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 LIAS - ISAE/ENSMA - Université de Poitiers 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 S5S5 v 3,v 4,v 5 v 3,v 4 v 5,v 6 v1,v3v1,v3 S1S1 S4S4 ES 8 ES 6 ES 4 ES 2 v1v1 ES 3 ES 1 v2v2 S3S3 v3v3 v2v2 ES 5 S2S2 v 3,v 4 v 1,v 2 ES 7 v6v6 8 End/Systems ES i 5 Switches S i 6 Virtual links v i  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)  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: F min ≤ data frame lenght ≤ F max BAG = minimum inter-generation time of frames on its source End/System:  guaranteed bandwidth for any data flow: F max / BAG ≥ BAG ES 1 (v 1 ) < BAG 5  Context  State of the art  Contribution  Conclusion The AFDX network: Virtual link 8 End/Systems ES i 5 Switches S i 6 Virtual links v i S5S5 v 3,v 4,v 5 v 3,v 4 v 5,v 6 v1,v3v1,v3 S1S1 S4S4 ES 8 ES 6 ES 4 ES 2 v1v1 ES 3 ES 1 v2v2 S3S3 v3v3 v2v2 ES 5 S2S2 v 3,v 4 v 1,v 2 ES 7 v6v6

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 ES 1 ES 2 S1S1 S2S2 ETE delay Objective: Guarantee the worst ETE delay of any frame of any flow v i crossing the AFDX ( Mandatory for certification ) Variable waiting durations in buffers (difficult to evaluate) 6  Context  State of the art  Contribution  Conclusion

Outline LIAS - ISAE/ENSMA - Université de Poitiers 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) 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 PolicyFIFO, … 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  Conclusion Network Calculus and Trajectory Approach  Global charge: sum of charges of all the flows encountered on any crossed node S S S S 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 LIAS - ISAE/ENSMA - Université de Poitiers 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) 10

Maximum transmission time : C i = F max / R (R = rate of the physical link) Minimum inter-generation time between two consecutive frames : T i = BAG 1 output port (Switch or End/System) a network node 1 virtual link v i flow, characterized by: ≥ T i i CiCi vivi i  Context  State of the art  Contribution  Conclusion Modelization of AFDX by the FA method (1/2) 11 Analysis of the worst ETE delay of flows with FA (1/10)

12 S5S5 v 3,v 4,v 5 v 3,v 4 v 5,v 6 v1,v3v1,v3 S1S1 S4S4 ES 8 ES 6 ES 4 ES 2 v1v1 ES 3 ES 1 v2v2 S3S3 v3v3 v2v2 ES S2S2 v 3,v 4 v 1,v ES 7 v6v6 v 1,v 3 S 22 ES 1 ES 2 S 52 S4S4 S 51 v1v1 v 3, v 4, v 5 v2v2 S 32 S 31 ES 3 ES 4 v2v2 v1v1 S 21 S1S1 v2v2 v6v6 v 3,v 4 v6v6 v5v5 v3v3 v1v1 v2v2 v 5,v 6 v3v3 v 3,v 4 v 5,v 6 Modelization by FA : AFDX :  Context  State of the art  Contribution  Conclusion Modelization of AFDX by the FA method (2/2) ES 1 S 51 S 52 Analysis of the worst ETE delay of flows with FA (2/10)

13 Worst ETE delay R i of a flow v i : The FA principle … - Maximum backlog encountered by f i on last i (  FIFO policy) - Maximum delay incurred by f i to arrive on last i : fifi fifi Generation time of f i Worst arrived time of f i  Context  State of the art  Contribution  Conclusion Analysis of the worst ETE delay of flows with FA (3/10)

14 How to compute ? Computation of the maximal delay … Generation time of f i - Iterative computation, knowing that fifi fifi L = propagation delay of a frame on the link between h and h+1  Context  State of the art  Contribution  Conclusion Analysis of the worst ETE delay of flows with FA (4/10)

15 Question: how to compute on a node h ? Theorem: considering a temporal interval [ a, b ] on h, the scenario leading, for any flow v j, to its greatest amount of work is obtained when: … with Maximum interference of frames of a same flow on a node h (1/3)  Context  State of the art  Contribution  Conclusion Analysis of the worst ETE delay of flows with FA (5/10)

16 Example: determination of the worst case backlog of a single flow v j on h: … [a, b] = [20, 110]  Context  State of the art  Contribution  Conclusion Maximum interference of frames of a same flow on a node h (2/3) Analysis of the worst ETE delay of flows with FA (6/10)  When no other frame of v j can catch up the frame f j on h  When one frame of v j catches up the frame f j on h  When always one frame of v j still catches up the frame f j on h  When two frames of v j catch up the frame f j on h

17 Example: determination of the worst case backlog of a single flow v j on h: General case: … … frames … [a, b] = [20, 110]  Context  State of the art  Contribution  Conclusion Maximum interference of frames of a same flow on a node h (3/3) Analysis of the worst ETE delay of flows with FA (7/10)

18  Usage of the request bound function theory for computing the maximal transmission duration of v j frames arrived in [ a,b ]:  Total transmission duration of frames of all the flows crossing h and arriving in [ a,b ]:  is computed based on … … t = b - a  Context  State of art  Contribution  Conclusion Analysis of the worst ETE delay of flows with FA (8/10) Maximum interference of frames of all the flows crossing a node h:

19 Comparative study of the FA method on an AFDX example (1/2) v 1,v 3 S 22 ES 1 ES 2 S 52 S4S4 S 51 v1v1 v 3, v 4, v 5 v2v2 S 32 S 31 ES 3 ES 4 v2v2 v1v1 S 21 S1S1 v2v2 v6v6 v 3,v 4 v6v6 v5v5 v3v3 v1v1 v2v2 v 5,v 6 v3v3 v 3,v 4 v 5,v 6 CiCi TiTi v1v v2v2 v3v3 50 v4v4 30 v5v5 v6v6 50 L = 16  Context  State of the art  Contribution  Conclusion Analysis of the worst ETE delay of flows with FA (9/10)

20 FANCNCNSTA v1v v2v v 3 (S 31 ) v 3 (S 51 ) v4v v5v N/A v6v 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 v 5, 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 v 1, v 2, v 3 but can compete with NC only for flows v 1, v 2, v 3 FA = Our approach whitout serialization 5) No method is better than the others Worst case ETE delays Analysis of the worst ETE delay of flows with FA (10/10) Comparative study of the FA method on an AFDX example (2/2)  Context  State of the art  Contribution  Conclusion

Outline LIAS - ISAE/ENSMA - Université de Poitiers 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) 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  Context  State of the art  Contribution  Conclusion  Extension to other policies: Fixed priorities, …

Thank you for your attention! LIAS - ISAE/ENSMA - Université de Poitiers ? 23