Part IV BGP Modeling

1. Part IV BGP Modeling

2. 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.

3. Underlying problem Distributed means of computing a solution. Shortest Paths RIP, OSPF, IS-IS X? BGP BGP is Solving What Problem? • 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 protocol

4. 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

5. 2 1 0 2 0 5 2 1 0 4 2 0 4 3 0 5 0 3 4 2 1 3 0 1 3 0 1 0 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. 2 most preferred … least preferred (not null)

6. 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

7. 2 1 0 2 0 5 2 1 0 4 2 0 4 3 0 5 0 3 4 2 1 3 0 1 3 0 1 0 A Solution to SPP • A solution need not represent a shortest path tree or a spanning tree

8. 1 1 1 0 0 0 2 2 2 There can be Multiple Solutions to an SPP 1 2 0 1 0 1 2 0 1 0 1 2 0 1 0 2 1 0 2 0 2 1 0 2 0 2 1 0 2 0 First solution Second solution DISAGREE

9. 1 1 1 0 0 0 2 3 2 2 3 3 Multiple Solutions Can Occur Due to Recovery: 1 0 1 2 3 0 1 0 1 2 3 0 primary link 2 3 0 2 1 0 2 3 0 3 1 0 backup link 3 2 1 0 3 0 3 2 1 0 3 0 Remove primary link Restore primary link

10. 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

11. 2 1 0 2 0 2 4 0 3 1 3 2 0 3 0 1 3 0 1 0 Bad Gadget: No Solution Stage 1: 1: [10] 2: [210] 3: [30] Stage 2: 1:[130] 2:[20] 3:[320] Back to stage 1

12. 2 1 0 2 0 2 4 0 3 1 3 2 0 3 0 1 3 0 1 0 Bad Gadget: No Solution Stage 1: 1: [10] 2: [20] 3: [320] Stage 2: 1:[130] 2:[210] 3:[30] Back to stage 1

13. 1 3 0 2 4 5 6 Has A Solution, But Can Get Trapped: 4 3 1 0 4 5 3 1 2 0 4 3 1 2 0 1 2 0 10 3 1 0 3 1 2 0 2 1 0 2 0 5 3 1 0 5 6 3 1 2 0 5 3 1 2 0 6 3 1 0 6 4 3 1 2 0 6 3 1 2 0 This part has a solution only when node 1 is assigned the direct path (1 0). As with DISAGREE, this part has two distinct solutions

14. 1 3 0 2 4 5 6 Has A Solution, But Can Get Trapped: 4 3 1 0 4 5 3 1 2 0 4 3 1 2 0 1 2 0 1 0 3 1 0 3 1 2 0 2 1 0 2 0 5 3 1 0 5 6 3 1 2 0 5 3 1 2 0 6 3 1 0 6 4 3 1 2 0 6 3 1 2 0 This part has a solution only when node 1 is assigned the direct path (1 0). As with DISAGREE, this part has two distinct solutions

15. 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

16. 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

17. 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 } } } }

18. SPVP and SPP • SPVP wanders around assignment space SPP Solvable SPVP Can Diverge must diverge must converge

19. 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

20. 1 3 0 2 1 0 1 0 2 0 1 2 0 3 4 3 4 2 0 4 2 0 3 0 4 3 0 Dispute Digraph Example 2 0 1 0 4 2 0 2 1 0 CYCLE 3 4 2 0 4 3 0 1 3 0 BAD GADGET II 3 0

21. Dispute Wheels u_0 • At u_i, rank of Q_i is less than or equal to rank of R_iQ_(i+1) • There exists a dispute wheel iff there exists • cycle in the dispute digraph R_k R_0 u_k u_1 R_1 Q_0 u_2 Q_1 Q_k Q_2 Q_(I+1) Q_i u_(i+1) R_i u_i

22. 1 2 0 3 Dispute Wheel Example 1 2 3 0 1 2 0 1 0 2 3 1 0 2 3 0 2 0 3 1 1 2 0 3 2 3 1 2 0 3 1 0 3 0

23. 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 ….