Evaluation of Runtime Monitoring Methods for Real-Time ... · Real-time system at runtime Why real-time system needs to be monitored? All inputs are assumed as the design speci cations

Evaluation of Runtime Monitoring Methods forReal-Time Event Streams

Biao Hu, Dr. Kai Huang, Gang Chen,Prof. Dr. Alois Knoll

Technische Universitat MunchenDepartment of Informatics

Robotics and Embedded Systems

Jan. 21. 2015

Biao Hu 1 / 31

Overview

1 Motivation

2 Background

3 ComparisonComparison based on standard arrival curvesComparison based on complex arrival curves

4 FPGA evaluations

5 Summary

Biao Hu 2 / 31

Outline

1 Motivation

2 Background


4 FPGA evaluations

5 Summary

Biao Hu 3 / 31

Motivation

Real-time system at runtime

Why real-time system needs to be monitored?

All inputs are assumed as the design specifications

The increasing complexity of system

Unexpected runtime behaviors happen

Monitor is used to guarantee the system runtime behaviors

What monitors do?

System events are monitored

Violation is reported by the monitor

Biao Hu 4 / 31

Motivation







What monitors do?



Biao Hu 4 / 31

Motivation







What monitors do?



Biao Hu 4 / 31

Motivation







What monitors do?



Biao Hu 4 / 31

Motivation







What monitors do?



Biao Hu 4 / 31

Motivation







What monitors do?



Biao Hu 4 / 31

Motivation







What monitors do?



Biao Hu 4 / 31

Subject of this paper

State-of-art

Dynamic counters (Kai et.al, 2011)

l-repetitive function (Neukirchner et.al, 2012)

Contributions

Analyzed the differences of dynamic counters and l-repetitivefunction

Developed a new approach to apply dynamic counters tomonitor periodic-burst events

Prototyped hardware implementations on FPGA andpresented FPGA resource usage

Biao Hu 5 / 31


State-of-art



Contributions




Biao Hu 5 / 31


State-of-art



Contributions




Biao Hu 5 / 31


State-of-art



Contributions




Biao Hu 5 / 31


State-of-art



Contributions




Biao Hu 5 / 31


State-of-art



Contributions




Biao Hu 5 / 31


State-of-art



Contributions




Biao Hu 5 / 31

Outline

1 Motivation

2 Background


4 FPGA evaluations

5 Summary

Biao Hu 6 / 31

Arrival Curve (Modular Performance Analysis)

Arrival curve: Event stream model,

αl(t − s) ≤ R[s, t) ≤αu(t − s), ∀t ≥ s ≥ 0, where

R[s, t) denote the number of events

in the time interval s ≤ τ < t.

System view of the M-JPEG

encoder

The corresponding RTC-MPA modelBiao Hu 7 / 31

Arrival Curve (Modular Performance Analysis)Arrival curve: Event stream model,

αl(t − s) ≤ R[s, t) ≤αu(t − s), ∀t ≥ s ≥ 0, where

R[s, t) denote the number of events

in the time interval s ≤ τ < t.

System view of the M-JPEG

encoder

The corresponding RTC-MPA modelBiao Hu 7 / 31

Distance Function (Compositional Performance Analysis)

Minimum/maximum distance function

The minimum distance function dmin(n) specifies the minimum distance

between n + 1 consecutive events in an event stream.

The maximum distance function dmin(n) specifies the maximum distance


An example: periodic events with jitter

Arrival Curve

(a) Upper Arrival Curves : αu(∆) = b∆+Jδ c

(b) Lower Arrival Curves : αl(∆) = max{0, b∆−Jδ c

Distance Function

(a) Minimum Distance Functions : dmin(n) = max{0, n · δ − J}(b) Maximum Distance Functions : dmax(n) = n · δ + J

Biao Hu 8 / 31








Arrival Curve



Distance Function


Biao Hu 8 / 31








Arrival Curve



Distance Function


Biao Hu 8 / 31

Dynamic counter

Assumption

Any monotonous and time-invariant arrival curve can be conservativelyapproximated as the minimum on a set of staircase functions with theform αu

i (∆) = Nui + b∆

δic.

∀∆ ∈ R≥0 : αu(∆) ≥ mini=1..n

(αui (∆))

Method: one dynamic counter is responsible for monitoringone staircase function

DC1 ↔ α1

DC2 ↔ α2

DC3 ↔ α3

min(DC1,DC2,DC3) ↔min(α1, α2, α3)

Biao Hu 9 / 31

Dynamic counter

Assumption


i (∆) = Nui + b∆

δic.

∀∆ ∈ R≥0 : αu(∆) ≥ mini=1..n

(αui (∆))


DC1 ↔ α1

DC2 ↔ α2

DC3 ↔ α3


Biao Hu 9 / 31

Dynamic counter

Assumption


i (∆) = Nui + b∆

δic.

∀∆ ∈ R≥0 : αu(∆) ≥ mini=1..n

(αui (∆))


DC1 ↔ α1

DC2 ↔ α2

DC3 ↔ α3


Biao Hu 9 / 31

Dynamic counter

Assumption


i (∆) = Nui + b∆

δic.

∀∆ ∈ R≥0 : αu(∆) ≥ mini=1..n

(αui (∆))


DC1 ↔ α1

DC2 ↔ α2

DC3 ↔ α3


Biao Hu 9 / 31

Dynamic counter

Assumption


i (∆) = Nui + b∆

δic.

∀∆ ∈ R≥0 : αu(∆) ≥ mini=1..n

(αui (∆))


DC1 ↔ α1

DC2 ↔ α2

DC3 ↔ α3


Biao Hu 9 / 31

Dynamic counter

Assumption


i (∆) = Nui + b∆

δic.

∀∆ ∈ R≥0 : αu(∆) ≥ mini=1..n

(αui (∆))


DC1 ↔ α1

DC2 ↔ α2

DC3 ↔ α3


Biao Hu 9 / 31

l-repetitive function

DefinitionA l-repetitive function is a special minimum distance function that

satisfies: d(n) =

dn(given), n ≤ l ,

maxω∈[1,l ]

(d(ω) + d(n − ω)), n > l .

Method: by constructing l-repetitive function, only the arrivaltime of most recent l events needs to be kept.

current time - trace buffer[1] < d1




Biao Hu 10 / 31



satisfies: d(n) =


maxω∈[1,l ]

(d(ω) + d(n − ω)), n > l .






b

b

b

b

b

b

b

b

1ms

2ms

3ms

4ms

5ms

6ms

7ms

8ms

9ms

10ms

11ms

12ms

1 2 3 4 5 6 7 8

d(n)

n

1

Biao Hu 10 / 31



satisfies: d(n) =


maxω∈[1,l ]

(d(ω) + d(n − ω)), n > l .






b

b

b

b

b

b

b

b

1ms

2ms

3ms

4ms

5ms

6ms

7ms

8ms

9ms

10ms

11ms

12ms

1 2 3 4 5 6 7 8

d(n)

nd1

d1

1

Biao Hu 10 / 31



satisfies: d(n) =


maxω∈[1,l ]

(d(ω) + d(n − ω)), n > l .






b

b

b

b

b

b

b

b

1ms

2ms

3ms

4ms

5ms

6ms

7ms

8ms

9ms

10ms

11ms

12ms

1 2 3 4 5 6 7 8

d(n)

nd1

d2

d1d2

1

Biao Hu 10 / 31



satisfies: d(n) =


maxω∈[1,l ]

(d(ω) + d(n − ω)), n > l .






b

b

b

b

b

b

b

b

1ms

2ms

3ms

4ms

5ms

6ms

7ms

8ms

9ms

10ms

11ms

12ms

1 2 3 4 5 6 7 8

d(n)

nd1

d2d3

d1d2

d3

1

Biao Hu 10 / 31



satisfies: d(n) =


maxω∈[1,l ]

(d(ω) + d(n − ω)), n > l .





current time - trace buffer[4] < d4b

b

b

b

b

b

b

b

1ms

2ms

3ms

4ms

5ms

6ms

7ms

8ms

9ms

10ms

11ms

12ms

1 2 3 4 5 6 7 8

d(n)

nd1

d2d3

d4

d1d2

d3

d4

1

Biao Hu 10 / 31

Outline

1 Motivation

2 Background


4 FPGA evaluations

5 Summary

Biao Hu 11 / 31

Standard arrival events (Richter et al., 2003)

Periodic events, Sporadic events, Periodic events withjitter,Periodic burst events.

1

2

3

4

δ 2δ 3δ 4δ

#event

∆0

αu(∆)

αl(∆)

1

1

2

3

4

d− 2d− 3d− 4d−

#event

∆0

αu(∆)

αl(∆)

1

1

2

3

4

δ 2δ 3δ 4δ

#event

∆0

αu(∆)

αl(∆)

1

123456

δ 2δ 3δ 4δ 5δ 6δ 7δ 8δ 9δ10δ

#event

∆0

αu(∆)

αl(∆)

1

Periodic events & Sporadic events

1 Periodic events

Arrival Curve: αu(∆) = d∆δ e, only needs one dynamic counter

Minimum Distance Function: d(n) = n · δ, l = 1.

2 Sporadic events

Arrival Curve: αu(∆) = d ∆d− e, only needs one dynamic counter

Minimum Distance Function: d(n) = n · d−, l = 1.

Biao Hu 12 / 31



1

2

3

4

δ 2δ 3δ 4δ

#event

∆0

αu(∆)

αl(∆)

1

1

2

3

4

d− 2d− 3d− 4d−

#event

∆0

αu(∆)

αl(∆)

1

1

2

3

4

δ 2δ 3δ 4δ

#event

∆0

αu(∆)

αl(∆)

1

123456

δ 2δ 3δ 4δ 5δ 6δ 7δ 8δ 9δ10δ

#event

∆0

αu(∆)

αl(∆)

1


1 Periodic events



2 Sporadic events



Biao Hu 12 / 31



1

2

3

4

δ 2δ 3δ 4δ

#event

∆0

αu(∆)

αl(∆)

1

1

2

3

4

d− 2d− 3d− 4d−

#event

∆0

αu(∆)

αl(∆)

1

1

2

3

4

δ 2δ 3δ 4δ

#event

∆0

αu(∆)

αl(∆)

1

123456

δ 2δ 3δ 4δ 5δ 6δ 7δ 8δ 9δ10δ

#event

∆0

αu(∆)

αl(∆)

1


1 Periodic events



2 Sporadic events



Biao Hu 12 / 31



1

2

3

4

δ 2δ 3δ 4δ

#event

∆0

αu(∆)

αl(∆)

1

1

2

3

4

d− 2d− 3d− 4d−

#event

∆0

αu(∆)

αl(∆)

1

1

2

3

4

δ 2δ 3δ 4δ

#event

∆0

αu(∆)

αl(∆)

1

123456

δ 2δ 3δ 4δ 5δ 6δ 7δ 8δ 9δ10δ

#event

∆0

αu(∆)

αl(∆)

1


1 Periodic events



2 Sporadic events



Biao Hu 12 / 31



1

2

3

4

δ 2δ 3δ 4δ

#event

∆0

αu(∆)

αl(∆)

1

1

2

3

4

d− 2d− 3d− 4d−

#event

∆0

αu(∆)

αl(∆)

1

1

2

3

4

δ 2δ 3δ 4δ

#event

∆0

αu(∆)

αl(∆)

1

123456

δ 2δ 3δ 4δ 5δ 6δ 7δ 8δ 9δ10δ

#event

∆0

αu(∆)

αl(∆)

1


1 Periodic events



2 Sporadic events



Biao Hu 12 / 31



1

2

3

4

δ 2δ 3δ 4δ

#event

∆0

αu(∆)

αl(∆)

1

1

2

3

4

d− 2d− 3d− 4d−

#event

∆0

αu(∆)

αl(∆)

1

1

2

3

4

δ 2δ 3δ 4δ

#event

∆0

αu(∆)

αl(∆)

1

123456

δ 2δ 3δ 4δ 5δ 6δ 7δ 8δ 9δ10δ

#event

∆0

αu(∆)

αl(∆)

1


1 Periodic events



2 Sporadic events



Biao Hu 12 / 31



1

2

3

4

δ 2δ 3δ 4δ

#event

∆0

αu(∆)

αl(∆)

1

1

2

3

4

d− 2d− 3d− 4d−

#event

∆0

αu(∆)

αl(∆)

1

1

2

3

4

δ 2δ 3δ 4δ

#event

∆0

αu(∆)

αl(∆)

1

123456

δ 2δ 3δ 4δ 5δ 6δ 7δ 8δ 9δ10δ

#event

∆0

αu(∆)

αl(∆)

1


1 Periodic events



2 Sporadic events



Biao Hu 12 / 31



1

2

3

4

δ 2δ 3δ 4δ

#event

∆0

αu(∆)

αl(∆)

1

1

2

3

4

d− 2d− 3d− 4d−

#event

∆0

αu(∆)

αl(∆)

1

1

2

3

4

δ 2δ 3δ 4δ

#event

∆0

αu(∆)

αl(∆)

1

123456

δ 2δ 3δ 4δ 5δ 6δ 7δ 8δ 9δ10δ

#event

∆0

αu(∆)

αl(∆)

1


1 Periodic events



2 Sporadic events



Biao Hu 12 / 31

Periodic events with jitter

Definition

1 Arrival Curve: α(∆) = d∆+Jδ e = N + b∆+J′

δ c, (0 < J ′ < δ)

2 dmin(n) = max{0, n · δ − J}When J is greater than δ, an initial burst N happens.

1

2

3

4

5

δ 2δ 3δ 4δ

#event

∆0 δ − J

α = 1 + ⌊∆+Jδ ⌋

α = 1 + ⌊∆δ ⌋

1

b

b

b

b

b

ut

ut

ut

ut

ut

δ

2δ

2δ

4δ

1 2 3 4 5

d(n)

n

δ − J

0

1

Biao Hu 13 / 31


Definition


δ c, (0 < J ′ < δ)


1

2

3

4

5

δ 2δ 3δ 4δ

#event

∆0 δ − J

α = 1 + ⌊∆+Jδ ⌋

α = 1 + ⌊∆δ ⌋

1

b

b

b

b

b

ut

ut

ut

ut

ut

δ

2δ

2δ

4δ

1 2 3 4 5

d(n)

n

δ − J

0

1

Biao Hu 13 / 31


Definition


δ c, (0 < J ′ < δ)

2 dmin(n) = max{0, n · δ − J}

When J is greater than δ, an initial burst N happens.

1

2

3

4

5

δ 2δ 3δ 4δ

#event

∆0 δ − J

α = 1 + ⌊∆+Jδ ⌋

α = 1 + ⌊∆δ ⌋

1

b

b

b

b

b

ut

ut

ut

ut

ut

δ

2δ

2δ

4δ

1 2 3 4 5

d(n)

n

δ − J

0

1

Biao Hu 13 / 31


Definition


δ c, (0 < J ′ < δ)


1

2

3

4

5

δ 2δ 3δ 4δ

#event

∆0 δ − J

α = 1 + ⌊∆+Jδ ⌋

α = 1 + ⌊∆δ ⌋

1

b

b

b

b

b

ut

ut

ut

ut

ut

δ

2δ

2δ

4δ

1 2 3 4 5

d(n)

n

δ − J

0

1

Biao Hu 13 / 31


Definition


δ c, (0 < J ′ < δ)


1

2

3

4

5

δ 2δ 3δ 4δ

#event

∆0 δ − J

α = 1 + ⌊∆+Jδ ⌋

α = 1 + ⌊∆δ ⌋

1

b

b

b

b

b

ut

ut

ut

ut

ut

δ

2δ

2δ

4δ

1 2 3 4 5

d(n)

n

δ − J

0

1

Biao Hu 13 / 31


Definition


δ c, (0 < J ′ < δ)


The jitter always exist when using dynamic counters orl -repetitive function

1 Only one dynamic counter

2 l = 1 for l-repetitive function

Biao Hu 14 / 31

Periodic burst events

0

123b56789

#Events

(b− 1)d 2δδ ∆

1

Definition

αu(∆) = b∆δ cb + min(d∆−d∆

δ ebd e, b)

where d is the minimum timing

separation, b is the maximum events

within an interval δ.

Monitoring method

1 l-repetitive function: l = b

2 dynamic counters: ?

Biao Hu 15 / 31

Periodic burst events

0

123b56789

#Events

(b− 1)d 2δδ ∆

1

Definition

αu(∆) = b∆δ cb + min(d∆−d∆

δ ebd e, b)

where d is the minimum timing

separation, b is the maximum events

within an interval δ.

Monitoring method

1 l-repetitive function: l = b

2 dynamic counters: ?

Biao Hu 15 / 31

Dynamic counters

Periodic burst is equivalent to a staircase function with aperiod d , and the constraint of b staircase functions with aperiod of δ.

Biao Hu 16 / 31

Dynamic counters

0

123b56

#Events

(b− 1)d δ ∆

=

0

123b56

#Events

(b− 1)d ∆ 0

123b56

#Events

δ ∆

∧ b ×

1


Biao Hu 16 / 31

Dynamic counters

0

123b56

#Events

(b− 1)d δ ∆

=

0

123b56

#Events

(b− 1)d ∆ 0

123b56

#Events

δ ∆

∧ b ×

1


Biao Hu 16 / 31

A case study of monitoring periodic burst by dynamiccounters

Periodic burst is equivalent to a staircase function with a period d , and

the constraint of b staircase functions with a period of δ.

A case simulation: b = 6, δ = 180, and d = 20

Biao Hu 17 / 31

A case study of monitoring periodic burst by dynamiccounters

Periodic burst is equivalent to a staircase function with a period d , and

the constraint of b staircase functions with a period of δ.

A case simulation: b = 6, δ = 180, and d = 20

0 50 100 150 200 2500

2

4

6

8

10

∆[µs]

#eve

nt

αuPB

R

R*

VD

(e1, e2, e3)

e∗

1

e∗

2

e∗

3

Biao Hu 17 / 31

Complex arrival curve of Type 1

Arrival curve is the minimum of a set of staircase functions, i.e.,

αu = mini=1:n{αu

i }, where αi = Nui + b∆

δic (Nu

i < Nui+1, δi < δi+1)

1 Dynamic counters: n counters

2 l-repetitive function: ?

Biao Hu 18 / 31


1

2

3

4

5

6

7

1 2 3 4 5 6 7 8 9 10 11 12

#event

∆

αu = mini=1:n

{αui }

1


αu = mini=1:n{αu


δic (Nu

i < Nui+1, δi < δi+1)



Biao Hu 18 / 31


1

2

3

4

5

6

7

1 2 3 4 5 6 7 8 9 10 11 12

#event

∆

αu = mini=1:n

{αui }

1


αu = mini=1:n{αu


δic (Nu

i < Nui+1, δi < δi+1)



Biao Hu 18 / 31


1

2

3

4

5

6

7

1 2 3 4 5 6 7 8 9 10 11 12

#event

∆

αu = mini=1:n

{αui }

1


αu = mini=1:n{αu


δic (Nu

i < Nui+1, δi < δi+1)



Biao Hu 18 / 31


1

2

3

4

5

6

7

1 2 3 4 5 6 7 8 9 10 11 12

#event

∆

αu = mini=1:n

{αui }

1

For l-repetitive function

1 Assume the repetitive segment is αgl that is given in the

offline analysis. αl(∆) =

{αgl (∆)(given), if ∆ ≤ dl ,

αgl (∆− k · dl), if ∆ > dl .

2 lim∆=+∞

{ mini=1..n

{αi}(∆)− αl(∆)} = Nux + b ∆

δmaxc − ∆

dll ≥ 0. ⇒

dl ≥ l · δmax .

Biao Hu 19 / 31


1

2

3

4

5

6

7

1 2 3 4 5 6 7 8 9 10 11 12

#event

∆

αu = mini=1:n

{αui }

1

1

2

3

4

5

6

7

1 2 3 4 5 6 7 8 9 10 11 12

#event

∆

αu = mini=1:n

{αui }

αl

dl

l

αgl (given)

1





αgl (∆− k · dl), if ∆ > dl .

2 lim∆=+∞

{ mini=1..n

{αi}(∆)− αl(∆)} = Nux + b ∆

δmaxc − ∆

dll ≥ 0. ⇒

dl ≥ l · δmax .

Biao Hu 19 / 31


1

2

3

4

5

6

7

1 2 3 4 5 6 7 8 9 10 11 12

#event

∆

αu = mini=1:n

{αui }

1

1

2

3

4

5

6

7

1 2 3 4 5 6 7 8 9 10 11 12

#event

∆

αu = mini=1:n

{αui }

αl

dl

l

αgl (given)

1





αgl (∆− k · dl), if ∆ > dl .

2 lim∆=+∞

{ mini=1..n

{αi}(∆)− αl(∆)} = Nux + b ∆

δmaxc − ∆

dll ≥ 0. ⇒

dl ≥ l · δmax .

Biao Hu 19 / 31


1

2

3

4

5

6

7

1 2 3 4 5 6 7 8 9 10 11 12

#event

∆

αu = mini=1:n

{αui }

αl

dl

l

αgl (given)

1


1 Error percent (EP): EP(∆) =∫ ∆

0 (αu(t)−αa(t))dt∫ ∆0 αu(t)dt

.

Biao Hu 20 / 31


1

2

3

4

5

6

7

1 2 3 4 5 6 7 8 9 10 11 12

#event

∆

αu = mini=1:n

{αui }

αl

dl

l

αgl (given)

1

1

2

3

4

5

6

7

1 2 3 4 5 6 7 8 9 10 11 12

#event

∆

αu = mini=1:n

{αui }

αl

dl

l

αgl (given)

error

1



0 (αu(t)−αa(t))dt∫ ∆0 αu(t)dt

.

Biao Hu 20 / 31


Arrival curve is segmentally repetitive, and each segment is sub-additive,

i.e., αl(∆) =


αgl (∆− k · dl), if ∆ > dl .

1 Dynamic counters: ?

2 l-repetitive function: l

Biao Hu 21 / 31


1

2

3

4

5

6

7

1 2 3 4 5 6 7 8 9 10 11 12

#event

∆

αl

dl

l

αgl (given)

1


i.e., αl(∆) =


αgl (∆− k · dl), if ∆ > dl .



Biao Hu 21 / 31


1

2

3

4

5

6

7

1 2 3 4 5 6 7 8 9 10 11 12

#event

∆

αl

dl

l

αgl (given)

1


i.e., αl(∆) =


αgl (∆− k · dl), if ∆ > dl .



Biao Hu 21 / 31


1

2

3

4

5

6

7

1 2 3 4 5 6 7 8 9 10 11 12

#event

∆

αl

dl

l

αgl (given)

1


i.e., αl(∆) =


αgl (∆− k · dl), if ∆ > dl .



Biao Hu 21 / 31


1

2

3

4

5

6

7

1 2 3 4 5 6 7 8 9 10 11 12

#event

∆

αl

dl

l

αgl (given)

1

For dynamic counters

1 Assume a set of staircase functions ( mini=1..n

{αi},αi = Nu

i + b∆δic) is used to approximate αl , where

δmax = maxi=1..n

{δi}.

2 lim∆=+∞

{ mini=1..n

{αl(∆)− αi}(∆)} = ∆dll − Nu

x − b ∆δmaxc ≥ 0 ⇒

dl <= l · δmax .

Biao Hu 22 / 31


1

2

3

4

5

6

7

1 2 3 4 5 6 7 8 9 10 11 12

#event

∆

αl

dl

l

αgl (given)

1

1

2

3

4

5

6

7

1 2 3 4 5 6 7 8 9 10 11 12

#event

∆

αu = mini=1:n

{αui }

αl

dl

l

αgl (given)

1



{αi},αi = Nu


δmax = maxi=1..n

{δi}.

2 lim∆=+∞

{ mini=1..n

{αl(∆)− αi}(∆)} = ∆dll − Nu

x − b ∆δmaxc ≥ 0 ⇒

dl <= l · δmax .

Biao Hu 22 / 31


1

2

3

4

5

6

7

1 2 3 4 5 6 7 8 9 10 11 12

#event

∆

αl

dl

l

αgl (given)

1

1

2

3

4

5

6

7

1 2 3 4 5 6 7 8 9 10 11 12

#event

∆

αu = mini=1:n

{αui }

αl

dl

l

αgl (given)

1



{αi},αi = Nu


δmax = maxi=1..n

{δi}.

2 lim∆=+∞

{ mini=1..n

{αl(∆)− αi}(∆)} = ∆dll − Nu

x − b ∆δmaxc ≥ 0 ⇒

dl <= l · δmax .

Biao Hu 22 / 31


1

2

3

4

5

6

7

1 2 3 4 5 6 7 8 9 10 11 12

#event

∆

αu = mini=1:n

{αui }

αl

dl

l

αgl (given)

1



0 (αl (t)−αa(t))dt∫ ∆0 αl (t)dt

.

Biao Hu 23 / 31


1

2

3

4

5

6

7

1 2 3 4 5 6 7 8 9 10 11 12

#event

∆

αu = mini=1:n

{αui }

αl

dl

l

αgl (given)

1

1

2

3

4

5

6

7

1 2 3 4 5 6 7 8 9 10 11 12

#event

∆

αu = mini=1:n

{αui }

αl

dl

l

αgl (given)

error

1



0 (αl (t)−αa(t))dt∫ ∆0 αl (t)dt

.

Biao Hu 23 / 31

A case study

Specifications

Input EventsI1: periodic (P = 60ms)I2: periodic (P = 5ms)I3: periodic (P = [60..110]ms)

Execution times T1: 35ms, T2: 2ms, T3: 4ms, T4: 12msschedulingparameters

priority T1: high, priority T2: lowpriority T3: low, priority T4: high

Arrival curve in Monitor 1 Arrival curve in Monitor 2

Biao Hu 24 / 31

A case study

Specifications

Input EventsI1: periodic (P = 60ms)I2: periodic (P = 5ms)I3: periodic (P = [60..110]ms)

Execution times T1: 35ms, T2: 2ms, T3: 4ms, T4: 12msschedulingparameters

priority T1: high, priority T2: lowpriority T3: low, priority T4: high

Arrival curve in Monitor 1 Arrival curve in Monitor 2

Biao Hu 24 / 31

A case study

1 2 3 4 5 6 70.94

0.95

0.96

0.97

0.98

0.99

1

Number of dynamic counters

l-EP

∆=5000 ms∆=2500 ms∆=1200 ms

Result in monitor 1 by dynamic

counters

1 2 3 4 5 6 7 8 9 100.94

0.95

0.96

0.97

0.98

0.99

1

l-repetitive: l

l-EP

∆=5000 ms∆=2500 ms∆=1200 ms

Result in monitor 1 by l-repetitive

function

The needed number of dynamic counters or l in repetitive segment withrespect to the period of input I3.

period [ms] 60 70 80 90 100 110#DC 13 16 18 21 23 25l 12 15 17 20 22 24

Biao Hu 25 / 31

A case study

1 2 3 4 5 6 70.94

0.95

0.96

0.97

0.98

0.99

1


l-EP

∆=5000 ms∆=2500 ms∆=1200 ms

Result in monitor 1 by dynamic

counters

1 2 3 4 5 6 7 8 9 100.94

0.95

0.96

0.97

0.98

0.99

1

l-repetitive: l

l-EP

∆=5000 ms∆=2500 ms∆=1200 ms

Result in monitor 1 by l-repetitive

function

The needed number of dynamic counters or l in repetitive segment withrespect to the period of input I3.

period [ms] 60 70 80 90 100 110#DC 13 16 18 21 23 25l 12 15 17 20 22 24

Biao Hu 25 / 31

Outline

1 Motivation

2 Background


4 FPGA evaluations

5 Summary

Biao Hu 26 / 31

Setup

Prototype both approaches in ALTERA Cyclone III EP3C120F780

Processor frequency: 50 MHz

Timer bits: 16 bit

Biao Hu 27 / 31

Setup

Prototype both approaches in ALTERA Cyclone III EP3C120F780

Processor frequency: 50 MHz

Timer bits: 16 bit

Biao Hu 27 / 31

FPGA Resource

Resource usage with the number of dynamic counters or l in l-repetitivefunction

1 2 3 4 5 60

100

200

300


Logic ElementsRegistersLABs

Dynamic counters

5 10 15 20 25 300

200

400

600

800

1000

l-repetitive: l



Biao Hu 28 / 31

FPGA Resource

Resource usage with the length of repetitive segment

0 1 2 3 4 50

50

100

150

200

250

300

Length of repeat segment (log(dl) [µs])


Dynamic counters

0 1 2 3 4 50

50

100

150

200

250

300

Length of repeat segment (log(dl) [µs])



Biao Hu 29 / 31

Outline

1 Motivation

2 Background


4 FPGA evaluations

5 Summary

Biao Hu 30 / 31

Summary

1 Analyzed the difference of dynamic counters monitoring andl-repetitive function monitoring by using standard arrivalcurves, and two typical complex arrival curves.

2 Developed a new monitoring scheme for dynamic counters tomonitor periodic burst events

3 Prototyped the two monitoring approaches in FPGA, andfound resource overhead is more sensitive to the number ofdynamic counters, and not sensitive to the length of onerepetitive segment.

Biao Hu 31 / 31

Summary




Biao Hu 31 / 31

Summary




Biao Hu 31 / 31

Summary




Biao Hu 31 / 31

Documents

Evaluation of Runtime Monitoring Methods for Real-Time ... · Real-time system at runtime Why real-time system needs to be monitored? All inputs are assumed as the design speci cations