Sensitivity Analysis in Real-Time Systems Enrico Bini Scuola - - PDF document

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Enrico Bini

Sensitivity Analysis in Real-Time Systems

ReTiS Lab

Real Time Systems Laboratory Scuola Superiore Sant'Anna

Why Sensitivity Analysis

The scenario in Real-Time System design:

stringent constraints from the hardware (energy

consumption, limited computational power…)

increasing demands from end users (new features,

low prices, short response times, safety,…)

highly competitive market!

Current solution:

The local guru selects a solution, based on its

expertise

The solution is verified, checked, tested and,

eventually, changed

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Current practice in RT Systems Design

select initial values is the system feasible? we can use more resources

YES YES

we must use less resources

NO NO

Goal: selecting the best parameters for optimizing system performance.

The RT system design in the parameter space

NO

param2 param1 utility function

? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?

Where?

YES

initial value

1

p

2

p

3

The ideal design phase

param2 param1 utility function

Problem: the design is made by attempts Ideally we would like…

to know the feasible region to know the utility function to perform the optimization

Challenging aspects

• 1. To highlight variables under the designer's

control.

• 2. Distinguish between cost and constraint.
• 3. Model the resource constraint (or a "suitable"

approximation).

• 4. Model the cost (or a "suitable" error bounded

function).

• 5. Find the optimal solution.

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Questions? Comments?

?

The Application Model

A task τi is modeled by (Ci, Ti, Di), where:

• Ci is the computation time;
• Ti is the period;
• Di is the deadline.

Tasks may be scheduled by

• Fixed Priority (FP), τ1 has the highest

priority;

• Earliest Deadline First (EDF).

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Results for FP

T1 T2

Sensitivity of the computation times Ci

Ci are design variables find the distance to boundary

from an initial value C1 C2

Sensitivity of the periods Ti

given Ci, Di and priorities, and

assuming Ti as design parameters

given an initial value find the distance to boundary

• ptimal

Results for EDF

T1 T2

Sensitivity of the computation times Ci

Ci are design variables find the distance to boundary

from an initial value C1 C2

Sensitivity of the periods Ti

given Ci, Di and priorities, and

assuming Ti as design parameters

given an initial value find the distance to boundary

• ptimal

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Results in Hierarchical Scheduling

T1 T2

Sensitivity of the computation times Ci

Ci are design variables find the distance to boundary

from an initial value C1 C2

Sensitivity of the periods Ti

given Ci, Di and priorities, and

assuming Ti as design parameters

given an initial value find the distance to boundary

• ptimal

Qu

1.

• E. Bini, G. C. Buttazzo, G. M. Buttazzo, "Rate Monotonic Analysis: the

Hyperbolic Bound", IEEE Transactions on Computers, 2003. 2.

• E. Bini, G. Buttazzo, "Schedulability Analysis of Periodic Fixed

Priority Systems", IEEE Transactions on Computers, 2004. 3.

• G. Lipari, E. Bini, "A Methodology for Designing Hierarchical

Scheduled Systems", Journal of Embedded Computing, 2004. 4.

• E. Bini, M. Di Natale, "Optimal Rate Selection in Fixed Priority

Systems", Real-Time Systems Symposium, 2005. 5.

• E. Bini, M. Di Natale, G. Buttazzo "Sensitivity Analysis for Fixed-

Priority Real-Time Systems", Journal of Real-Time Systems, 2007. 6.

• E. Bini, G. Buttazzo, "The Space of EDF Feasible Deadlines",

Euromicro Conference on Real-Time Systems, 2007.