A Forward end-to-end delays Analysis for packet switched networks

A Forward end-to-end delays Analysis for packet switched networks

Georges Kemayo, Frédéric Ridouard, Henri Bauer, Pascal Richard

LIAS, Université de Poitiers, ISAE/ENSMA, France

RTNS’2014

October 08-10, 2014, Versailles, France

Outline

LIA

S -

ISA

E/E

NS

MA

- U

nive

rsit

é d

e P

oiti

ers

1

3

2

4

Context

The AFDX network

Conclusion and future work

Contribution

State of the art

End-to-End delay variability

Network Calculus and Trajectory Approach

Forward end-to-end delay Analysis (FA)

2

Analysis of AFDX networks used in avionics systems

AFDX = Avionics Full Duplex Switched Ethernet

Fully static Switched Ethernet network

« End/Systems » interconnected by « switches » and « physical links »

A physical link between 2 components is full duplex

no loss of frames due to collisions

The AFDX network: Generalities (1/2)

3

S5

v3,v4,v5 v3,v4

v5,v6

v1,v3

v5,v6

S1

S4

ES8

ES6

ES4

ES2

v1

ES3

ES1v2 S3v3

v2 ES5

S2 v3,v4

v1,v2

ES7 v6

8 End/Systems ESi

5 Switches Si

6 Virtual links vi

Context State of the

art Contribution Conclusion

AFDX = Avionics Full Duplex Switched Ethernet

End/System:

Switch:

4

Control and Routing

… …

Message 1

Message n

The AFDX network: Generalities (2/2)



Virtual link = static, unidirectionnal and monotransmitter logical channel

generated by only one source End/System towards one or many End/Systems (multicast) avionics data flows correspond to virtual links Any virtual link respects a traffic contract:

Fmin ≤ data frame lenght ≤ Fmax

BAG = minimum inter-generation time of frames on its source End/System:

guaranteed bandwidth for any data flow: Fmax / BAG

≥ BAG

ES1 (v1)

< BAG

5



The AFDX network: Virtual link

8 End/Systems ESi

5 Switches Si

6 Virtual links viS5

v3,v4,v5 v3,v4

v5,v6

v1,v3

v5,v6

S1

S4

ES8

ES6

ES4

ES2

v1

ES3

ES1v2 S3v3

v2 ES5

S2 v3,v4

v1,v2

ES7 v6

The ETE delay of a data frame in the AFDX:

Necessity to use a method to compute the worst ETE delay

The AFDX network: Notion of ETE delay

ES1

ES2

S1

S2

ETE delay

Objective: Guarantee the worst ETE delay of any frame of any flow vi

crossing the AFDX (Mandatory for certification)

Variable waiting durations in buffers

(difficult to evaluate)

6



Outline

LIA

S -

ISA

E/E

NS

MA

- U

nive

rsit

é d

e P

oiti

ers

1

3

2

4

Context

The AFDX network


Contribution

State of the art




7

Simulation

The variability of the waiting duration in each crossed buffer implies:

The ETE delay is between a lower bound and an exact worst case

End-to-End delay Variability

Lower bound of the ETE delay

Exact worst case ETE delay

Upper bound of the ETE delay

time

ETE delay distribution obtained by simulation

Worst ETE delay (observed)

Network Calculus, Trajectory Approach

8

Model Checking

Context State of the art Contribution Conclusion

miss of rare Scenarios

Combinatorial explosion when computing the exact worst ETE delay

Can miss some rare scenarios leading to the exact worst ETE delay

Network Calculus, Trajectory Approach

9

Network Calculus Trajectory Approach

Theory (min,+) algebra Real-time scheduling

Policy FIFO, … FIFO, …

Serialization

Pessimism (Bauer et al. IEEE TII’10) (Li et al. RTNS’11)

Global charge > 1

Absence of optimism (Kemayo et al. ETFA’13)

FA

Real-time scheduling

FIFO

FA (Forward end-to-end delay Analysis) correct the disadvantages of the existing methods

What is the necessity to design a new method?

(coming soon )

(to be studied)

Context State of the art Contribution ConclusionNetwork Calculus and Trajectory Approach

Global charge: sum of charges of all the flows encountered on any crossed node

S2 12

1S

Serialization:

Frames 1 and 2 are serialized, frame 1 cannot delay frame 2

Frames 1 and 2 not are serialized they can delay each other

Outline

LIA

S -

ISA

E/E

NS

MA

- U

nive

rsit

é d

e P

oiti

ers

1

3

2

4

Context

The AFDX network


Contribution

State of the art




10

Maximum transmission time: Ci = Fmax / R (R = rate of the physical link)

Minimum inter-generation time between two consecutive frames: Ti = BAG

1 output port (Switch or End/System) a network node

1 virtual link vi flow, characterized by:

≥ Ti

i

Ci

vii



Modelization of AFDX by the FA method (1/2)

11

Analysis of the worst ETE delay of flows with FA (1/10)

12

S5

v3,v4,v5 v3,v4

v5,v6

v1,v3

v5,v6

S1

S4

ES8

ES6

ES4

ES2

v1

ES3

ES1v2 S3v3

v2 ES5

2

1

2 1

S2 v3,v4

v1,v2 1

2

ES7 v6

v1,v3

S22

ES1

ES2

S52S4

S51

v1

v3,v4,v5

v2

S32

S31

ES3

ES4

v2

v1

S21

S1

v2

v6

v3,v4

v6

v5

v3,v4

v3

v1

v2

v5,v6

v3

v3,v4

v5,v6

Modelization

by FA :

AFDX :



Modelization of AFDX by the FA method (2/2)

ES1

S51

S52


13

Worst ETE delay Ri of a flow vi:

The FA principle

ifirst

…

- Maximum backlog encountered by fi on lasti ( FIFO policy)

- Maximum delay incurred by fi to arrive on lasti: max ilastiS

ilast

iR

fi

Generation time of fi

max ilastiS

g ilastiBkl iC

max gi ilast lasti i i iR S Bkl C

Worst arrived time of fi




14

How to compute ?

Computation of the maximal delay

h

ifirst

…

Generation time of fi

- Iterative computation, knowing that

maxhiS

1h 1maxh

iS

L

max ilastiS

max ilastiS

max 0ifirstiS

fi

ghiBkl

iC

1max max gh h hi i i iS S Bkl C L

L = propagation delay of a frame on the link between h and h+1




15

Question: how to compute on a node h ? ghiBkl

jTjTjT

Theorem: considering a temporal interval [a,b] on h, the scenario leading, for any flow vj, to its greatest amount of work is obtained when:

jf

minhjSmaxh

jS maxhjSmaxh

jS

jfirst

a bh

…

1min minh hj j jS S C L with min 0jfirst

jS

Maximum interference of frames of a same flow on a node h (1/3)




16

Example: determination of the worst case backlog of a single flow vj on h:

jfirst

20a 110b h

…

max 60hjS min 30h

jS

jf

30

80

40jT [a, b] = [20, 110]

jT

60

0

60

jT40jT

60

40 jT

70

0

70

jT40jT

70

40

max 70hjS

jT

90

0

90

jT40jT

90

40

max 90hjS max 120h

jS

jT

120

0

120

jT40jT

120

40jT80

120





When no other frame of vj can catch up the frame fj on h max 6 ,0hjS

When one frame of vj catches up the frame fj on h max 7 ,0hjS

When always one frame of vj still catches up the frame fj on h max 9 ,0hjS

When two frames of vj catch up the frame fj on h max 1 ,20hjS

17

Example: determination of the worst case backlog of a single flow vj on h:

General case:

jfirst

a bh

…

jTjT

maxhjSmaxh

jS 0k

jf

minhjS

jT…framesk

jfirst

20a 110b h

…

min 30hjS

jf

30

80

40jT [a, b] = [20, 110]

jT

70

0

70

jT40jT

70

40

max 70hjS

jT

90

0

90

jT40jT

90

40

max 90hjS max 120hjS

jT

120

0

120

jT40jT

120

40jT80

120





18

Usage of the request bound function theory for computing the maximal transmission

duration of vj frames arrived in [a,b]:

Total transmission duration of frames of all the flows crossing h and arriving in [a,b]:

( ) ( )j h

h hi

v

W t RBF t

is computed based onghiBkl

jfirst

a bh

…

jT jf

minhjS

…jTjT

maxhjSmaxh

jS t = b - a

Context State of art Contribution ConclusionAnalysis of the worst ETE delay of flows with FA (8/10)

ghiBklMaximum interference of frames of all the flows crossing a node h:

( )hiRBF t

( )hW t

19

Comparative study of the FA method on an AFDX example (1/2)

v1,v3

S22

ES1

ES2

S52S4

S51

v1

v3,v4,v5

v2

S32

S31

ES3

ES4

v2

v1

S21

S1

v2

v6

v3,v4

v6

v5

v3,v4

v3

v1

v2

v5,v6

v3

v3,v4

v5,v6

Ci Ti

v1

10

100

v2 100

v3 50

v4 30

v5 30

v6 50

L = 16




20

FA NC NCNS TA

v1 82 85 85 82

v2 72 73 73 72

v3 (S31) 82 87 87 82

v3 (S51) 112 100.8 126.7 82

v4 112 100.8 126.7 82

v5 112 100.8 126.7 N/A

v6 82 77.6 92 72

NC = Network Calculus taking into account the serialization

NCNS = Network Calculus Not taking into account the Serialization

TA = Trajectory Approach taking into account the serialization

Remarks:1) TA is not optimistic in this example

2) TA cannot compute the delay of flow v5, its global charge is greater than 1

3) FA is better than NCNS, 4) FA is more pessimistic than TA, but obtains same results for flows v1, v2, v3

but can compete with NC only for flows v1, v2, v3

FA = Our approach whitout serialization

5) No method is better than the others

Wor

st c

ase

ET

E d

elay

s


Comparative study of the FA method on an AFDX example (2/2)



Outline

LIA

S -

ISA

E/E

NS

MA

- U

nive

rsit

é d

e P

oiti

ers

1

3

2

4

Context

The AFDX network


Contribution

State of the art




21

Conclusion and Perspectives

22

Future work on FA:

Take into account the serialization

Large cases comparison with others existing methods

Conclusion:

Analysis of the ETE delay of flows on AFDX networks

Comparative study of the ETE delay computation methods for the AFDX

Proposition of a new method, Forward end-to-end delay Analysis, for the AFDX

FIFO policy



Extension to other policies: Fixed priorities, …

Thank you for your attention!

LIA

S -

ISA

E/E

NS

MA

- U

nive

rsit

é de

Poi

tier

s

?

23

A Forward end-to-end delays Analysis for packet switched networks

Documents