Part IV BGP Modeling
BGP Is Not Guaranteed to
Converge!
 BGP is not guaranteed to converge to a
stable routing. Policy inconsistencies
can lead to “livelock” protocol
oscillations.
 Goal:
 Design a simple, tractable and complete
model of BGP modeling
 Example application: sufficient condition to
guarantee convergence.
2
BGP is Solving What Problem?
Underlying problem
Distributed means of
computing a solution.
Shortest Paths
RIP, OSPF, IS-IS
X?
BGP
 X can
 aid in the design of policy analysis algorithms and
heuristics,
 aid in the analysis and design of BGP and
extensions,
 help explain some BGP routing anomalies,
 provide a fun way of thinking about the protocol3
Separate Dynamic and Static
Semantics
 Static semantics:
 BGP policies  Stable Paths Problem
 Dynamic semantics:
 BGP  SPVP
 SPVP: Simple Path Vector Protocol
 A distributed algorithm for solving Stable Paths
Problem
4
What is Stable Paths
Problem?
Example:
 A graph of nodes and
edges,
 Node 0, called the origin,
 For each non-zero node, a
set or permitted paths to
the origin. This set always
contains the “null path”.
 A ranking of permitted
paths at each node. Null
path is always least
preferred.
222 10 0
5
5210
2
4
420
430
3
30
0
1
130
10
most preferred
…
least preferred (not 5null)
A Solution to SPP
 A solution is an assignment of permitted
paths to each node such that
 node u’s assigned path is either the null
path or is a path uwP, where wP is
assigned to node w and {u,w} is an edge
in the graph,
 each node is assigned the highest ranked
path among those consistent with the
paths assigned to its neighbors
6
A Solution to SPP
 A solution
need not
represent a
shortest path
tree or a
spanning tree
210
20
5
5210
2
4
420
430
3
30
0
1
130
10
7
There can be Multiple
Solutions to an SPP
120
10
120
10
1
120
10
1
0
0
2
210
20
DISAGREE
1
2
210
20
First solution
0
2
210
20
Second solution
8
Multiple Solutions Can Occur
Due to Recovery:
10
1230
1
230
210
2
1
primary
link
0
2
0
1
10
1230
2
230
310
0
backup
link
3210
30
3
Remove primary link
3
3
3210
30
Restore primary link
9
Ranking BGP Paths







Highest local Preference
Shortest AS path Length
Origin: IGP<EGP<INCOMPLETE
Lowest MED value
IBGP preferred over EBGP
Lowest IGP cost
Tie breaking
10
Bad Gadget: No Solution
Stage 1:
1: [10]
2: [210]
3: [30]
Stage 2:
1:[130]
2:[20]
3:[320]
Back to stage 1
2
210
20
4
0
1
130
10
3
320
30
11
Bad Gadget: No Solution
Stage 1:
1: [10]
2: [20]
3: [320]
Stage 2:
1:[130]
2:[210]
3:[30]
Back to stage 1
2
210
20
4
0
1
130
10
3
320
30
12
Has A Solution, But Can Get
Trapped:
4
310
3120
5
5310
563120
53120
4310
453120
43120
1
3
120
10
0
6
2
6310
643120
63120
This part has a solution only
when node 1 is assigned the
direct path (1 0).
210
20
As with DISAGREE, this part
has two distinct solutions 13
Has A Solution, But Can Get
Trapped:
4
310
3120
5
5310
563120
53120
4310
453120
43120
1
3
120
10
0
6
2
6310
643120
63120
This part has a solution only
when node 1 is assigned the
direct path (1 0).
210
20
As with DISAGREE, this part
has two distinct solutions 14
How To Solve An SPP?
 Exponential complexity
 Just enumerate all path assignments,
And check stability of each….
 NP-complete
 3-SAT can be reduced to SPP
15
Distributed Algorithms to
Solve SPP
 OSPF-like




Distributed topology, path ranks
Solve SPP locally
Exponential worst case
How to avoid loops if multiple solutions exist?
 RIP-like:





Pick the best path form neighbors’ paths
Tell neighbors about changes
Can diverge
Not guaranteed to find a solution even if it exists
No bound on convergence time
16
SPVP Protocol
 Pick the best path available at any time
process spvp[u] {
receive P from w 
{ rib-in(uw) := u P
if rib(u) != best(u) {
rib(u) := best(u)
foreach v in peers(u) {
send rib(u) to v
}
}
}
}
17
SPVP and SPP
 SPVP wanders around assignment
space
SPP Solvable
must converge
SPVP Can Diverge
must diverge
18
A sufficient condition for
sanity
If an instance of SPP has an
acyclic dispute digraph, then
Static (SPP)
Dynamic (SPVP)
solvable
safe (can’t diverge)
unique solution
predictable restoration
all sub-problems
uniquely solvable
robust with respect to
link/node failures
19
Dispute Digraph Example
130
10
210
20
1
2
0
20
10
420
210
3420
3
4
3420
30
420
430
BAD GADGET II
CYCLE
430
130
30
20
Dispute Wheels
R_k
u_0
u_k
Q_0
Q_k
•At
u_i,
rank
of
Q_i
u_1
R_1 is less than or equal
u_2to rank of R_iQ_(i+1)
Q_1
R_0
Q_2
Q_(I+1)
Q_i
u_(i+1)
R_i
u_i
•There exists a
dispute wheel iff
there exists
cycle in the dispute
digraph
21
Dispute Wheel Example
1230
120
10
2310
230
20
1
2
3
1
1
2
0
0
3
3
2
3120
310
30
22
A Dynamic Solution
 Extend SPVP with a history attribute,
 A route’s history contains a path in the
dispute digraph that “explains” how the route
was obtained,
 A route history will contain a dispute cycle if
and only if a policy dispute is dynamically
realized.
 If a route’s history contains a cycle, then
suppress it ….
23