Resource Augmentation for Performance Guarantees in Embedded Real-time Systems

Abhilash ThekkilakattilLicentiate Thesis PresentationVästerås, November 30, 2012

Real-time tasks

Dependable Real-time Systems

web images

Timing characteristics of the physical components

Fault tolerance requirements

Event occurrences:periodic and sporadic

Periodic and Sporadic Real-time Tasks

job1 job2

Worst Case Execution Time

(Min/Exact) Inter-arrival time

Release time

Relative deadline

Task worst case execution time scales with processor frequency

Assumption: probabilistic task release times for sporadic tasks

Real-time Scheduling Real-time scheduling: guarantee task completions before their deadline

Non-preemptive Scheduling

Low runtime overhead Increased blocking times: low utilization Mutual exclusion by construction

Preemptive Scheduling

Ability to achieve high utilization Preemption costs Need for synchronization protocols

high priority

low priority

preemption costhigh priority

low priority

blocking

Limited Preemption Scheduling

Best of preemptive and non-preemptive: preempt only when necessary

high priority

low priority

Bounded non-preemptive region

preemption cost

Preemption Related Overheads

● Context switch related overheads: Overhead involved in saving and retrieving the context of the preempted

task

● Cache related preemption delays Overhead involved in reloading cache lines Order of 100s of micro-seconds Vary with the point of preemption Increased bus contention

● Pipeline related overheads Clear the pipeline upon preemption Refill the pipeline upon resumption

CPU frequency:

P: Power consumptionC: Effective capacitanceV: Applied voltageF: CPU frequency

Processor power consumption:

min max

CPU frequencyCPU frequencyCPU frequencyCPU frequencyCPU frequencyCPU frequency CPU frequency

Frequency Scaling in Modern Processors

Hypothesis:

Processor speed-up can be used to provide non-preemption guarantees

Research Questions

Q1: How can we control preemptions in periodic real-time task systems using CPU frequency scaling?

Q2: How can we control preemptions in sporadic real-time task systems using CPU frequency scaling when the probabilities of the task releases are known?

Research Contributions- Question 1

Q1: How can we control preemptions in periodic real-time task systems using CPU frequency scaling?

Paper A: Reducing the Number of Preemptions in Real-Time Systems Scheduling by CPU Frequency Scaling, Abhilash Thekkilakattil, Anju S Pillai, Radu Dobrin, Sasikumar Punnekkat, The 18th International Conference on Real-Time and Network Systems, Toulouse, France, November, 2010

Overview:

1.Offline preemption identification

2.Preemption elimination Calculate the minimum frequency required to eliminate the preemption Analyze the effect of preemption elimination on the rest of the schedule

3. Iteration: until no more preemptions can be eliminated

Preemption Elimination: Periodic Tasks

C=1 C=4

D starts earlier

C=1

C=2

4 8 12 16 20 24 28 32 36 400

4 8 12 16 20 24 28 32 36 400

4 8 12 16 20 24 28 32 36 400

4 8 12 16 20 24 28 32 36 400

Task

A

B

C

D

Rate monotonic schedule

Modes M1 M2 M3

Frequency (Hz)

100 150 300

FC1=6F1=600 Hz FC1=1.5F1=150 Hz

FD1=4F1=400 Hz

FC2=3F1=300 Hz

WCET Period

1 4

2 8

6 20

4 40

Task 1 2 3 4 5 6 7 8 9

A 100 100 100 100 100 100 100 100 100

B 100 100 100 100 100 - - - -

C 100 100 - - - - - - -

D 100 - - - - - - - -

10

100

-

-

-

150 300

Task instance frequencies (Hz)Processor modes

Before elimination: 7After step 1: 7After step 2: 4After step 3: 4After step 4: 2

Overview:

1.Offline Phase Determine permitted deviations in the minimum inter-arrival times of the tasks

using probabilities

2.Online Phase Online preemption control algorithm Speed-up busy period before a preemption

Research Contributions- Question 2

Q2: How can we control preemptions in sporadic real-time task systems using CPU frequency scaling when the probabilities of the task releases are known?

Paper B: Probabilistic Preemption Control using Frequency Scaling for Sporadic Real-time Tasks, Abhilash Thekkilakattil, Radu Dobrin, Sasikumar Punnekkat, The 7th IEEE International Symposium on Industrial Embedded Systems, Karlsruhe, Germany, June, 2012

Preemption Elimination: Sporadic Tasks

Task WCET Inter-arrival time

A 1 5

B 3 7

C 3 20

5 10

5 10

5 10

A

B

C

Original Rate Monotonic Schedule

Offline Phase

Task WCET Time period

Relaxation to min. inter-arrival times for threshold probability

=0.20

Relaxation to min. inter-arrival times for threshold probability

=0.24

A 1 5 1 3

B 3 7 1 3

C 3 20 1 3

0 2 4 5 6 7 8 9 10

0.04

0.08

3

0.24

1

0.20

0.020.040.04

0.080.080.1

0.08

(time)

Tas

k re

leas

e pr

obab

ility

Online Phase

Task WCET Inter-arrival time

Relaxation

A 1 5 1

B 3 7 1

C 3 20 1

5 10

5 10

5 10

A

B

C

C = CA + CB + CC = 7t = 6 (since we use release time probabilities)

Speed = 7/6

We speed-up to max. speed: simplicity

earliest possible preemption point earliest possible preemption point

C = CB = 3 t = 1Speed = 3/1

Summary: Paper A and B

Manipulate processor speed to control the task preemptive behavior

Requires no significant modifications to the schedulerRequires no significant modifications to the task attributesTrade-offs: energy vs. number of preemption Effective: significant preemption reduction shown in simulations Limitations: increased energy consumption

“There is more to life than simply increasing its speed.”

Mahatma Gandhi

What is the bound on the required speed-up?

Resource Augmentation

Introduced by B. Kalyanasundaram and K. Pruhs, “Speed is as powerful as clairvoyance,” Journal of ACM, 2000.

How good is any given online scheduler when compared to an all powerful malevolent adversary?

- Efficiency or ‘goodness’ of the scheduler

Give more resources to the scheduler to satisfy the goal function– Most commonly considered resource: processor (speed-up)

Is the speed-up required bounded (affordable)?

Previous work: upper-bounds on the speed-up to,– Ensure optimal performance for non-clairvoyant online schedulers compared to a

clairvoyant scheduler (Kalyanasundaram et. al)– Guarantee FPS schedulability for all feasible task sets (Baruah et. al and Davis et. al)

Research Questions

Q1: How can we control preemptions in periodic real-time task systems using CPU frequency scaling?

Q2: How can we control preemptions in sporadic real-time task systems using CPU frequency scaling when the probabilities of the task releases are known?

Q3: What is the resource augmentation bound that guarantees the feasibility of a specified non-preemption behavior in a real-time system?

Q3: What is the resource augmentation bound that guarantees the feasibility of a specified non-preemption behavior in a real-time system?

Paper C: Quantifying the Sub-Optimality of Non-Preemptive Real-time Scheduling, Abhilash Thekkilakattil, Radu Dobrin, Sasikumar Punnekkat, Technical Report, MRTC, November, 2012

Overview:

1.Processor speed-up to guarantee specified non-preemption behavior Upper-bound of 4Li/Dmin

• Li : required length of the Non-Preemptive Region (NPR)• Dmin : shortest deadline

•Processor speed-up to guarantee non-preemptive scheduling1. Upper-bound of 4Cmax/Dmin

• Cmax : largest execution time in the task set

•Processor speed-up to bound preemption overheads Derivation of non-preemption requirements Sensitivity analysis to calculate the optimal processor speed

Research Contributions- Question 3

Resource Augmentation for Preemption Control

t

DBF(t)

DBF(t): demand bound function at ‘t’

Li: Length of the NPR

Li

S = max (DBF(t)/ (t - Li))

S ≤ t / (t - Li)

S ≤ y / (y - 1) [ y = t/Li ]

case 1: S ≤ 2 [ y ≥ 2 ] case 2: S ≤ 4 [ 1 ≤ y < 2 ] case 3: S ≤ 4Li/t [ 0 < y < 1 ]

Is S bounded ?

DBF(t)DBF(t)/S

=> S ≤ 4Li/Dmin [ t = Dmin ]

Proof in thesis

?

Preemption Behavior of Scheduling Paradigms

high priority

low priority

preemption cost

high priority

low priority

Bounded non-preemptive region

Fully preemptive scheduler

Limited preemptionscheduler

Controlling thelength of thenon-preemptive region

Unbounded number of preemptions

Requires synchronization protocols

Bounded number of preemptions: bounded by the length of the non-preemptive regions

Control the bound on the number of preemptions

May require synchronization protocols

Does not require synchronization protocols

Bounded non-preemptive region

high priority

low priority

Bounding Preemption Costs

non-preemptive region (bounded length Q iS)

No. of preemptions pi (processor speed: S)

Enable preemptions at optimal preemption points

Executing critical sections within non-preemptive regions

high priority

low priority

Step 2. Perform sensitivity analysis to calculate the optimal processor speed

Step 1. Derive non-preemption requirements to control preemption related overheads

What does the processor speed-up bound mean?

Feasibility of Real-time Tasks

Feasibility: Does a schedule that guarantees no deadline misses exist for a given real-time task set?

Preemptive EDF: optimal uni-processor scheduling algorithm

Non-preemptive EDF (non-idling): optimal non-preemptive scheduling algorithm

How good is non-preemptive scheduling when compared to uni-processor optimal preemptive scheduling algorithms such as EDF?

Set of uni-processor feasible task sets

Set of limited preemption feasible task set on a uni-processor

Set of non-idling non-preemptive feasible task sets on a uni-processor

1

4Cmax/Dmin

4L/Dmin

The Feasibility Bucket

We can quantify the ‘goodness’ or sub-optimality of non-preemptive scheduling in terms of the processor speed-up required to guarantee a fully non-preemptive schedule for the uni-

processor feasible task sets.

Set of uni-processor feasible task sets

Set of limited preemption feasible task set on a uni-processor

Set of non-idling non-preemptive feasible task sets on a uni-processor

Speed at which all uni-processor feasible task sets are guaranteed a non-preemptive execution for L units

Speed at which all uni-processor feasible task sets are guaranteed a fully non-preemptive schedule (under non-idling paradigm)

Slower

Processor Speed

faster

Summary: Paper C

Guarantee specified preemption behavior

• Upper-bound on the required speed-up

Sub-optimality of non-preemptive scheduling• Resource augmentation bound for non-preemptive scheduling

• If there exists a scheduling algorithm that can schedule a given set of real-time tasks on a uni-processor, then non-preemptive EDF can schedule it, if given a processor that is 4Cmax/Dmin times faster

Method to bound preemption related costs• Derive corresponding non-preemption requirements

• Sensitivity analysis based method to find the required optimal speed-up

We have addressed the problem of providing non-preemption guarantees in a real-time system using processor speed-up.

“Failure is simply the opportunity to begin again, this time more intelligently.”

Henry Ford

…which is exactly the design philosophy behind fault tolerant real-time systems that uses temporal redundancy.

Fault Tolerant Real-time Scheduling

Temporal redundancy under transient faults

Fault tolerance related overhead

Fault tolerance feasibility (FT-feasibility): existence of a real-time schedule that is fault tolerant under a specified fault hypothesis

• Transient faults• Temporal redundancy

Guaranteeing FT-feasibility: ensure sufficient slack for at least one successful execution of all the tasks

• Control fault tolerance related overheads• Control task execution times

Fault Tolerance Feasibility

Nature of errors- Normally continuous events e.g., a vehicle passing through electromagnetic fields

- Occur continuously over a period of time: error bursts

Challenging to handle in classical FT-feasibility analysis- Need to map continuous events into singleton events

How can we guarantee FT-feasibility under error bursts?- Hypothesis: use a faster processor

faults/errors as singleton events

error burst

traditional FT-feasibility analysis

Research Questions

Q1: How can we control preemptions in periodic real-time task systems using CPU frequency scaling?

Q2: How can we control preemptions in sporadic real-time task systems using CPU frequency scaling when the probabilities of the task releases are known?

Q3: What is the resource augmentation bound that guarantees the feasibility of a specified non-preemption behavior in a real-time system?

Q4: What is the resource augmentation bound that guarantees the fault tolerance feasibility in real-time systems under error bursts?

Q4: What is the resource augmentation bound that guarantees the fault tolerance feasibility in real-time systems under error bursts?

Paper D: Resource Augmentation for Fault-Tolerance Feasibility of Real-time Tasks under Error Bursts, Abhilash Thekkilakattil, Radu Dobrin, Sasikumar Punnekkat and Huseyin Aysan, The 20 th International Conference on Real-time and Network Systems (shortlisted for best paper award), ACM, Pont à Musson, France, November, 2012

Overview:

1.Fault tolerance feasibility (FT-feasibility) analysis Builds on the optimality of EDF to schedule real-time tasks Derive a sufficient condition for FT-feasibility

2.Resource augmentation bounds to guarantee FT-feasibility Processor speed-up to make up for the slack deficit to enable temporal

redundancy Upper-bound (error burst length ≤ Dmin/2): 6 Upper-bound (general case): 3y/(y-1), y=t/error burst length

Research Contributions- Question 4

Problem Description

Questions:

●How can we perform an FT-feasibility analysis for a given set of temporally redundant real-time tasks under a specified error burst length?

●If the real-time task set is not found to be FT-feasible, what is the lowest processor speed that guarantees its FT-feasibility under the error burst?

Definitions

t

Tlength

worst case error overhead (Et)

ε

Worst Case Temporal Wastage (Werr(t))

=maximum wasted execution time

∑wasted execution time

ε Tlength

Assumptions

● Scheduler: Fault Tolerant Earliest Deadline First (FT-EDF)- schedule task executions and re-execution according to their deadlines

● Objective: find the Worst Case Temporal Wastage at time t- Break down into cases

● Strategy: we assume that there are no deadline misses under the error burst and derive the sufficient condition for this to be true

t’t

abs. deadline of τi

Error detection

τi

Case 1

τi

τj

τk

t’ t

τi

τj

τk

t’ t

τi

τj

τk

t’ t

Worst Case Temporal Wastage at t when the error burst hits only a single job

scenario A: Werr(t)=2(Ck – ε)

scenario B: Werr(t)= 2(Cj – ε)

scenario C: Werr(t)= 2(Ci – ε)

ε

Case 2

ε

ε

ε

τi

τj

τk

τl

t’ t

ε

Tlength

Worst Case Temporal Wastage at t when the error burst hits more than one job

(Cl – ε)

(Ck – ε)

(Cj – ε)

(Ci – ε) (Ci – ε)

Werr(t) = 2(Ci – ε) + ∑ (Cm – ε) , Dm ≤ Di

Case 3

t’t dk

overhead at dk = overhead at toverhead at dk = overhead at d(k-1)

Under EDF, the tasks released in the interval [t’,t] having a deadline greater than t are not hit by the error burst

τj

τi

Worst Case Temporal Wastage at the absolute deadline of a job that is not hit by the error burst

(abs. deadline of τi)

d(k-1)

Worst Case Temporal Wastage: General Case

Werr(t) = Max

Case 3 : WCTW at the previous absolute deadline•If τi is not hit by the error burst

Case 1 : max{2(Ck – ε)} , Dk ≤ Di

•When the error burst hits only a single job

Case 2 : 2(Ci – ε) + ∑ (Ck – ε) , Dk ≤ Di

•When the error burst hits more than one job

t is the absolute deadline of a task τi

FT-Feasibility: A Sufficient Condition

DBF(t)Tlength

t

Et

Et + DBF(t) ≤ t

Et = Werr(t) + Tlength

Problem Description

Questions:

●How can we perform an FT-feasibility analysis for a given set of temporally redundant real-time tasks under a specified error burst length?

●If the real-time task set is not found to be FT-feasible, what is the lowest processor speed that guarantees its FT-feasibility under the error burst?

Resource Augmentation for FT-feasibility

t

DBF(t)deadline miss

Tlength

S = max{(DBF(t)+ Werr(t) )/ (t -Tlength)}

Is S bounded ?

X + Y’ = Werr(t) /S

S ≤ 6 [ y ≥ 2 => Tlength ≤ Dmin/2 ]

X + Y = Werr(t)

DBF(t)DBF(t)/S

Put Werr(t) = 2DBF(t) and DBF(t) = t

S ≤ 3t/(t - Tlength )

S ≤ 3y/(y-1) [ y = t/ Tlength ]

Summary: Paper D

Fault tolerance feasibility analysis of real-time tasks●A sufficient condition for FT-feasibility

Resource augmentation bounds for FT-feasibility

●Speed-up ≤ 6 if Tlength ≤ Dmin/2

●If there exists a scheduling algorithm that can schedule a given set of real-time tasks on a uni-processor, under an error burst whose length is ≤ Dmin/2, then FT-EDF can schedule it, if given a processor that is 6 times faster.

Conclusions

Main contributions

• Preemption control method using processor speed-up

•Offline method for periodic tasks

•Combined offline-online method for sporadic tasks

• Guarantee specified preemption behavior

•Bounds on the required processor speed-up

•Method to bound the preemption related overheads in the schedule

• A sufficient condition for FT-feasibility

• Bounds on the required processor speed-up that guarantees FT-feasibility

• Quantification of the sub-optimality of non-preemptive scheduling

Future Work

● Extensions to multi-processor scheduling- Non-preemption guarantees

- FT-feasibility

● Utilization based tests- Non-preemptive scheduling

- Fault Tolerance

● Contracts for component based real-time systems- Processor speed-up for non-preemption and FT-feasibility guarantees

● Notion of feasibility: augment the notion of feasibility with the extra resources required

- E.g., Feasibility on m number of speed-s processor

- Presence of runtime overheads

…indeed there is more to life than simply increasing its speed.

Thank You !

Questions ?