An Analysis of BGP Convergence Properties

• Introduction– The BGP protocol– NP completeness

• Routing anomalies

• Complexity analysis

• Summery

• BGP - the de-facto EGP.

• Policy-based path-vector protocol.– nlri, next-hop, as-path, loc-pref

• Implemented with little global knowledge.

• Protocol divergence.– Dynamic solution.– Static solution.

Static Solution:

• Programs Routing Policies Analysis

• The Route Arbiter Project– Routing Policy Specification Language

(RPSL).– Internet Route Registries (IRRs).– Software Tools (RAToolSet).

Introduction(BGP)

Introduction(NP-Completeness)

• Non Deterministic Turing Machine (NDTM).• NP problems class.• NP-Complete problems class.• Reductions.• ANP-Hard, ANP ANP-Complete.• The 3-SAT problem:

(xyz)(xyz)(xyz)

Routing Anomalies

The DISAGREE System

1

0

2

d

1

0

2

d

1

0

2

d

•AS 1 prefers route 1-2-0.

•AS 2 prefers route 2-1-0.

Routing Anomalies

1

0

2

d

1

0

2

d

Start

1 - 0

1 - 02 - 0

1 - 2 - 02 - 1 - 0

2 - 0

1 - 02 - 1 - 0

1 - 2 - 02 - 0

{1}

{2}

{1,2}

{1,2} {1,2}

{1}{1,2}

{2}{1,2}

{1}

{1}

{2}

{2}

{1}

{2}

{1} {2}{1,2}

{1} {2}{1,2}

Routing Anomalies

The BAD GADGET System

•All AS want to reach destination d in AS 0.

•Each AS prefers the counter-clockwise path of length 2.

1

0

2

3

1

0

2

3

1

0

2

3

1

0

2

3

1

0

2

3

Routing Anomalies

The BAD GADGET System1

0

2

3

1

0

2

3

1

0

2

3

1

0

2

3

1

0

2

3

1

0

2

3

Routing Anomalies

The BAD GADGET System

• All AS 2 export rules:– nlri = d loc-pref = 1

• AS 2 import(2<-1) rules:– (nlri = d as-path = [3,0]) loc-pref = 2– nlri = d loc-pref = 1

• AS 2 import(2<-3) rules:– nlri = d loc-pref = 1

Complexity Analysis

The ASSIGN System

An example of a 3-SAT problem:

(xyz)(xyz)(xyz)

W

~X

X

~Y

Y

~Z

Z

Q

d

W

~X

X

~Y

Y

~Z

Z

Q

d

X=True, Y=False, Z=False

Complexity Analysis

The ASSIGN System

Complexity Analysis

REACHABILITY

(single destination)

W

~X

X

~Y

Y

~Z

Z

Q

d

C 3C 2C 1

W

~X

X

~Y

Y

~Z

Z

Q

d

C 3C 2C 1

C2 import(C2C1) rule:

• nlri = d (x as-path y as-path z as-path) loc-pref = 1

(xyz)(xyz)(xyz)

Complexity Analysis

ASYMMETRY

W

~X

X

~Y

Y

~Z

Z

Q

d1

C 3C 2C 1

d2

Complexity AnalysisSOLVABILITY

(single destination)

W

~X

X

~Y

Y

~Z

Z

Q

d

C 3C 2C 1

1

0

2

3

Complexity Analysis

Relevant Routing Issues

• REACHABILITY.

• ASYMMETRY.

• SOLVABILITY.

• TRAPPED.

• K-ROBUST.

• UNIQUE.

Summery

Static Analysis approach problems:

• Routing policies are not shared.

• Complexity results A need to rely on heuristics analysis rather than on exact analysis.