Half-modelling of shaping in FIFO net with network calculus Context - - PowerPoint PPT Presentation

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Half-modelling of shaping in FIFO net with network calculus Context - - PowerPoint PPT Presentation

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Half-modelling of shaping in FIFO net Marc Boyer Half-modelling of shaping in FIFO net with network calculus Context Network calculus: overview Marc Boyer Network calculus: topologies Previous works (tandem topologies) Local delay

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SLIDE 1

Half-modelling

  • f shaping in

FIFO net Marc Boyer Context Network calculus:

  • verview

Network calculus: topologies Previous works (tandem topologies)

Local delay and shaping LUB

Our contribution Conclusion

Half-modelling of shaping in FIFO net with network calculus

Marc Boyer RTNS 2010 – nov. 4th 2010

Marc Boyer (ONERA, France) Half-modelling of shaping in FIFO net RTNS 2010 – nov. 4th 2010 1 / 24

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SLIDE 2

Half-modelling

  • f shaping in

FIFO net Marc Boyer Context Network calculus:

  • verview

Network calculus: topologies Previous works (tandem topologies)

Local delay and shaping LUB

Our contribution Conclusion

Outline

1 Context 2 Network calculus: overview 3 Network calculus: topologies 4 Previous works (tandem topologies)

Local delay and shaping PBOO without shaping (LUB)

5 Our contribution 6 Conclusion

Marc Boyer (ONERA, France) Half-modelling of shaping in FIFO net RTNS 2010 – nov. 4th 2010 2 / 24

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SLIDE 3

Half-modelling

  • f shaping in

FIFO net Marc Boyer Context Network calculus:

  • verview

Network calculus: topologies Previous works (tandem topologies)

Local delay and shaping LUB

Our contribution Conclusion

Outline

1 Context 2 Network calculus: overview 3 Network calculus: topologies 4 Previous works (tandem topologies)

Local delay and shaping PBOO without shaping (LUB)

5 Our contribution 6 Conclusion

Marc Boyer (ONERA, France) Half-modelling of shaping in FIFO net RTNS 2010 – nov. 4th 2010 3 / 24

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SLIDE 4

Half-modelling

  • f shaping in

FIFO net Marc Boyer Context Network calculus:

  • verview

Network calculus: topologies Previous works (tandem topologies)

Local delay and shaping LUB

Our contribution Conclusion

Worst Case Traversal Time: What and Why

Net in real-time systems Embedded systems are:

real-time ( = ⇒ real-time scheduling) communicating:

net real-time app. real-time app.

Marc Boyer (ONERA, France) Half-modelling of shaping in FIFO net RTNS 2010 – nov. 4th 2010 4 / 24

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SLIDE 5

Half-modelling

  • f shaping in

FIFO net Marc Boyer Context Network calculus:

  • verview

Network calculus: topologies Previous works (tandem topologies)

Local delay and shaping LUB

Our contribution Conclusion

Worst Case Traversal Time: What and Why

Net in real-time systems Embedded systems are:

real-time ( = ⇒ real-time scheduling) communicating: network delay (traversal time)

net real-time app. real-time app. Traversal time

Marc Boyer (ONERA, France) Half-modelling of shaping in FIFO net RTNS 2010 – nov. 4th 2010 4 / 24

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SLIDE 6

Half-modelling

  • f shaping in

FIFO net Marc Boyer Context Network calculus:

  • verview

Network calculus: topologies Previous works (tandem topologies)

Local delay and shaping LUB

Our contribution Conclusion

Worst Case Traversal Time: What and Why

Net in real-time systems Embedded systems are:

real-time ( = ⇒ real-time scheduling) communicating: network delay (traversal time) = ⇒ need of end-to-end delay bound (WCTT)

net real-time app. real-time app. Traversal time ≤ WCTT ≤ WCTT-bound

Marc Boyer (ONERA, France) Half-modelling of shaping in FIFO net RTNS 2010 – nov. 4th 2010 4 / 24

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SLIDE 7

Half-modelling

  • f shaping in

FIFO net Marc Boyer Context Network calculus:

  • verview

Network calculus: topologies Previous works (tandem topologies)

Local delay and shaping LUB

Our contribution Conclusion

Worst Case Traversal Time: What and Why

Net in real-time systems Embedded systems are:

real-time ( = ⇒ real-time scheduling) communicating: network delay (traversal time) = ⇒ need of end-to-end delay bound (WCTT) = ⇒ traffic contract and service guarantee

net real-time app. real-time app. Traversal time ≤ WCTT ≤ WCTT-bound

Marc Boyer (ONERA, France) Half-modelling of shaping in FIFO net RTNS 2010 – nov. 4th 2010 4 / 24

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SLIDE 8

Half-modelling

  • f shaping in

FIFO net Marc Boyer Context Network calculus:

  • verview

Network calculus: topologies Previous works (tandem topologies)

Local delay and shaping LUB

Our contribution Conclusion

Outline

1 Context 2 Network calculus: overview 3 Network calculus: topologies 4 Previous works (tandem topologies)

Local delay and shaping PBOO without shaping (LUB)

5 Our contribution 6 Conclusion

Marc Boyer (ONERA, France) Half-modelling of shaping in FIFO net RTNS 2010 – nov. 4th 2010 5 / 24

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SLIDE 9

Half-modelling

  • f shaping in

FIFO net Marc Boyer Context Network calculus:

  • verview

Network calculus: topologies Previous works (tandem topologies)

Local delay and shaping LUB

Our contribution Conclusion

Basic ideas

Theory designed to compute WCTT bounds Used to certify A380 Strong mathematical background: (min, +) dioid F =

  • f : ❘ → ❘

x < y = ⇒ f (x) ≤ f (y) x < 0 = ⇒ f (x) = 0

  • (f ∗ g)(t) =

inf

0≤u≤t(f (t − u) + g(u))

(1) (f ⊘ g)(t) = sup

0≤u

(f (t + u) − g(u)) (2)

Marc Boyer (ONERA, France) Half-modelling of shaping in FIFO net RTNS 2010 – nov. 4th 2010 6 / 24

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SLIDE 10

Half-modelling

  • f shaping in

FIFO net Marc Boyer Context Network calculus:

  • verview

Network calculus: topologies Previous works (tandem topologies)

Local delay and shaping LUB

Our contribution Conclusion

Reality modelling

Data flow: R(t) amount of data up to time t (cumulative curve) Server: transforms input into output R

S

− → R′ Arrival curve: α ∀t, d ≥ 0 : R(t + d) − R(t) ≤ α(d) ⇐ ⇒ R ≤ R ∗ α Service curve: β iff R′ ≥ R ∗ β Traffic contract Service guarantee Token bucket Periodic Delay Rate-latency t b r γr,b t b t d δd t T R βR,T

Marc Boyer (ONERA, France) Half-modelling of shaping in FIFO net RTNS 2010 – nov. 4th 2010 7 / 24

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SLIDE 11

Half-modelling

  • f shaping in

FIFO net Marc Boyer Context Network calculus:

  • verview

Network calculus: topologies Previous works (tandem topologies)

Local delay and shaping LUB

Our contribution Conclusion

First results

Given: an arrival traffic contract a service guarantee S R R’ α β

Marc Boyer (ONERA, France) Half-modelling of shaping in FIFO net RTNS 2010 – nov. 4th 2010 8 / 24

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SLIDE 12

Half-modelling

  • f shaping in

FIFO net Marc Boyer Context Network calculus:

  • verview

Network calculus: topologies Previous works (tandem topologies)

Local delay and shaping LUB

Our contribution Conclusion

First results

Given: an arrival traffic contract a service guarantee it can compute a delay bound (h)

  • utput traffic contract

S R R’ α β α h α′ = α ⊘ β

Marc Boyer (ONERA, France) Half-modelling of shaping in FIFO net RTNS 2010 – nov. 4th 2010 8 / 24

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SLIDE 13

Half-modelling

  • f shaping in

FIFO net Marc Boyer Context Network calculus:

  • verview

Network calculus: topologies Previous works (tandem topologies)

Local delay and shaping LUB

Our contribution Conclusion

Outline

1 Context 2 Network calculus: overview 3 Network calculus: topologies 4 Previous works (tandem topologies)

Local delay and shaping PBOO without shaping (LUB)

5 Our contribution 6 Conclusion

Marc Boyer (ONERA, France) Half-modelling of shaping in FIFO net RTNS 2010 – nov. 4th 2010 9 / 24

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SLIDE 14

Half-modelling

  • f shaping in

FIFO net Marc Boyer Context Network calculus:

  • verview

Network calculus: topologies Previous works (tandem topologies)

Local delay and shaping LUB

Our contribution Conclusion

Pay burst only once principle

S R S′ R′′ R′ Pay burst only once The sequence S, S′ can be replaced by a virtual server S; S′ with service curve β ∗ β′. Interest End-to-end delay is less than sum of individual delays. h(α, β ∗ β′) ≤ h(α, β) + h(α, β′) (3) Proof R′′ ≥ R′ ∗ β ≥ (R ∗ β) ∗ β′ = R ∗ (β ∗ β′)

Marc Boyer (ONERA, France) Half-modelling of shaping in FIFO net RTNS 2010 – nov. 4th 2010 10 / 24

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SLIDE 15

Half-modelling

  • f shaping in

FIFO net Marc Boyer Context Network calculus:

  • verview

Network calculus: topologies Previous works (tandem topologies)

Local delay and shaping LUB

Our contribution Conclusion

FIFO Aggregate scheduling

S R′

1

R′

2

R1 R2 ✶ ✶

Marc Boyer (ONERA, France) Half-modelling of shaping in FIFO net RTNS 2010 – nov. 4th 2010 11 / 24

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SLIDE 16

Half-modelling

  • f shaping in

FIFO net Marc Boyer Context Network calculus:

  • verview

Network calculus: topologies Previous works (tandem topologies)

Local delay and shaping LUB

Our contribution Conclusion

FIFO Aggregate scheduling

S R′

1

R′

2

R1 R2 First FIFO result: aggregated delay (Th. 1) If d = h(α1 + α2, β) is the delay for the aggregated flow, then δd is a service curve for each flow. α′

i(t) = (α′ i ⊘ δd)(t) = α(t + d)

✶ ✶

Marc Boyer (ONERA, France) Half-modelling of shaping in FIFO net RTNS 2010 – nov. 4th 2010 11 / 24

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SLIDE 17

Half-modelling

  • f shaping in

FIFO net Marc Boyer Context Network calculus:

  • verview

Network calculus: topologies Previous works (tandem topologies)

Local delay and shaping LUB

Our contribution Conclusion

FIFO Aggregate scheduling

S R′

1

R′

2

R1 R2 First FIFO result: aggregated delay (Th. 1) If d = h(α1 + α2, β) is the delay for the aggregated flow, then δd is a service curve for each flow. α′

i(t) = (α′ i ⊘ δd)(t) = α(t + d)

Second FIFO result: residual service (Th. 2) Let be θ ≥ 0 then, βθ

i is a service curve for flow Ri

βθ

i = [β − αj ⊘ δθ]+ ✶{>θ}

α′

i = αi ⊘ βθ i

with ✶{>θ}(x) = 1 if x > θ, 0 otherwise.

Marc Boyer (ONERA, France) Half-modelling of shaping in FIFO net RTNS 2010 – nov. 4th 2010 11 / 24

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SLIDE 18

Half-modelling

  • f shaping in

FIFO net Marc Boyer Context Network calculus:

  • verview

Network calculus: topologies Previous works (tandem topologies)

Local delay and shaping LUB

Our contribution Conclusion

Outline

1 Context 2 Network calculus: overview 3 Network calculus: topologies 4 Previous works (tandem topologies)

Local delay and shaping PBOO without shaping (LUB)

5 Our contribution 6 Conclusion

Marc Boyer (ONERA, France) Half-modelling of shaping in FIFO net RTNS 2010 – nov. 4th 2010 12 / 24

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SLIDE 19

Half-modelling

  • f shaping in

FIFO net Marc Boyer Context Network calculus:

  • verview

Network calculus: topologies Previous works (tandem topologies)

Local delay and shaping LUB

Our contribution Conclusion

Considered topologies

S1 S2 R R′′ R′ I1 I ′

1

I2 I ′

2

Tandem topology One flow of interest R One interfering flow Ii per server Si

Marc Boyer (ONERA, France) Half-modelling of shaping in FIFO net RTNS 2010 – nov. 4th 2010 13 / 24

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SLIDE 20

Half-modelling

  • f shaping in

FIFO net Marc Boyer Context Network calculus:

  • verview

Network calculus: topologies Previous works (tandem topologies)

Local delay and shaping LUB

Our contribution Conclusion

Two approaches

Local delay and shaping Global delay as sum of local delays Use of Th 1 (FIFO: aggregate result) University of Toulouse (IRIT, Networks and Telecommunication group) PBOO without shaping End to end delay with Pay Burst Only Once result Use of Th 2 (FIFO: residual service) University of Pisa (Computing Networking Group)

Marc Boyer (ONERA, France) Half-modelling of shaping in FIFO net RTNS 2010 – nov. 4th 2010 14 / 24

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SLIDE 21

Half-modelling

  • f shaping in

FIFO net Marc Boyer Context Network calculus:

  • verview

Network calculus: topologies Previous works (tandem topologies)

Local delay and shaping LUB

Our contribution Conclusion

Shaping modelling

Applicative traffic is shaped by link capacity. new kind of curve (CPL) aggregate delay simple to compute

Marc Boyer (ONERA, France) Half-modelling of shaping in FIFO net RTNS 2010 – nov. 4th 2010 15 / 24

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SLIDE 22

Half-modelling

  • f shaping in

FIFO net Marc Boyer Context Network calculus:

  • verview

Network calculus: topologies Previous works (tandem topologies)

Local delay and shaping LUB

Our contribution Conclusion

Computation by sum of local delays

S1 S2 R R′′ R′ I1 I ′

1

I2 I ′

2

modelling: CPL arrival curve for R and Ii (full shaping) propagation of result: aggregate delay end-to-end delay: sum of individual delays

slide-23
SLIDE 23

Half-modelling

  • f shaping in

FIFO net Marc Boyer Context Network calculus:

  • verview

Network calculus: topologies Previous works (tandem topologies)

Local delay and shaping LUB

Our contribution Conclusion

Computation by sum of local delays

S1 S2 R R′′ R′ I1 I ′

1

I2 I ′

2

h(αR + αI1, β1) modelling: CPL arrival curve for R and Ii (full shaping) propagation of result: aggregate delay end-to-end delay: sum of individual delays

slide-24
SLIDE 24

Half-modelling

  • f shaping in

FIFO net Marc Boyer Context Network calculus:

  • verview

Network calculus: topologies Previous works (tandem topologies)

Local delay and shaping LUB

Our contribution Conclusion

Computation by sum of local delays

S1 S2 R R′′ R′ I1 I ′

1

I2 I ′

2

h(αR + αI1, β1) αR′ modelling: CPL arrival curve for R and Ii (full shaping) propagation of result: aggregate delay end-to-end delay: sum of individual delays

slide-25
SLIDE 25

Half-modelling

  • f shaping in

FIFO net Marc Boyer Context Network calculus:

  • verview

Network calculus: topologies Previous works (tandem topologies)

Local delay and shaping LUB

Our contribution Conclusion

Computation by sum of local delays

S1 S2 R R′′ R′ I1 I ′

1

I2 I ′

2

h(αR + αI1, β1) αR′ h(αR′ + αI1, β2) modelling: CPL arrival curve for R and Ii (full shaping) propagation of result: aggregate delay end-to-end delay: sum of individual delays

slide-26
SLIDE 26

Half-modelling

  • f shaping in

FIFO net Marc Boyer Context Network calculus:

  • verview

Network calculus: topologies Previous works (tandem topologies)

Local delay and shaping LUB

Our contribution Conclusion

Computation by sum of local delays

S1 S2 R R′′ R′ I1 I ′

1

I2 I ′

2

h(αR + αI1, β1) αR′ h(αR′ + αI1, β2) + modelling: CPL arrival curve for R and Ii (full shaping) propagation of result: aggregate delay end-to-end delay: sum of individual delays

Marc Boyer (ONERA, France) Half-modelling of shaping in FIFO net RTNS 2010 – nov. 4th 2010 16 / 24

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SLIDE 27

Half-modelling

  • f shaping in

FIFO net Marc Boyer Context Network calculus:

  • verview

Network calculus: topologies Previous works (tandem topologies)

Local delay and shaping LUB

Our contribution Conclusion

PBOO optimisation (LUB)

S1 S2 R R′′ R′ I1 I ′

1

I2 I ′

2

modelling: token bucket curve for R and Ii (no shaping) propagation of result: equivalent server end-to-end delay: PBOO hard point: choice of θi

slide-28
SLIDE 28

Half-modelling

  • f shaping in

FIFO net Marc Boyer Context Network calculus:

  • verview

Network calculus: topologies Previous works (tandem topologies)

Local delay and shaping LUB

Our contribution Conclusion

PBOO optimisation (LUB)

S1 S2 R R′′ R′ I1 I ′

1

I2 I ′

2

Sθ1

1

Sθ2

2

R R′′ modelling: token bucket curve for R and Ii (no shaping) propagation of result: equivalent server end-to-end delay: PBOO hard point: choice of θi

slide-29
SLIDE 29

Half-modelling

  • f shaping in

FIFO net Marc Boyer Context Network calculus:

  • verview

Network calculus: topologies Previous works (tandem topologies)

Local delay and shaping LUB

Our contribution Conclusion

PBOO optimisation (LUB)

S1 S2 R R′′ R′ I1 I ′

1

I2 I ′

2

Sθ1

1

Sθ2

2

R R′′ modelling: token bucket curve for R and Ii (no shaping) propagation of result: equivalent server end-to-end delay: PBOO hard point: choice of θi

slide-30
SLIDE 30

Half-modelling

  • f shaping in

FIFO net Marc Boyer Context Network calculus:

  • verview

Network calculus: topologies Previous works (tandem topologies)

Local delay and shaping LUB

Our contribution Conclusion

PBOO optimisation (LUB)

S1 S2 R R′′ R′ I1 I ′

1

I2 I ′

2

Sθ1

1

Sθ2

2

R R′′ h(α, βθ1

1 ∗ βθ2 2 )

modelling: token bucket curve for R and Ii (no shaping) propagation of result: equivalent server end-to-end delay: PBOO hard point: choice of θi

Marc Boyer (ONERA, France) Half-modelling of shaping in FIFO net RTNS 2010 – nov. 4th 2010 17 / 24

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SLIDE 31

Half-modelling

  • f shaping in

FIFO net Marc Boyer Context Network calculus:

  • verview

Network calculus: topologies Previous works (tandem topologies)

Local delay and shaping LUB

Our contribution Conclusion

PBOO optimisation (LUB)

S1 S2 R R′′ R′ I1 I ′

1

I2 I ′

2

Sθ1

1

Sθ2

2

R R′′ infθ1,θ2

  • h(α, βθ1

1 ∗ βθ2 2 )

  • modelling: token bucket curve for R and Ii (no shaping)

propagation of result: equivalent server end-to-end delay: PBOO hard point: choice of θi

Marc Boyer (ONERA, France) Half-modelling of shaping in FIFO net RTNS 2010 – nov. 4th 2010 17 / 24

slide-32
SLIDE 32

Half-modelling

  • f shaping in

FIFO net Marc Boyer Context Network calculus:

  • verview

Network calculus: topologies Previous works (tandem topologies)

Local delay and shaping LUB

Our contribution Conclusion

Outline

1 Context 2 Network calculus: overview 3 Network calculus: topologies 4 Previous works (tandem topologies)

Local delay and shaping PBOO without shaping (LUB)

5 Our contribution 6 Conclusion

Marc Boyer (ONERA, France) Half-modelling of shaping in FIFO net RTNS 2010 – nov. 4th 2010 18 / 24

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SLIDE 33

Half-modelling

  • f shaping in

FIFO net Marc Boyer Context Network calculus:

  • verview

Network calculus: topologies Previous works (tandem topologies)

Local delay and shaping LUB

Our contribution Conclusion

Contribution: half-modelling of shaping

S1 S2 R R′′ R′ I1 I ′

1

I2 I ′

2

Sθ1

1

Sθ2

2

R R′′ infθ1,θ2

  • h(α, βθ1

1 ∗ βθ1 1 )

  • modelling: CPL curve for R and token bucket for Ii (half

modelling of shaping) propagation of result: equivalent server end-to-end delay: PBOO hard point: choice of θi

Marc Boyer (ONERA, France) Half-modelling of shaping in FIFO net RTNS 2010 – nov. 4th 2010 19 / 24

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SLIDE 34

Half-modelling

  • f shaping in

FIFO net Marc Boyer Context Network calculus:

  • verview

Network calculus: topologies Previous works (tandem topologies)

Local delay and shaping LUB

Our contribution Conclusion

Experiment

Three identical servers Identical interfering flows Two rates CPL, approximated by token bucket if needed

Marc Boyer (ONERA, France) Half-modelling of shaping in FIFO net RTNS 2010 – nov. 4th 2010 20 / 24

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SLIDE 35

Half-modelling

  • f shaping in

FIFO net Marc Boyer Context Network calculus:

  • verview

Network calculus: topologies Previous works (tandem topologies)

Local delay and shaping LUB

Our contribution Conclusion

Experimental results ;-)

Configurations Conf 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 R 1 1 1 1 5 5 5 5 1 1 1 1 1 1 1 1 T 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 r

1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 6 1 6 1 6 1 6

b 1 1 5

1 5

1 1 5

1 5 1 10 1 10 5 10 1 50 1 10 1 10 5 10 1 50

r′

1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 6 1 6 1 6 1 6

b′ 1 5 1

1 5

1 5 1

1 5 1 10 5 10 1 10 1 50 1 10 5 10 1 10 1 50

ρ = r+r′

R

67% 67% 67% 67% 13% 13% 13% 13% 67% 67% 67% 67% 33% 33% 33% 33% Delai R crossing SI; SII LUB 5.50 13.50 11.50 2.70 2.61 4.21 3.47 2.12 2.35 3.15 2.95 2.07 2.32 3.12 2.80 2.06

  • Loc. Shap.

5.41 10.50 9.75 2.81 2.43 2.62 2.54 2.09 2.49 3.12 2.92 2.23 2.27 2.60 2.44 2.08

  • Half. Shap.

4.75 12.75 7.75 2.55 2.41 4.01 2.47 2.08 2.27 3.07 2.57 2.05 2.22 3.02 2.32 2.04 Delai R crossing SI; SII; SIII LUB 7.50 19.50 13.50 3.90 3.81 6.21 4.67 3.16 3.45 4.65 4.05 3.09 3.42 4.62 3.90 3.08

  • Loc. Shap.

8.81 18.50 15.87 4.58 3.66 4.07 3.83 3.14 4.05 5.19 4.76 3.63 3.47 4.20 3.72 3.17

  • Half. Shap.

6.75 18.75 9.75 3.75 3.61 6.01 3.67 3.12 3.37 4.57 3.67 3.07 3.32 4.52 3.42 3.06 Gain on the new method for R crossing SI; SII

  • vs. LUB

13.63% 5.55% 32.60% 5.55% 7.61% 4.72% 28.65% 1.87% 3.19% 2.38% 12.71% 0.72% 4.13% 3.07% 17.14% 0.93%

  • vs. Loc. Shap.

12.30%

  • 21.42%

20.51% 9.46% 0.78%

  • 52.81%

2.83% 0.36% 8.69% 1.60% 11.96% 7.91% 2.34%

  • 16.30%

4.91% 1.79% Gain on the new method for R crossing SI; SII; SIII

  • vs. LUB

10.00% 3.84% 27.77% 3.84% 5.21% 3.20% 21.29% 1.25% 2.17% 1.61% 9.25% 0.48% 2.80% 2.07% 12.30% 0.62%

  • vs. Loc. Shap.

23.46%

  • 1.35%

38.58% 18.23% 1.22%

  • 47.64%

4.06% 0.64% 16.80% 11.94% 22.83% 15.37% 4.29%

  • 7.54%

8.09% 3.48%

Marc Boyer (ONERA, France) Half-modelling of shaping in FIFO net RTNS 2010 – nov. 4th 2010 21 / 24

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SLIDE 36

Half-modelling

  • f shaping in

FIFO net Marc Boyer Context Network calculus:

  • verview

Network calculus: topologies Previous works (tandem topologies)

Local delay and shaping LUB

Our contribution Conclusion

Interpretation

new method always better than LUB (direct generalisation)

gain depends on burst sizes gain independent on path lenght

new method vs “shaping+local delays”

depends on interfering burst size (not shaped) gain increases with path length (PBOO)

Marc Boyer (ONERA, France) Half-modelling of shaping in FIFO net RTNS 2010 – nov. 4th 2010 22 / 24

slide-37
SLIDE 37

Half-modelling

  • f shaping in

FIFO net Marc Boyer Context Network calculus:

  • verview

Network calculus: topologies Previous works (tandem topologies)

Local delay and shaping LUB

Our contribution Conclusion

Outline

1 Context 2 Network calculus: overview 3 Network calculus: topologies 4 Previous works (tandem topologies)

Local delay and shaping PBOO without shaping (LUB)

5 Our contribution 6 Conclusion

Marc Boyer (ONERA, France) Half-modelling of shaping in FIFO net RTNS 2010 – nov. 4th 2010 23 / 24

slide-38
SLIDE 38

Half-modelling

  • f shaping in

FIFO net Marc Boyer Context Network calculus:

  • verview

Network calculus: topologies Previous works (tandem topologies)

Local delay and shaping LUB

Our contribution Conclusion

Conclusion

To have better bounds, two aspects must be modelled: shaping pay burst only once FIFO in network calculus: local delay and shaping PBOO without shaping Our contribution: Half modelling of shaping + PBOO O(n log(n)) complexity (sorting and sums) Future works: full modelling of shaping

Marc Boyer (ONERA, France) Half-modelling of shaping in FIFO net RTNS 2010 – nov. 4th 2010 24 / 24