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Holistic schedulability analysis for multipacket messages in AFDX networks

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Abstract

The ARINC-664, Part 7 (AFDX) standard defines a communication network based on Ethernet and the UDP/IP protocols. Contrary to general-purpose Ethernet, the timing behavior in AFDX is deterministic due to the use of special network switches and end systems with static routing tables and traffic policing at the sending end through mechanisms called virtual links. Even though the latencies in this network are bounded, there are scheduling and contention effects that need to be analyzed. In this paper we develop a response-time analysis for multipacket messages transmitted through an AFDX network including the scheduling of the virtual links and sub-virtual links, and also the contention in the end systems and in the switches. This analysis allows us to obtain worst-case latencies and output jitter for the network messages with a precise modeling of the sending and receiving ends. These results can be integrated in a holistic approach with the response time analysis of the threads in the processing nodes to obtain end-to-end response times in heterogeneous distributed systems.

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Notes

  1. Recall that we assume that this L T latency is only charged once per BAG, as this is the implicit assumption in the equations that appear in subclause 3.2.4.2 in Airlines Electronic Engineering Committee (2005).

Abbreviations

•:

Busy Period: identified with ‘BP’

•:

Equal or Higher priority: identified with ‘EHP’

•:

End System: identified with ‘ES’

•:

Higher priority: identified with ‘HP’

•:

Interference: identified with the letter ‘I’

•:

Jitter: identified with the letter ‘J’

•:

Latency: identified with the letter ‘L’

•:

Lower priority: identified with ‘LP’

•:

Message stream: identified with ‘MS’

•:

Number of instances of a message in the busy period: identified with letter ‘Q’, as in the response time analysis literature

•:

Response time: identified with the letter ‘R’

•:

Switch: identified with “Sw”

•:

Switch queue: identified with “SQ”

•:

Transmission on the Ethernet link: identified as “Tr”

•:

Virtual Link Queue: identified with ‘VLQ’

•:

Work: identified with letter ‘w’ as is done in response time literature

•:

BAG i : the bandwidth allocation gap for virtual link VL i , in time units

•:

BP k : the length of the busy period for any message of VL k

•:

EHP(VL k ): the set of VLs that have as destination port in a switch the outgoing port of VL k with an equal or higher priority, including itself

•:

ES k : the set of VLs in the same end system as VL k (excluding itself)

•:

HP(VL k ): the set of VLs that have as destination port in a switch the outgoing port of VL k , with a higher priority

•:

I VL(ik): the worst-case interference on a message from stream σ i being sent through VL k from the messages of the other VLs in the same end system (see Eq. (17))

•:

Jp j : the worst-case release jitter of the packets arriving at the switch through VL j

•:

Lmax i : largest Ethernet frame for virtual link VL i , in bytes

•:

L Tr(i) the worst-case transmission latency on the Ethernet link of a last packet of a message belonging to stream σ i (see Eq. (9))

•:

\(L_{Tr_{max (k)}}\): the worst-case transmission latency on the Ethernet link of the largest-size packet of VL k (see Eq. (10))

•:

L VL(ik): the latency of a message from stream σ i being sent through VL k due to the scheduling of the virtual links in a specific end system (see Eq. (11))

•:

L VLQ(ik): the worst-case latency of a message from stream σ i in the VL k queue, including the effects of the messages that can be already awaiting on VL k itself (see Eq. (15))

•:

L SVL(imk): the latency of a message from stream σ i being sent through sub-VL SVL mk belonging to VL k due to the scheduling of the VLs in a specific end system (see Eq. (19))

•:

L SVLQ(imk): the worst-case latency for the last packet of a message in the SVL mk queue, including the effects of the messages that can be awaiting in SVL mk and on the other sub-VLs sharing VL k (see Eq. (26))

•:

L Sw(ik): total latency in the switch for the last packet of message stream σ i being sent through VL k (see Eq. (28))

•:

L SQ(ik): the time that the last packet of message stream σ i being sent through VL k is waiting in the switch’s output port queue, due to the interference of the rest of the packets in that output queue (see Eq. (35))

•:

LP(VL k ): the set of VLs that have as destination port in a switch the outgoing port of VL k , with a lower priority

•:

MS(VL k ): the set of message streams that share VL k with message stream σ i (excluding itself)

•:

MI(VL k ): the set of message streams using VL k , including message stream σ i

•:

N(SVL mk ): the set of sub-VLs that share VL k with SVL mk excluding itself

•:

Q i : Number of instances of message stream σ i in a worst-case busy period

•:

R ij : The worst case-response time of step ij in an end-to-end flow (see Fig. 9 and Eq. (47))

•:

VL i : Virtual link number i

•:

w i (q): the worst-case latency of the last packet of the q-th instance of a message from stream σ i to reach the VL scheduler (see Eq. (12))

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Acknowledgements

The authors want to thank the anonymous reviewers for their many detailed comments which have allowed enhancing the paper significantly.

This work has been funded in part by the Spanish Government and FEDER funds under grant TIN2011-28567-C03-02 (HI-PARTES).

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Authors and Affiliations

  1. Computers and Real-Time Group, Universidad de Cantabria, 39005, Santander, Spain

    J. Javier Gutiérrez, J. Carlos Palencia & Michael González Harbour

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  1. J. Javier Gutiérrez
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  2. J. Carlos Palencia
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  3. Michael González Harbour
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Correspondence to Michael González Harbour.

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Gutiérrez, J.J., Palencia, J.C. & González Harbour, M. Holistic schedulability analysis for multipacket messages in AFDX networks. Real-Time Syst 50, 230–269 (2014). https://doi.org/10.1007/s11241-013-9192-2

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