Analysis of TDMA Crossbar Real-Time Switch Design for AFDX...

Analysis of TDMA Crossbar Real-Time Switch Design for AFDX Networks

Lei Rao ‡ †*, Qixin Wang‡, Xue Liu†, Yufei Wang‡

‡Department of Computing, The Hong Kong Polytechnic University, China†School of Computer Science, McGill University, Canada

* Presenter, now working at General Motors Research Lab, United States. Contact information: [email protected]

March 29, 2012

Content

Problem Statement and Analysis

Resource Planning Problem and Approximation Algorithm

Related Work

Background

Conclusion

AFDX is a data network for safety-critical applications that utilizes dedicated bandwidth while providing deterministic Quality of Service (QoS). – from wikipedia

AFDX Network

10/100Mbit switched Ethernet

Based upon IEEE 802.3 and ARINC 664

Bridges the gap on reliability of guaranteed bandwidth in ARINC 664

Adopted by Airbus A380, Boeing 787 Dreamliner etc

Background: Avionics Full DupleX (AFDX) Switched Ethernet

AFDX: Properties

• Properties in AFDX: Redundancy for reliable transmission Virtual links with traffic shaping for end-

systems’ communication

• Elements in an AFDX network: AFDX End-system AFDX Switch AFDX Links

AFDX: Virtual Links and Switches

Each VL conducts one unicast flow from a source-end to a destination-end (e.g. E1 to E5) ;

Along the VL’s route, before entering each AFDX node, the VL flow must behave as if policed by a token bucket;

With the per hop token bucket policing and proper switch architecture design, we can guarantee end-to-end real-time for each VL.

Problem Statement: AFDX Switch Architecture Design

• AFDX standard leaves the switch architecture design open– Challenge

• Vendors want to reuse the legacy switch architecture instead of a complete re-design

– Design goals• Build AFDX networks using a popular real-time switch,

which we call TDMA crossbar real-time switch• Compliance with many mainstream non-real-time

switch architectures

AFDX Switch Architecture Design

• Basic idea & approaches– Prove that TDMA crossbar real-time switched

network is AFDX compliant• Traffic pattern & e2e real-time delay bound

– Discuss the AFDX network’s resource planning problem

• NP-hard– Re-model and approximate the NP-hard problem

Background: TDMA Crossbar Real-Time Switch architecture

• Features– Packets are buffered at the inputs

• All packets are fragmented into same-size units called cells• Each input carries out per-flow queueing

– Outputs fetch/ forward cells synchronously and periodically

• The period is called a cell-time• Each output runs a static TDMA schedule of M cell-time

• Advantages– Simple design/schedulability analysis– High switch utilization– Complie/simplifie with mainstream Internet switch

architecture

Cell time: 1 2 3 4 5

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Demand

a cell to send to O1




TDMA scheduling frame of M cell-time, e.g., M = 5

Case Study: TDMA Crossbar Real-Time Switch Scheduling

Fit all real-time flows’ periods into frame, e.g., (11, 3) (5, 2), i.e., (10, 4) (11,3): sending a message of 3 cells every 11 cell-time

VM-task (5,2): the real-time task is served 2 cell-time units during each clock period of 5 cell times

We consider messages in terms of a cell-time e.g 1 cell = 1 bit; 1 cell-time =1 ns

Demand


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Schedule

Scheduling

Algorithm

Theorem 1 (Schedulability): If demand matrix’ every color ≤ M cell, then have config. time scheduler with O(N4) time cost [TII10].


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Case Study: TDMA Crossbar Real-Time Switch Scheduling

Analysis: AFDX Compliance

AFDX compliance

Along the VL’s route, before entering each AFDX switch, the VL flow must behave as if policed by a token bucket;

With the per hop token bucket policing and proper switch architecture design, we can guarantee end-to-end real-time for each VL

Lf : flow f’s in-network maximum packet lengthHf : total number of hops for a flowM: frame sizePf : flow f’s in-network periodCf : per-frame allocated slots

Analysis: AFDX Compliance

• Theorem 2 (AFDX Compliance)– Per flow analysis with network calculus– Giving end to end delay

src end: source a: arrival curve for each flow at a switchs: service curve for each flow at a switchv: TDMA crossbar real-time switchdes end: destination өf : flow f’s required cell timeuf : flow f’s utilization

src end V0 V1 VHf-1 VHf

..af

(0)sf

(0)af

(1)sf

(1)

af(Hf-1)

sf(Hf-1)

af(Hf)

(des end)

Resource Planning ProblemP(G(V,E),F): TDMA crossbar real-time switch AFDX network resource planning problem

• AFDX network G(V,E), where V is the set of all switches and E is the set of links between the switches• F is the set of flow in the AFDX network

Objectivenetwork utility maximization

Constraintsswitch schedulability

Constraintsend-to-end delay guarantee

Resource Planning Problem: NP-HardObjectivenetwork utility maximization

Constraintsswitch schedulability

Constraintsend-to-end delay guarantee

• Knapsack problem has been known as NP-Hard• An instance of knapsack problem ҡ(Ξ, size,

value, Өs ,Өv ) can be reduced to an instance of TDMA crossbar real-time switched AFDX network resource planning problem:– Construct an AFDX network of three nodes: one

source-end, connected by one TDMA crossbar switch to one destination end.

– becomes equivalent to asking ‘is the constructed resource planning problem results in a maximum ≥

Өv ’

Analysis: Why NP-Hard

Approximation Algorithm

To address the challenge that resource planning problem P(G(V,E),F) is NP-Hard, we propose a re-modeling approach, upon which, we propose an approximation algorithm for P(G(V,E),F)Definition: A configuration function cfg is a function of F →

{0,1,…,ᴧ-1}, where ᴧ

denotes all the alternatives of solutions

Let U~ and U* be the total utility corresponding to cfg~ and the actual optimal cfg* respectively. We have

ᴧ: the maximum number of alternatives in the networkΠ: the set of all ports

Related Work

• Analysis of real-time behavior of AFDX networks upon switches [TII 09, ECRTS 06, INFOCOM 11]

• Industrial fieldbus designs [IECON 09]• TDMA Crossbar Switch Design [TII 10]• Knapsack problem approximation algorithm

Conclusion

• TDMA crossbar real-time switch design for AFDX networks– We proved that TDMA crossbar real-time switched

network is AFDX compliant– We proved the corresponding AFDX network’s resource

planning problem is NP-Hard– We proposed a re-modeling approach

• We proposed an approximation algorithm

Thanks & Questions

Background: Token Bucket

A token bucket flow is defined by (ρ,σ)

ρ

denotes the bucket refilling rate at which

tokens(credits) are accumulated

ρf = Lmax

f (1+Jf / BAGf )

σ is the bucket size

σf = Lmax

f / BAGf

Lmax

f : the maximum packet bit length

BAGf : the bandwidth allocation gap

Jf : the maximum admissible jitter

Background: BAG

• How to affect QoS? -- Bandwidth• BAG (bandwidth allocation gap) • Primary bandwidth control scheme• Minimum time interval between two

successive frames BAG BAG

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Input Ports


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Output Ports


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Per-Flow-Queueing


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cells


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cell cell cell

cell cell

cell


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Synchronous periodic cell forwarding Cell-Time


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Matching


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Why Matching? An input/output can only send/receive one cell per cell-time


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Internal Matching: if an input has multiple per-flow-q for the same output, only one is picked every cell-time.


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Analysis of TDMA Crossbar Real-Time Switch Design for AFDX...

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