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
LIAS - ISAE/ENSMA - Université de Poitiers
Outline
1
Context
 The AFDX network
2
State of the art
 End-to-End delay variability
 Network Calculus and Trajectory Approach
3
Contribution
 Forward end-to-end delay Analysis (FA)
4
Conclusion and future work
2




The AFDX network: Generalities (1/2)
Context
State of the art
Contribution
Conclusion
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
ES1
ES2
ES3
ES4
v1
v2
v3,v4
v5,v6
S1
S2
S4
v1,v2
v3
v3,v4
v5,v6
S3
v1,v3
v2
v3,v4,v5
S5
v6
ES5
ES6
ES7
ES8
8 End/Systems ESi
5 Switches Si
6 Virtual links vi
3
The AFDX network: Generalities (2/2)




Context
State of the art
Contribution
Conclusion
AFDX = Avionics Full Duplex Switched Ethernet

End/System:
Message 1
Message n

Switch:
…
…
Control and
Routing
4
The AFDX network: Virtual link




Context
State of the art
Contribution
Conclusion
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:
≥ BAG
< BAG
ES1 (v1)

guaranteed bandwidth for any data flow: Fmax / BAG
ES1
ES2
ES3
ES4
v1
v2
v3,v4
v5,v6
S1
S2
S4
v1,v2
v3
v3,v4
v5,v6
S3
v1,v3
v2
v3,v4,v5
S5
v6
ES5
ES6
ES7
ES8
8 End/Systems ESi
5 Switches Si
6 Virtual links vi
5




The AFDX network: Notion of ETE delay
Context
State of the art
Contribution
Conclusion
The ETE delay of a data frame in the AFDX:
S1
ES1
S2
ES2
ETE delay
Variable waiting
durations in buffers
(difficult to evaluate)
Objective: Guarantee the worst ETE delay of any frame of any flow vi
crossing the AFDX (Mandatory for certification)
Necessity to use a method to compute the worst ETE delay
6
LIAS - ISAE/ENSMA - Université de Poitiers
Outline
1
Context
 The AFDX network
2
State of the art
 End-to-End delay variability
 Network Calculus and Trajectory Approach
3
Contribution
 Forward end-to-end delay Analysis (FA)
4
Conclusion and future work
7




End-to-End delay Variability
Context
State of the art
Contribution
Conclusion
The variability of the waiting duration in each crossed buffer implies:
 The ETE delay is between a lower bound and an exact worst case
Can miss some rare scenarios
leading to the exact worst ETE delay
ETE delay distribution
obtained by simulation
Combinatorial explosion when
computing the exact worst ETE delay
Simulation
Model Checking
Network Calculus,
Trajectory Approach
miss of rare
Scenarios
Lower bound of the
ETE delay
Worst ETE delay Exact worst case Upper bound of
(observed)
ETE delay
the ETE delay
time
8




Network Calculus and Trajectory Approach
Context
State of the art
Contribution
Conclusion
What is the necessity to design a new method?
 FA (Forward end-to-end delay Analysis)  correct the disadvantages of the existing methods
Network Calculus
Trajectory Approach
FA
Theory
(min,+) algebra
Real-time scheduling
Real-time scheduling
Policy
FIFO, …
FIFO, …
FIFO
Serialization
(coming soon
Pessimism
(Bauer et al. IEEE TII’10)
(Li et al. RTNS’11)
)
(to be studied)
Global charge > 1
Absence of optimism
(Kemayo et al. ETFA’13)
 Global charge: sum of charges of all the flows encountered on any crossed node
Serialization:
1
2
S
Frames 1 and 2 not are serialized
they can delay each other
2
1
S
Frames 1 and 2 are serialized,
frame 1 cannot delay frame 2
9
LIAS - ISAE/ENSMA - Université de Poitiers
Outline
1
Context
 The AFDX network
2
State of the art
 End-to-End delay variability
 Network Calculus and Trajectory Approach
3
Contribution
 Forward end-to-end delay Analysis (FA)
4
Conclusion and future work
10
Analysis of the worst ETE delay of flows with FA (1/10)




Context
State of the art
Contribution
Conclusion
Modelization of AFDX by the FA method (1/2)
1 output port (Switch or End/System)
1 virtual link vi


a network node
flow, characterized by:
≥ Ti
vi
i
i
Ci
Maximum transmission time: Ci = Fmax / R (R = rate of the physical link)
Minimum inter-generation time between two consecutive frames: Ti = BAG
11
Analysis of the worst ETE delay of flows with FA (2/10)




Context
State of the art
Contribution
Conclusion
Modelization of AFDX by the FA method (2/2)
v1
ES1
AFDX :
S1
v2
ES2
v3,v4
ES3
S3
v3
S2
v5,v6
ES4
v1,v2
1
2
v3,v4
S5
v5,v6
S4
ES1
ES2
Modelization v ,v
3 4
by FA :
ES3
v5,v6
ES4
1
v3,v4,v5
v6
2
ES5
ES6
ES7
ES8
S32
v2
S1
v1
v2
v2
2
v2
v1
v1
v1,v3
v2
1
v3
v3,v4
v5,v6
S21
S22
S4
v3
v3,v4
v5
v6
S31
S51
S52
v1,v3
v3,v4,v5
v6
12
Analysis of the worst ETE delay of flows with FA (3/10)




Context
State of the art
Contribution
Conclusion
The FA principle
Worst ETE delay Ri of a flow vi:
i
- Maximum delay incurred by fi to arrive on lasti: S maxlast
i
- Maximum backlog encountered by fi on lasti ( FIFO policy)
…
firsti
Generation time of fi
i
S maxlast
i
i
Bklglast
i
Ci
Worst arrived time of fi
fi
lasti
Ri

i
i
Ri  S max last
 Bklg last
 Ci
i
i

13
Analysis of the worst ETE delay of flows with FA (4/10)




Context
State of the art
Contribution
Conclusion
lasti
Computation of the maximal delay S maxi
i
How to compute S maxlast
?
i
firsti
- Iterative computation, knowing that Smaxi
Generation time of fi
Bklgih
…
firsti
0
Ci
fi
h
S max ih
L
h 1
S maxih1
S max ih 1  S max ih  Bklg ih  Ci   L
L = propagation delay of a frame on the link between h and h+1
14




Analysis of the worst ETE delay of flows with FA (5/10)
Context
State of the art
Contribution
Conclusion
Maximum interference of frames of a same flow on a node h (1/3)
Question: how to compute Bklgih on a node h ?
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:
…
first j
Tj
Tj
Tj
S max hj
S max hj
S max hj
fj
S min hj
h
a
Sminhj 1  Sminhj  C j  L
b
with
first j
S min j
0
15
Analysis of the worst ETE delay of flows with FA (6/10)




Context
State of the art
Contribution
Conclusion
Maximum interference of frames of a same flow on a node h (2/3)
Example: determination of the worst case backlog of a single flow vj on h:
[a, b] = [20, 110]
80
…
first j
h
Tj
40
120
Tj  40
hh
max
90
SSSmax
70
maxj jhj120
60
Sminhj  30
Tj
Tj
80
0
90 120
6070
a  20
40
 120
6070 90
Tj
 120
 90
70
60
fj
30
b  110
 When Smaxhj  60, no other frame of vj can catch up the frame fj on h
 When Smaxhj  70, one frame of vj catches up the frame fj on h
 When S max hj  90, always one frame of vj still catches up the frame fj on h
 When Smax hj  120, two frames of vj catch up the frame fj on h
16
Analysis of the worst ETE delay of flows with FA (7/10)




Context
State of the art
Contribution
Conclusion
Maximum interference of frames of a same flow on a node h (3/3)
Example: determination of the worst case backlog of a single flow vj on h:
[a, b] = [20, 110]
80
first j
Tj
40
…
120
Tj  40
maxhjhhjj70
90
120
SSmax
Sminhj  30
Tj
Tj
80
0
 120
70 90
120
7090
h
40
Tj
 120
 90
70
fj
30
a  20
General case:
…
first j
b  110
k frames
Tj
Tj
…
S max hj
S max hj
Tj
fj
Smin hj
k0
h
a
b
17
Analysis of the worst ETE delay of flows with FA (8/10)




Context
State of art
Contribution
Conclusion
Maximum interference of frames of all the flows crossing a node h: Bklgih
…
first j
Tj
Tj
Tj
…
S max hj
S max hj
fj
S min hj
t=b-a
h
a
b
Usage of the request bound function theory for computing the maximal transmission
duration of vj frames arrived in [a,b]: RBFi h (t )
Total transmission duration of frames of all the flows crossing h and arriving in [a,b]:
W h (t ) 
 RBF
v j  h
i
h
(t )
 Bklgih is computed based on W h (t )
18
Analysis of the worst ETE delay of flows with FA (9/10)




Context
State of the art
Contribution
Conclusion
Comparative study of the FA method on an AFDX example (1/2)
v2
v1
v1
ES1
S1
v1
v2
v2
ES2
v3,v4
ES3
v5,v6
ES4
v2
S32
v3
v3,v4
v5,v6
S21
v3
v3,v4
S22
v5
S4
Ci
v6
100
v2
100
10
S51
v1,v3
v3,v4,v5
S52
v6
Ti
v1
v3
S31
50
v4
30
v5
30
v6
50
L = 16
19
Analysis of the worst ETE delay of flows with FA (10/10)




Context
State of the art
Contribution
Conclusion
Worst case ETE delays
Comparative study of the FA method on an AFDX example (2/2)
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
NCNS = Network Calculus Not
v4
112
100.8
126.7
82
taking into account the Serialization
v5
112
100.8
126.7
N/A
TA = Trajectory Approach taking
v6
82
77.6
92
72
FA = Our approach whitout
serialization
NC = Network Calculus taking
into account the serialization
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, but can compete with NC only for flows v1, v2, v3
4) FA is more pessimistic than TA, but obtains same results for flows v1, v2, v3
5) No method is better than the others
20
LIAS - ISAE/ENSMA - Université de Poitiers
Outline
1
Context
 The AFDX network
2
State of the art
 End-to-End delay variability
 Network Calculus and Trajectory Approach
3
Contribution
 Forward end-to-end delay Analysis (FA)
4
Conclusion and future work
21
Conclusion and Perspectives




Context
State of the art
Contribution
Conclusion
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
Future work on FA:
 Take into account the serialization
 Large cases comparison with others existing methods
 Extension to other policies: Fixed priorities, …
22
LIAS - ISAE/ENSMA - Université de Poitiers
Thank you for your attention!
?
23