Failure recovery of overlay tree based structures
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Doctoral Thesis. Failure Recovery of Overlay Tree-based Structures. Ing. Vladim í r Dynda Doc. RNDr. Ing. Petr Zem á nek, CSc. (supervisor). Czech Technical University in Prague Faculty of Electrical Engineering Department of Computer Science and Engineering. Agenda. Introduction

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Failure Recovery of Overlay Tree-based Structures

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Failure recovery of overlay tree based structures

Doctoral Thesis

Failure Recoveryof Overlay Tree-basedStructures

Ing. Vladimír Dynda

Doc. RNDr. Ing. Petr Zemánek, CSc.

(supervisor)

Czech Technical University in Prague

Faculty of Electrical Engineering

Department of Computer Science and Engineering


Agenda

Agenda

  • Introduction

  • Solution

    • BR Platform

    • Bypass Routing

    • Leader Link Election

    • Tree Reconnection

  • Summary of Results

  • Conclusion

Vladimír Dynda: Failure Recovery of Overlay Tree-based Structures


Agenda1

Agenda

  • Introduction

  • Solution

    • BR Platform

    • Bypass Routing

    • Leader Link Election

    • Tree Reconnection

  • Summary of Results

  • Conclusion

Vladimír Dynda: Failure Recovery of Overlay Tree-based Structures


Introduction

Introduction

  • Problem statement

TR= (TM\FC, CE’ )

T4

T = (TM, CE)

TM

T5

CE

T6

T3

FC

T0

T2

S= (N, L)

T1

Vladimír Dynda: Failure Recovery of Overlay Tree-based Structures

1


Introduction1

Introduction

  • Problem statement

    • Failure recovery

      • Reconnection ofT0, T1, ..., TN-1intoa restored network TR= (TM \FC, CE’)

    • Correctness – TR is acyclic

    • Completeness –TRcontains all the fragments

Vladimír Dynda: Failure Recovery of Overlay Tree-based Structures

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Introduction2

Introduction

  • Problem statement

    • Environment

      • Asynchronous distributed system

      • No central authority / no global knowledge

      • Unlimited sizes of S and T

      • Arbitrary traffic directionin T

    • Failures

      • Node failures only

      • Fail stop failure model

      • Failures must not split S

Vladimír Dynda: Failure Recovery of Overlay Tree-based Structures

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Introduction3

Introduction

  • Goals of the thesis

    • Proposal of a generic recovery platform

    • Illustration of the tree restoration methods

    • Simulation & verification of the theoretical properties

    • Survey of possible applications

Vladimír Dynda: Failure Recovery of Overlay Tree-based Structures

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Introduction4

Introduction

  • State of the art

    • On-demand / preplanned recovery

    • Preplanned methods

      • Employ pre-computed backup structures

    • Existing preplanned methods

      • Complete graph (Narada)

      • Ancestor list (Yang-Fei, EFTMRP, HMTP)

      • Administrative hierarchy (Nice, Nemo)

      • Secondary trees (Dual-tree, Coop-net)

      • Link to random nodes (HMTP, Yoid)

Vladimír Dynda: Failure Recovery of Overlay Tree-based Structures

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Introduction5

Introduction

  • State of the art

    • Weaknesses of the existing methods

      • Poor scalability

      • Restricted set of applicable trees

      • Single points of failure

      • Fixed level of fault tolerance

      • Unrecoverable multiple failures

      • Non-local restoration

Vladimír Dynda: Failure Recovery of Overlay Tree-based Structures

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Agenda2

Agenda

  • Introduction

  • Solution

    • BR Platform

    • Bypass Routing

    • Leader Link Election

    • Tree Reconnection

  • Summary of Results

  • Conclusion

Vladimír Dynda: Failure Recovery of Overlay Tree-based Structures


Br platform

BR Platform

  • Bypass ring platform

    • Ensures correctness and completeness

    • Forms a basis for a tree reconnection

    • Fabric of redundant links in T:

      • Bypass rings of optional diameter

      • Alternative paths in the event of failure

      • Location & routing among the fragments

Vladimír Dynda: Failure Recovery of Overlay Tree-based Structures

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Br platform1

BR Platform

  • Failure recovery

Bypass routing

Tree reconnection

Leader link election

Bypass rings

BC(FC)

n1

Leader

BRT(n1,4)

BRT(n2,2)

BRT(n1,3)

BRT(n1,2)

FC

n1

n2

TR= (TM\FC, CE’ )

n2

T = (TM, CE)

Vladimír Dynda: Failure Recovery of Overlay Tree-based Structures

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Br platform2

BR Platform

  • Elemental steps of the recovery

    • Initialization of the platform

    • Failure detection

    • Designated nodes discovery

    • Leader link election

    • Tree reconnection

    • Bypass rings reconfiguration

Bypass routing

Correctness

&

Completeness

Vladimír Dynda: Failure Recovery of Overlay Tree-based Structures

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Agenda3

Agenda

  • Introduction

  • Solution

    • BR Platform

    • Bypass Routing

    • Leader Link Election

    • Tree Reconnection

  • Summary of Results

  • Conclusion

Vladimír Dynda: Failure Recovery of Overlay Tree-based Structures


Bypass routing

Bypass Routing

  • Partially ordered tree (POT)

Ordered rays

Ordered neighbor

sequence

R-(A0,3C)

R+(A0,3C)

17

CE

E8

9F

BT(A0,3C)

B9

72

67

79

09

0F

3C

A0

93

B2

1D

SeqT(A0)

24

SeqT(3C)

42

T = (TM, CE)

5E

4A

F7

11

R+(A0,3C)

Vladimír Dynda: Failure Recovery of Overlay Tree-based Structures

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Bypass routing1

Bypass Routing

  • Bypass ring BRT(n, d)

R+(n,n1)

R-(n,n0)

dmax = 4

BT(n,n1)

BRT(n,4)

BRT(n,dmax)

BRT(n,3)

BT(n,n0)

n1

BRT(n,2)

n0

R-(n,n1)

R+(n,n2)

R+(n,n0)

n2

n

n3

R-(n,n3)

SeqT(n)

BT(n,n2)

R+(n,n3)

BT(n,n3)

R-(n,n2)

Vladimír Dynda: Failure Recovery of Overlay Tree-based Structures

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Bypass routing2

BRT(nm,dmax)

BRT(n2,5)

BRT(n2,4)

BRT(n1,3)

BRT(n1,2)

Bypass Routing

  • Bypass rings

R+(n,n1)

ndmax

n5

n4

n3

FC

n2

n1

n

BT(n,n1)

T = (TM, CE)

Vladimír Dynda: Failure Recovery of Overlay Tree-based Structures

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Bypass routing3

Bypass Routing

  • Routing algorithm

    • <FC>T = BT(ni, nj), njAT(ni)  FC

ni1

nj1

BC(FC)

BT(ni2,nj2)

BT(ni3,nj3)

FC

T = (TM, CE)

nj3

R+(ni1,nj1)

ni3

nj2

ni2

BT(ni1,nj1)

Vladimír Dynda: Failure Recovery of Overlay Tree-based Structures

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Bypass routing4

BRT(A0,4)

BRT(3C,3)

BRT(3C,2)

Bypass routing

  • Example

BC(FC)

R+(72,3C)

CE

17

E8

9F

72

B9

0F

67

FC

79

09

3C

A0

93

B2

1D

24

T = (TM, CE)

42

5E

4A

F7

11

Vladimír Dynda: Failure Recovery of Overlay Tree-based Structures

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Bypass routing5

Bypass Routing

  • Properties

    • Memory overhead at node nT:O(degT(n) * dmax)

    • Routing is successful iflenX(ni, ni+1)  dmax, X = R+(ni, nj)for all neighborsni andni+1 BC(FC)

    • Lower bound of maximum size ofFC:dmax/2 nodes for arbitrary clusters

Vladimír Dynda: Failure Recovery of Overlay Tree-based Structures

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Agenda4

Agenda

  • Introduction

  • Solution

    • BR Platform

    • Bypass Routing

    • Leader Link Election

    • Tree Reconnection

  • Summary of Results

  • Conclusion

Vladimír Dynda: Failure Recovery of Overlay Tree-based Structures


Leader link election

Leader Link Election

  • Leader link election(LLE)

    • Guarantees correctness

    • Communication structure – BC(FC)

    • Node states

      • Passive – initial state of the election

      • Active – leader candidates

      • Relay – election is lost

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Leader link election1

ID(nN-1) < ID(n0)

Leader Link Election

  • LLE on ordered rings

ID(n0) < ID(n1) < ... < ID(nN-1)

Leader

ELECTION(n0)

n0

nN-1

ID(n0) < ID(n1)

n1

ELECTION(n1)

FC

n6

n2

ID(n1) < ID(n2)

n

BC(FC) = BRT(n,2)

SeqT(n)

n5

n3

n4

<FCAT(FC)>

Vladimír Dynda: Failure Recovery of Overlay Tree-based Structures

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Leader link election2

A1.BA < A1.16

Leader Link Election

  • LLE in partially ordered trees

Sweep process

Hierarchical identifier

HIDT(nr,ni)

ELECTION(4F.*)

Leader

BC(FC)

R+

HIDT(4F,D8)

D8

4F.A1.BA.D8

SWEEP(4F.A1)

BA

HIDT(4F,97)

97

4F.A1.BA.97

ELECTION(A1.BA.97)

A1

4F

HIDT(4F,16)

4F.A1.16

16

nr

SeqT(nr)

SeqT(A1)

FC

<FCAT(FC)>

Vladimír Dynda: Failure Recovery of Overlay Tree-based Structures

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Leader link election3

17

9F

67

79

93

24

3C.A0 < 3C.A0

A0.B9 < A0.1D

42

5E

4A

F7

11

Leader Link Election

  • Example

CE

Leader

ELECTION(3C.A0.1D)

E8

72

FC

B9

SWEEP(3C.A0)

0F

nr

nr

09

3C

A0

ELECTION(A0.B9.CE)

B2

1D

T = (TM, CE)

<FCAT(FC)>

Vladimír Dynda: Failure Recovery of Overlay Tree-based Structures

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Leader link election4

Leader Link Election

  • Properties

    • Average message complexity:O(N logbN); b is the average branching factor of FC nodes in T

    • Time complexity: O(N)

Vladimír Dynda: Failure Recovery of Overlay Tree-based Structures

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Agenda5

Agenda

  • Introduction

  • Solution

    • BR Platform

    • Bypass Routing

    • Leader Link Election

    • Tree Reconnection

  • Summary of Results

  • Conclusion

Vladimír Dynda: Failure Recovery of Overlay Tree-based Structures


Tree reconnection

Tree Reconnection

  • Reconnection methods

    • Reconnect the fragments located by the routing algorithm

    • Abide by the results of LLE

    • Designed to meet the specific application requirements

    • Influence properties of the restored tree

Vladimír Dynda: Failure Recovery of Overlay Tree-based Structures

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Tree reconnection1

Tree Reconnection

  • LR method

BC(FC)

n1

n2

n3

Vladimír Dynda: Failure Recovery of Overlay Tree-based Structures

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Tree reconnection2

Tree Reconnection

  • HR-x method

HR-1

(q0, qi) if i  1 (mod x)

(qi-1, qi) otherwise

BC(FC)

n1

= q0

q3

q1

q2

q2

q1

n2

= q0

= q3

n3

q5 =

q0 =

q1

q4

q2

q3

Vladimír Dynda: Failure Recovery of Overlay Tree-based Structures

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Tree reconnection3

Tree Reconnection

  • HR-x method

HR-2

(q0, qi) if i  1 (mod x)

(qi-1, qi) otherwise

BC(FC)

n1

n2

n3

Vladimír Dynda: Failure Recovery of Overlay Tree-based Structures

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Tree reconnection4

17

9F

67

79

93

24

42

5E

4A

F7

11

Tree Reconnection

  • Example

CE

ELECTION(3C.A0.1D)

E8

72

FC

B9

SWEEP(3C.A0)

0F

09

3C

A0

ELECTION(A0.B9.CE)

B2

TR= (TM\FC, CE’ )

1D

<FCAT(FC)>

HR-2

Vladimír Dynda: Failure Recovery of Overlay Tree-based Structures

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Tree reconnection5

Tree Reconnection

  • Properties

Vladimír Dynda: Failure Recovery of Overlay Tree-based Structures

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Tree reconnection6

Tree Reconnection

  • Properties

Vladimír Dynda: Failure Recovery of Overlay Tree-based Structures

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Agenda6

Agenda

  • Introduction

  • Solution

    • BR Platform

    • Bypass Routing

    • Leader Link Election

    • Tree Reconnection

  • Summary of Results

  • Conclusion

Vladimír Dynda: Failure Recovery of Overlay Tree-based Structures


Summary of results

Summary of Results

  • Properties of the BR platform

    • Node memory overhead:

      • O(degT(n) * dmax)

    • Average message complexity:

      • O(N logbN) for arbitrary failures

      • Nfor single failures

    • Lower bound of max. recoverable failure:

      • dmax/2 nodes for arbitrary failed clusters

      • dmax-1 nodes for internal failed clusters

Vladimír Dynda: Failure Recovery of Overlay Tree-based Structures

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Summary of results1

Summary of Results

  • Simulation results

    • Successfully recovered cluster

      • Average diameter: dmax-2

      • Average size: 1.5 dmax

    • Linear recovery time

    • dmax parameter

      • Controls fault-tolerance vs. costs

      • dmax=4 provides ample tolerance for GFS

Vladimír Dynda: Failure Recovery of Overlay Tree-based Structures

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Summary of results2

Summary of Results

  • Properties of the platform

    • Locality

    • Multiple failure recovery

    • Scalability

    • Application requirements consideration

      • Optional level of fault tolerance

      • Protection selectivity

      • Designated nodes discovery

      • Tree reconnection method

    • Independence of the protected tree type

Vladimír Dynda: Failure Recovery of Overlay Tree-based Structures

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Summary of results3

Summary of Results

  • Applications

    • Overlay multicast

      • Applicable in all types

    • Network-layer multicast

      • Extension with BR(n,1) needed

    • Sample application – GFS multicast

      • Designed for large-scale P2P systems

      • Based on a layered administrative hierarchy

      • Employs BR platform to achieve fault-tolerance

Vladimír Dynda: Failure Recovery of Overlay Tree-based Structures

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Agenda7

Agenda

  • Introduction

  • Solution

    • BR Platform

    • Bypass Routing

    • Leader Link Election

    • Tree Reconnection

  • Summary of Results

  • Conclusion

Vladimír Dynda: Failure Recovery of Overlay Tree-based Structures


Conclusion

Conclusion

  • Thesis summary

    • Analysis of overlay trees environment and identification of recovery properties

    • Proposal of BR platform

    • Design of the specialized leader election

    • Illustration of the tree reconnection

    • Simulation of the platform

    • Outline of the overlay multicast scheme

Vladimír Dynda: Failure Recovery of Overlay Tree-based Structures

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Conclusion1

Conclusion

  • Ideas for further research

    • Autonomous management of fault-tolerance level and protection selectivity

    • More sophisticated tree reconnection methods

    • Extension of the platform fornetwork-layer multicast

Vladimír Dynda: Failure Recovery of Overlay Tree-based Structures

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Failure recovery of overlay tree based structures

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