Post on 14-Jan-2016
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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.