Varying-Speed Processor Sanjoy Baruah and Zhishan Guo Department of - - PowerPoint PPT Presentation

Scheduling Mixed-Criticality Implicit- Deadline Sporadic Task Systems upon a Varying-Speed Processor

Sanjoy Baruah and Zhishan Guo Department of Computer Science, UNC Chapel Hill

The Multi-WCET MC Task Model

• The Liu & Layland (LL) sporadic task model:

Task τi = (ci, Ti)

– Worst-case execution requirement – Minimum inter-arrival separation (period)

• WCET-analysis tools may be more or less conservative
• Example: x := a + b

– 3~321 cycles

ciLO ciHI t Static Analysis Measurement Based

Other Dimensions -- Periods

• The Liu & Layland (LL) sporadic task model:

Task τi = (ci, Ti)

– Worst-case execution requirement – Minimum inter-arrival separation (period)

• Time/Event-triggered periodic tasks

– Fixed/Varying duration between executions – Minimum duration needs to be estimated – Estimations are more or less pessimistic for validating safety-critical or non-critical functions

Other Dimensions -- CPU Speeds

• Advanced hardware features

– Main frequency is forced down when ambient temperature is too high, to prevent permanent damage to the chip.

Other Dimensions -- CPU Speeds

• Advanced hardware features

– Main frequency is forced down when ambient temperature is too high, to prevent permanent damage to the chip. – Detect if signals are late at the circuit level; and recover by delaying next clock tick.

Other Dimensions -- CPU Speeds

• Advanced hardware features

– Main frequency is forced down when ambient temperature is too high, to prevent permanent damage to the chip. – Detect if signals are late at the circuit level; and recover by delaying next clock tick.

• GALS: Globally Asynchronous Locally Synchronous

– locally synchronous modules that communicate asynchronously – local clocks may be paused, stretched, or data-driven

Previous Work

• Multiple dimensions to such MC modeling

– upper bound on the execution time of code – lower bound on the processor speed – lower bound on duration between external interrupts (periods) – …

Previous Work

• Steve Vestal. Preemptive scheduling of multi-criticality systems

with varying degrees of execution time assurance. RTSS 2007.

• Alan Burns and Robert I. Davis. Mixed Criticality Systems - A
• Review. 4th Ed., June 2014. http://www-users.cs.york.ac.uk/burns/review.pdf
• Multiple dimensions to such MC modeling

– upper bound on the execution time of code – lower bound on the processor speed – lower bound on duration between external interrupts (periods) – …

Previous Work

• Sanjoy Baruah and Zhishan Guo. Mixed-criticality scheduling upon

varying-speed processors. RTSS2013.

– Job Set,& dual criticality level – Table driven & LP based – Optimal (w.r.t. processing speeds)

• Zhishan Guo and Sanjoy Baruah. Implementing Mixed-criticality Systems

Upon a Preemptive Varying-speed Processor. LITES, 1(2):3:1 - 3:19, 2014. – Multiple criticality levels + O(n log n) algorithm for the 2-level case

• Multiple dimensions to such MC modeling

– upper bound on the execution time of code – lower bound on the processor speed – lower bound on duration between external interrupts (periods) – …

This Work

• Multiple dimensions to such MC modeling

– upper bound on the execution time of code – lower bound on the processor speed – lower bound on duration between external interrupts (periods) – …

COMBINATION

This Work

• Example: Adaptive Variable-Rate Tasks

– The task activation is triggered at specific rotation angles – Varying rotation speeds lead to varying WCETs & periods

• Multiple dimensions to such MC modeling

– upper bound on the execution time of code – lower bound on the processor speed – lower bound on duration between external interrupts (periods) – …

COMBINATION

Alessandro Biondi, Alessandra Melani, Mauro Marinoni, Marco Di Natale, Giorgio Buttazzo, Exact Interference of Adaptive Variable-Rate Tasks Under Fixed-Priority Scheduling, ECRTS 2014

This Work

• MC implicit-deadline sporadic tasks (multi-WCET)
• Varying-speed uni-processor
• Dual-criticality
• Multiple dimensions to such MC modeling

– upper bound on the execution time of code – lower bound on the processor speed – lower bound on duration between external interrupts (periods) – …

COMBINATION

Model - Varying-Speed Processor

Clock frequency time

Model - Varying-Speed Processor

time Clock frequency

ρ 1

Processor speed ≥ 1 Processor speed < 1, but ≥ ρ Processor speed < ρ

Model - Varying-Speed Processor

Clock frequency

Normal mode Degraded mode Non-functional

time time

ρ 1

Model - Varying-Speed Processor

Normal mode Degraded mode Non-functional

time

May switch mode at any time

ρ 1

Model - Varying-Speed Processor

• It is not a priori known when, or whether, processor

degradation and/or jobs exceeding their LO-WCET estimations will occur (non-clairvoyant).

Normal mode Degraded mode Non-functional

time

May switch mode at any time

ρ 1

ciLO ciHI t

Problem

• MC sporadic task set

– LO-Criticality Behavior Each job signals completion without exceeding ; – HI-Criticality Behavior Each job signals completion without exceeding , some job does not signal completion after executing .

• Varying-speed uni-processor

ciLO ciHI

Normal mode Degraded mode Non-functional

ciLO

Processor speed ≥ 1 Processor speed < 1, but ≥ ρ Processor speed < ρ

Correctness

• MC sporadic task set

– LO-Criticality Behavior Each job signals completion without exceeding ; – HI-Criticality Behavior Each job signals completion without exceeding , some job does not signal completion after executing .

• Varying-speed uni-processor

ciLO ciHI

Normal mode Degraded mode Non-functional

ciLO

AND

Processor speed ≥ 1 Processor speed < 1, but ≥ ρ Processor speed < ρ

Correctness

• MC sporadic task set

– LO-Criticality Behavior Each job signals completion without exceeding ; – HI-Criticality Behavior Each job signals completion without exceeding , some job does not signal completion after executing .

• Varying-speed uni-processor

ciLO ciHI

Normal mode Degraded mode Non-functional

ciLO

OR

Processor speed ≥ 1 Processor speed < 1, but ≥ ρ Processor speed < ρ

Contribution & Related work

• EDF-VD

– Originally designed for Multi-WCET only – [Baruah et al., European Symposium on Algorithms 2011] – [Baruah et al., ECRTS 2012]

• Multi-WCET + Varying-Speed Processor
• VDF - Virtual Deadline First

– Non-Monitoring: VDF-NM, VDF-NM+ – Self-Monitoring: VDF-WM – Correctness, Speedup, Schedulability Experiments

Self-Monitoring: the processor “immediately” knows if and when degradation occurs. Extended

Algorithm - Overview

• VDF - Virtual Deadline First

– Prior to run-time

• Schedulability test
• Virtual deadlines are assigned proportionally to original

deadlines with a common factor x ( 0<x<1 )

– During run-time

• EDF -- assigned virtual deadlines
• Revert to original deadlines when a HI-criticality behavior is

detected , and drop LO-criticality tasks

Algorithm - Example

ρ = 0.5,

I ciLO ciHI pi (di) χi τLO 1 1 2 (2) LO τHI 2 3 10 (10) HI

t

τLO τHI

t 10 20 10 20

Algorithm - Example

ρ = 0.5, x=0.4

I ciLO ciHI pi (di’) χi τLO 1 1 2 (2) LO τHI 2 3 10 (4) HI

t

τLO τHI

t 10 20 10 20

Algorithm - Example

• During Run-Time

– When NO HI-Criticality Behavior is detected…

ρ = 0.5, x=0.4

I ciLO ciHI pi (di’) χi τLO 1 1 2 (2) LO τHI 2 3 10 (4) HI

t 10 20 13

Algorithm - Example

ρ = 0.5, x=0.4

I ciLO ciHI pi (di’) χi τLO 1 1 2 (2) LO τHI 2 3 10 (4) HI

t 10 20

HI-Criticality Behavior DETECTED at t=13

13

• During Run-Time

– When HI-Criticality Behavior is detected… time time

Algorithm - Monitor

ρ = 0.5, x=0.4

I ciLO ciHI pi (di’) χi τLO 1 1 2 (2) LO τHI 2 3 10 (4) HI

t 10 20

HI-Criticality Behavior DETECTED at t=13 for NON-MONITORING system

13

• During Run-Time

– When HI-Criticality Behavior is detected…

VDF-NM, VDF-NM+ Self-Monitoring: the processor “immediately” knows if and when degradation occurs, which may lead to EARLIER detection of HI-Criticality Behavior VDF-WM

Algorithm - VDF-NM & VDF-NM+

• VDF - Virtual Deadline First

– Prior to run-time

• Schedulability test
• Virtual deadlines are assigned proportionally to original

deadlines with a common factor x ( 0<x<1 )

t

τLO τHI

t

Task Set with Constrained Deadlines VDF-NM: Density Based Schedulability Test VDF-NM+: PTAS, for any desired degree of accuracy EDF-schedulability checked by binary search of x in (0,1) VDF-WM: Density Based Schedulability Test

Experiments

VDF-NM: VDF-NM+: VDF-WM:

Experiments

VDF-NM: VDF-NM+: VDF-WM:

Experiments

x

VDF-NM: VDF-NM+: VDF-WM: Among the 1000 generated task sets with utilizations of 0.7, about 66% of them passed the schedulability test for VDF-WM.

Experiments

VDF-NM: VDF-NM+: VDF-WM:

Outline

• Motivation
• Model
• Problem Description
• Algorithm
• Schedulability Experiments
• Conclusion and further work

Conclusion

• Model

– Multi-WCET mixed-criticality sporadic task set with implicit deadlines – Platforms with varying-speed performance during run-time

Conclusion

• Model

– Multi-WCET mixed-criticality sporadic task set with implicit deadlines – Platforms with varying-speed performance during run-time

• Algorithms

– VDF-NM, VDF-NM+, VDF-WM – Correctness and Sufficient Constraints – Speedup Bound of 1.618 – Schedulability Experiments

Measurement

• Speedup Bound
• Given any MC task system τ

Any Hypothetical Clairvoyant Algorithm

Speed ≥ 1 Speed < 1, but ≥ ρ

Correct

Measurement

• Speedup Bound
• Given any MC task system τ

Algorithm A (with speedup b≥1) Any Hypothetical Clairvoyant Algorithm

Speed ≥ 1 Speed < 1, but ≥ ρ Speed ≥ b Speed < b, but ≥ ρ b

Correct Correct

Further Work

• Tightness for speedup bound (1.618)

– Or a smaller speedup bound (1.333) ?

Further Work

• Tightness for speedup bound?
• Multi-Processor

– Heterogeneous System – Define Degraded?

Process speed < 1, but ≥ ρ Zhishan Guo and Sanjoy Baruah. Mixed-criticality scheduling upon varying-speed multiprocessors. EmbeddedCom 2014.

Clock frequency

Further Work

• Tightness for speedup bound?
• Multi-Processor
• Multiple levels of criticality

– More than two thresholds for processor speeds

time

sn sd sf Normal mode ≥2 Degraded modes Non-functional

Thank you!

Zhishan Guo zsguo@cs.unc.edu

Relationship with prior work

• Multi-WCET task model (previous works)
• Ji - (ai, di, [ciHI, ciLO], χi)
• Execution speed = 1
• Varying-speed model
• Ji - (ai, di, ci, χi), sn, sd
• E.g.,

ciLO ciHI t ci t ? t s(t) 1 0.5 ci

ci/sd

t 1 0.5 ci s(t)

ci/sn

t 1 0.5 ci s(t)

A slower processor can be transformed into longer WCET

Mixed-Criticality

• Modern safety-critical systems…

– are very complex – are implemented upon non-deterministic platforms – need rigorous correctness proofs

• Need significant resource over-provisioning, which leads to

highly inefficient resource usage at run-time!

• Real-time systems should be correct and have efficient

implementations:

• safety-critical: correctness matters -> rigorous design methodologies
• resource-constrained platforms: need efficient implementation ->

scheduling theory

• Scheduling penalty increases with

system complexity -- SWaP

Mixed-Criticality

• Modern safety-critical systems…

Need significant resource over-provisioning, which leads to highly inefficient resource usage at run-time!

• Scheduling theory is applied to models… that are conservative
• Performance penalties due to being conservative are increasing
• Critical and non-critical functions co-exist
• MC Scheduling: two independent analyses of a single system
• Validate safety-critical functionalities using conservative

approximations

• Validate all functionalities using less pessimistic approximations
• x := a + b Best case: 3 cycles

Worst case: 321 cycles

Mixed-Criticality

• The analysis of Mixed-Criticality embedded systems has been

identified as one of the core foundational focal areas in the emerging discipline of Cyber-Physical Systems, including:

• automotive systems;
• avionics;
• medical devices
• intelligent highways;
• next-generation ATC;
• smart grid
• …