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Deferrable Scheduling for Temporal Consistency: Schedulability Analysis and

Overhead Reduction

Ming Xiong: Lucent Bell LabsSong Han: City University of Hong

KongDeji Chen: Emerson Process

Management

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Outline• Overview and motivation• Deferrable scheduling alg and

analysis:– Deferrable Scheduling (DS): A fixed

priority scheduling alg for maintaining freshness of real-time data (RTSS05)

– A sufficient condition for DS feasibility (schedulability)

– DS with Hyper-period algs for reducing on-line scheduling overhead

• Performance Studies• Conclusions and Future Work

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RTDB Model for Maintaining Temporal Validity of Real-Time Data

Real-TimeDatabases

Network

Sensor 1

Sensor 2

Sensor N

. . . .

• A real-time object in RTDBs models a real world entity, e.g., position of an aircraft• Values are sampled by sensors, and propagated to RTDBs• Real-time data in RTDBs must remain fresh in order to react to abnormal situations timely

• Transactions may be triggered to deal with abnormal situations

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What is Data Temporal Validity in RTDBs?

Temporal Validity: keep data valid relative to real world

Time

Value

X

• Real-time data values change continuously• Data values are sampled periodically• A validity interval is associated with a data value• Within validity interval, a data value is fresh (temporally valid)

– deviation from real world is acceptable

0 1 2 3 4 5

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Prior Work: Half-Half (HH) & More-Less (ML)

Definition:• X : Real-Time Data • V : Validity Interval

Length• T : Trans Updating X

• P : Period of T

• D : Relative Deadline of T

V

t

P=D

t+V/2 t +Vt

Observation : Data validity can be guaranteed if Period + Relative Deadline Validity LengthHalf-Half : Sample at twice the rate of change (P = D = V/2)

More-Less : P V/2 & D V/2

P=D

D

t t+V/2 t +Vt

PML

HH

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Intuition of Deferrable Scheduling

• More-Less: Periodic approach that is unnecessarily pessimistic– More-Less uses the worst-case response time (WCRT) of a

transaction as its relative deadline – Period (Ti) = Validity Length (Ti) - WCRT (Ti) – Relative deadline and period are fixed for all instances of a

transaction• DS: Sporadic approach that allows variable separations

and relative deadlines for instances of a transaction– DS uses response time of an instance as the relative

deadline of the instance– Separation(Ti,j, Ti,j+1) = Validity Length(Ti) – ResponseTime(Ti,j+1)– Relative deadline and separation of two instances are varied for all

instances of a transaction• DS increases the average separation of two consecutive

instances

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Deferrable Scheduling: Example Illustration

Validity Length Vi

ri,0 di,1ri,1

di,1r’i,1

Ti,0 Ti,1

Higher-priority preemption

di,0

Di Di

How to determine the response time of Ti,1 if it completes at di,1?

ri,j: Sampling(Release) time of Ti,j

di,j: Absolute deadline of Ti,j

Vi

di,2

Vi

d’i,2

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Deferrable Scheduling:Key Steps

• Release time ri,j for transaction instance Ti,j is derived backwards from its deadline di,j :

1) di,j+1 = ri,j + Vi (validity constraint)

2) ri,j+1 = di,j+1 – ResponseTime(Ti,j+1 )

3) ResponseTime(Ti,j+1 ) = HPPreemption(ri,j+1, di,j+1 ) + Ci

HPPreemption(ri,j+1, di,j+1 ) is the total amount of processor demand from higher priority transactions during [ri,j+1, di,j+1 ].

4) HPPreemption(ri,j+1, di,j+1 ) can be derived only if the schedule of all higher priority transactions of Ti up to di,j+1

have been determined

• Note that Eq 2) above can be solved by an iterative algorithm in fixed priority scheduling

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DS Feasibility Analysis: A Sufficient Condition

• Theorem: Given a synchronous sensor transaction set T, if T can be scheduled by More-Less, then it can also be scheduled by Deferrable Scheduling.– Synchronous means that the first

instances of all transactions are released at the same time

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Proof Sketch of the Theorem

• T can be scheduled by More-Less: WCRTML (Ti) <= Validity Length (Ti)/2

• T can be scheduled by More-Less: WCRT (Ti) <= WCRTML (Ti)

• WCRT (Ti) <= Validity Length (Ti)/2:T can be scheduled by Deferrable Scheduling.

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WCRTML (Ti) <= Validity Length (Ti)/2

• True by the definition of More-Less

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WCRT (Ti) <= WCRTML (Ti)

• Prove by contradiction.• For any 1 < k <= m and

WCRT (Tk) > WCRTML (Tk),• we could find 1 <= l < k and

WCRT (Tl) > WCRTML (Tl).• Tl could be found from the schedule that

produces WCRT (Tk) • But we know:

WCRT (T1) = WCRTML (T1)

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T can be scheduled by Deferrable Scheduling

• If ri,k+1 <= di,k, then T is schedulable.• According to DS-FP:

ri,k = di,k – Ri,k

di,k+1 = ri,k + Vi

ri,k+1 = di,k+1-Ri,k+1

• We have: ri,k+1 – di,k + Ri,k+1 + Ri,k = Vi

• Since: Ri,k+1 + Ri,k <= 2 WCRT (Ti) <= Vi

• We have: ri,k+1 – di,k <= 0

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Reducing DS On-line Scheduling Overhead

• Worst-case time complexity of on-line scheduling is O(mVm

2) – It is much higher than More-Less (O(1))

• Time complexity of on-line scheduling can be reduced by making DS based hyper-period schedule (off-line)– Periodic on-line scheduling (O(1))– On-line space overhead to maintain

schedule information is low

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Deferrable Scheduling with Hyper-period (DESH)

• Criteria for hyper-period: two consecutive instances of a transaction satisfy the validity constraint– Two instances in the same hyper-period– Two instances across two hyper-periods

• Off-line Schedule Adjustment (DESH-SA) Alg– Finds an interval [0, tend] in a partial DS schedule

that has its utilization close to Uest

– Adjusts the schedule backwards from tend so that the schedule in [0, tend] can be repeated on-line without violating the validity constraint

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DESH-SA Alg

• Finds an idle time t– Repeats the schedule in [0, t] for Ti if Ti and

its higher priority transactions satisfy the validity constraint for the last instance before t and the first instance after t

– Otherwise, • Pushes back the first Ti instance after t and sets t

as its deadline, and computes its release time• If its release time < its prior instance’s absolute

deadline, adjusts the schedule of its prior instance (may incur ripple effect)

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Performance Studies

• Experiments are conducted by simulation– Single CPU RTDB with all real-time data

in main memory– Sensor and triggered transactions are

generated following an air traffic control application

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Performance Results: DESH Algs

• DESH-SA has CPU utilization close to DS

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

10 15 20 25 30 50 100 150 200 250 300

Number of Sensor Transacti ons

CPU

Util

izat

ion

More-Less DS(Theoreti cal Est. ) DESH-SA

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Performance Results:Hyper-period Length

DESH-SA

360

365

370

375

380

385

390

395

10 15 20 25 30 50 100 150 200 250 300

Number of Sensor Transacti ons

Hype

r-pe

riod

Len

gth

(X 1

000

ms)

DESH-SA

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Conclusions• Introduced Deferrable Scheduling (DS) for

fixed priority transactions maintaining real-time data freshness

• Proposed a sufficient condition for DS feasibility

• Developed DS based algorithm that schedule transactions with hyper-period while reducing on-line scheduling overhead to O(1)

• Experimental results demonstrated that DS significantly outperforms More-Less

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Future Work

• Open questions:– Is time 0 a critical instant for synchronous

sensor transactions ?– What is a sufficient and necessary condition

for DS feasibility ?– What is processor utilization bound for DS

feasibility ?– How much can DS improve the feasibility of

More-Less ?