Task Mapping and Bandwidth Reservation for Mixed Hard/Soft Fault-Tolerant Embedded Systems

Task Mapping and Bandwidth Reservation forMixed Hard/Soft Fault-Tolerant Embedded Systems

Prabhat Kumar SaraswatPaul PopJan Madsen

16th IEEE Real-Time and Embedded Technology and Applications Symposium

April 14, 2010, Stockholm, Sweden

2 DTU Informatics, Technical University of Denmark

Introduction• Trend: Integration of different

applications on the same platform

• Critical (e.g., ABS)– Deadline miss – catastrophe – Based on worst-case assumptions

• Best effort (e.g., multimedia)– Deadline miss – performance degradation – Variability in execution times– Worst-case leads to overdesign

• Bridging the gap: partitioned architectures

• Fault tolerance


Problem Description

• Given: A mixed hard/soft fault-tolerant application and a distributed platform

• Determine: Mapping and Utilization

• Such that:– Deadlines for all hard real-time tasks are satisfied (Even in

case of faults)– Probability of meeting of deadline for soft tasks is maximized

Soft Task

Hard Task

Utilization?Mapping?

Application Platform

k transient faults

?

??

?

??

?


Application Model

Hard real-time tasks

WCET Deadline Period

Soft real-time tasks

Pro

babili

tyExecution Time

PDF

Deadline

Period

Periodic

• Set of tasks• Mixed task set – Hard and Soft tasks• All tasks are periodic• Tasks can tolerate transient or no faults


Constant Bandwidth Server• Temporal partitioning of hard/soft tasks.

– Each soft task is assigned a CBS with parameters:

• Qi – maximum server budget

(bandwidth)

• Ti – server period (period of the

soft task)

– A soft task is allowed to execute for only Qi units of time every period Ti

– Hard tasks and CBS servers execute under EDF

– Probability of meeting the deadline (QoS) depends on Qi

Processor

Hard

Soft

Util.


3

2 4 6 8 10 12 14 16 18 20 22

2+72 2+7+7 2+7+7+71

HardWCET=2Period=3

Soft task

CBSBandwidth = 2

Period = 7

CBS Example [Abeni 98]


Platform Model

A

τ12 τ1

2

With checkpointing

and fault recovery

Checkpointing Overhead

Error Detection Overhead

Recovery Overhead

τ1

Execution Segment

Without checkpointing

τ11

Fault model

•Equidistant checkpointing with rollback recovery

•Execution of task is divided into segments

•After each segment checkpoints (state of a task) are stored in a stable storage

•In case of fault, the state is restored from the stored checkpoint


Schedulability analysis• Utilization based test is used to check if the task set mapped on a

processor is schedulable

• Sum of utilizations of the following:– Hard tasks

• Considering checkpointing overheads

– Soft tasks• CBS parameters – Server budget and the period

– Recovery Utilization• Utilization needed to recover the hard tasks incase of faults

considering worst case scenario


Stochastic Analysis

• CBS server is modeled as a queue

• A request of Ck units arrives every Ti units of time.

• At most Qi units can be served every Ti units

• The probability that a job Jk finishes before its deadline is related to Vk

• Vk (the length of queue at kTi) is a Markov Chain describing the system

• A stationary solution for the state probability vector of Vk is calculated

• QoS is calculated from this stationary solution

Qi

Execution time

Pro

bab

ilit

y

Vk = max{0,Vk-1 – Qi} + cj


Bandwidth Allocation using PDFs

0

0.25

0.5

0.75

1

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80

Allocated processor bandwidth value (Q)

Qo

S

Task

Task

Initial

AET

QoS74.50

PDFs

QoS94.74

Utilization for Hard tasks

Spare Utilization

Uti

l. =

1

WCET

Over design!Implementation not

possible

(49.02%, 23)

(99.98%, 37)

AET

(99.98%, 22)

(89.50%, 38)

PDFs

Using PDFs

better design decisions

can be taken

(40) (60) (80)(11) (17)

period = 100

Naive approach:•Allocate Q proportional to their AETs

For 1

Util = 11/(11+17) x 0.6

For 2Util = 17/(11+17) x 0.6


Mapping Example

Optimal solution using PDFsQoS: 94.22 %

P5

N1

6

55

17

55

23

45

P5

N2

17

55

26

55

10

65

N1

Optimal solution using AETs

P5

9

55

15

55

23

45

P5

N2

19

55

24

55

10

65

QoS: 72.10 %

TaskWCET

N1 N2

23 25

8 10

TaskAET

N1 N2

5 8

10 12

14 15

17 20

WCET

Period

Q

Periodi

i


Tabu Search Mapping and Bandwidth Allocation (TSMBA) • Iterative exploration of design space• Use of Tabu List to avoid revisiting of already explored solutions• TSMBA

– Takes as input, the application and the architecture model– An initial solution, can be unschedulable – Produces a solution containing

• Mapping for all tasks• Set of bandwidth values for all soft tasks

• Solutions are evaluated on the basis of this Cost function:

• Minimize cost function = Schedulable solutions and Maximized QoS


Tabu Search - Moves

Diversification move – mapping and bandwidth for all tasks are changed

τ1

τ2 τ5

τ3

τ4 τ6

τ1 6τ2 11τ3 16τ4 21

QoS: 63%

τ2 τ5

τ3

τ4 τ6

τ1 6τ2 11τ3 16τ4 21

QoS: 48%

mapping move

τ1

τ2 τ5

τ3

τ4 τ6

τ1 6τ2 15τ3 16τ4 21

QoS: 71%

τ1

bandwidth move

τ1

N1 N2

N1 N2N1 N2


Experimental Setup• Proposed optimizing strategy (TSMBA) vs straightforward (SF) strategy• SF strategy

– Used when only AETs are available, not PDFs– Maximizing the difference between allocated Q value and AET for all

soft tasks– Cost Function avg / dev

• Generated synthetic benchmarks:– PDFs to match the shape of real-life benchmarks

• Messages (bus utilization should not be greater than 1, non preemptive EDF)

• Assume that all half of the hard tasks are safety critical

AET WCETAllocated Qavg


Experimental results

Synthetic benchmarks

• QoS resulted by TSMBA is better than SF on an average of 29.60%• TSMBA finds schedulable solutions much earlier than SF approach


Experimental results

Real-life benchmarks

• QoS resulted by TSMBA is better than SF on an average of 28.04%


Conclusions• A Tabu Search based heuristic is proposed to perform design

optimizations

• Results in implementation where deadlines of hard tasks are satisfied (even in case of faults) and QoS for soft tasks is maximized

• Better design choices can be made by taking stochastic execution times of soft tasks into consideration.


Thanks

Questions?

Documents

Task Mapping and Bandwidth Reservation for Mixed Hard/Soft Fault-Tolerant Embedded Systems