum) offset from time zero at which a job Ji of workflow Fi arrives

• Ci,j: worst-case processing time of Ji on resource j

• Di: end-to-end deadline of Ji

Intuition

7/11/2012 F. Saremi et al., On Schedulability and Time Composability of Data Aggregation Networks 5

Workflow graph and execution trace for

seemingly candidate aggregation

composition approach

Jl: job under considerationJh: higher priority jobJl1, Jl2, Jl3, Jl4: lower priority jobsNon-preemptive scheduling

End-to-End Delay (𝐽l) = 88 - ɛDelay Bound (𝐽l) = ?

• Using Delay Composition Theorem for Pipelines

7/11/2012 F. Saremi et al., On Schedulability and Time Composability of Data Aggregation Networks 6

E2E Delay (𝐽l) = 88 - ɛ > Delay Bound (𝐽l) = 80 + 3ɛ !?

Revisit Event

• Due to reversal in the arrival order, it is possible for 𝐽𝑖 to again delay 𝐽𝑖′ at a downstream stage

7/11/2012 F. Saremi et al., On Schedulability and Time Composability of Data Aggregation Networks 7

Ji’: job under considerationJi : higher priority jobJl1, Jl2, Jl3: lower priority jobsNon-preemptive scheduling

Along the other branch, 𝐽𝑖 delays job 𝐽𝑖′ and arrives ahead of it to the

merge-stage

Along one branch, 𝐽𝑖′ completes execution and arrives ahead of 𝐽𝑖 to the

merge-stage

Non-preemptive Delay Composition Theorem for Aggregation Workflows

Under a non-preemptive scheduling policy that assigns the same priority across all stages for each job, the worst-case end-to-end delay of a job of work flow 𝐹𝑘 in an aggregation tree is bounded as,

where Offi is the offset of job Ji from time zero.

7/11/2012 F. Saremi et al., On Schedulability and Time Composability of Data Aggregation Networks 8

Delay Bound Proof Sketch

• By induction on the number of revisit events

7/11/2012 F. Saremi et al., On Schedulability and Time Composability of Data Aggregation Networks 9

Preemptive Delay Composition Theorem for Aggregation Workflows

Assuming a preemptive scheduling policy that assigns the same priority across all stages for each job, the worst-case end-to-end delay of a job of workflow 𝐹𝑘 in an aggregation tree is bounded as,

where Offi is the offset of job Ji from time zero.

7/11/2012 F. Saremi et al., On Schedulability and Time Composability of Data Aggregation Networks 10

Schedulability Analysis• The schedulability of a job 𝐽𝑘 of an aggregation workflow can

be determined by analyzing the schedulability of an equivalent hypothetical uniprocessor constructed by reduction rules obtained based on the composition theorem.

7/11/2012 F. Saremi et al., On Schedulability and Time Composability of Data Aggregation Networks 11

The reduction process on an

aggregation tree

Evaluation

• How different parameters can affect the performance of the Aggregation Delay Composition framework?– How accurately are the worst-case e2e delays estimated?– How efficiently are system resources utilized?

– With respect to the following system and load parameters• The number of stages• The number of tasks• Job resolution• Deadline ratio• Offset resolution

7/11/2012 F. Saremi et al., On Schedulability and Time Composability of Data Aggregation Networks 12

End-to-End Delay Bound Accuracyw.r.t. the Number of Stages

7/11/2012 F. Saremi et al., On Schedulability and Time Composability of Data Aggregation Networks 13

Under preemptive scheduling, 6% and 24% improvement respectively at 7 and 63 stages

Under non-preemptive scheduling, 14% and 34% improvement respectively at 7 and 63 stages

Less Pessimistic

More Pessimistic

7/11/2012 F. Saremi et al., On Schedulability and Time Composability of Data Aggregation Networks 14

End-to-End Delay Bound Accuracyw.r.t. the Number of Tasks

Under both non-preemptive and preemptive scheduling, more than 20% improvement when the number of jobs over 80

Less Pessimistic

More Pessimistic

Resource Utilizationw.r.t. Job Resolution

7/11/2012 F. Saremi et al., On Schedulability and Time Composability of Data Aggregation Networks 15

Consistent improvement under both non-preemptive and preemptive scheduling

(The drop in DCA under non-preemptive is due to the blocking delay component becoming significantly large as job sizes increase)

Many small jobs A few big jobs

7/11/2012 F. Saremi et al., On Schedulability and Time Composability of Data Aggregation Networks 16

Resource Utilizationw.r.t. Deadline Ratio

Consistent improvement under both non-preemptive and preemptive scheduling

(The drop in both DCA and Holistic under non-preemptive scheduling is due to larger blocking delays being imposed on higher priority jobs as the variability in deadlines increases)

Homogenous deadlines Wide range of deadlines

7/11/2012 F. Saremi et al., On Schedulability and Time Composability of Data Aggregation Networks 17

Resource Utilizationw.r.t. Offset Resolution

Improvement when offset resolution below 100 times of the minimum job deadline

LogarithmicScale

Small offsets Wide range of offsets

Conclusions• Investigated timing properties and delay composability of multi-

criticality distributed workload in multisensor data aggregation systems

• Elaborated on why it is challenging to analyze such systems

• Proposed a theoretical framework to analyze schedulability of multisensor data aggregation systems characterized by the “MERGE” primitive under non-preemptive as well as preemptive scheduling

• Confirmed by extensive simulation results that our theoretical framework is significantly more accurate than traditional analysis techniques and effectively utilizes distributed resources, and that it is especially beneficial for large systems.

7/11/2012 F. Saremi et al., On Schedulability and Time Composability of Data Aggregation Networks 18

Thank you.

Questions … ?

19F. Saremi et al., On Schedulability and Time Composability of Data Aggregation Networks7/11/2012