1. Sept. 28 200Internet routing seminar (Fall 2000) An analysis of BGP convergence Properties Timothy G. Griffin Gordan Wilfong Presented by Tian Bu

2. Sept. 28 200Internet routing seminar (Fall 2000) Outlines A BGP abstract model BGP routing anomalies BGP routing complexity Real-world BGP vs. abstract model Conclusion and Future research

3. Sept. 28 200Internet routing seminar (Fall 2000) BGP Abstract Model G = –V = AS, E = peering relation S = <G,Policy(G),s 0 ) Evaluation state –A tuple s =, c i is current contends of AS i Announcement –nlri, next_hop, as_path, loc_pref Best router selection –Compare loc_pref, path length and next_hop

4. Sept. 28 200Internet routing seminar (Fall 2000) BGP Abstract model (Cont.) Router record transformation –BGP-specific path-vector trans. PVT(w <- v)[R] –Policy trans. Import: import (w <- v)[R] Export: export (w <- v)[R] AS Choices – router i in state s =  import(i  j)[PVT(i  j)[export(i  j)[c j ]]]  j is i’s neighbor State transform.  is defined as if i  A c i ` = c i else c i ` =  Select(Choice(i,s)) A

5. Sept. 28 200Internet routing seminar (Fall 2000) Model not capture Address containment and aggregation –Network address are treated as flat space Ignore MED, ORIGIN, ATOMIC AGGREGATE and AGGERAGATOR. Multiple link between pair of ASs iBGP Default router

6. Sept. 28 200Internet routing seminar (Fall 2000) Evaluation graph 1-0 2-1-0 S0S0 1-0 2-0 1-2-0 2-1-0 2-0 1-2-0 2-0 {1} {2} {1} {1,2} {1} {1,2} {2} {1} {2} {1,2} {2} {1,2} 0 12 1-0 2-0

7. Sept. 28 200Internet routing seminar (Fall 2000) Solvability and routing tree Final state s  s  v  V If final state exists  BGP system S is solvable Routing graph –Routing(d,s): a graph of all AS path to d in state s All routing graphs are trees in a final state T = routing(d,s), s 0, s are initial, final state resp. s 0  s V(T) v

8. Sept. 28 200Internet routing seminar (Fall 2000) Router anomalies Bad Gadget –unsolvable Surprise –Vulnerable to link failure Disagree –Multiple solution Precarious –Trap, sink into a sub-graph

9. Sept. 28 200Internet routing seminar (Fall 2000) BAD GADGET Router i, (i>0) prefer to take router (i+2)%3 to reach router 0 No solution 12 0 3

10. Sept. 28 200Internet routing seminar (Fall 2000) Surprise It is a solvable Become BAD GADGET after 4-5 break 0 1 2 3 45

11. Sept. 28 200Internet routing seminar (Fall 2000) Disagree Router 1, 2 all prefer to go through the other Two solution depends on the AS activation sequence 0 12 0 12 0 12 ?

12. Sept. 28 200Internet routing seminar (Fall 2000) Precarious The existence of solution  converge to solution. The existence of trap 1 0 2

13. Sept. 28 200Internet routing seminar (Fall 2000) BGP converge problems REACHABILITY –In final state s, whether AS v has a path to AS w ASYMMETRY –In final state s, whether the as path from AS v to w is the reverse path from AS w to v SOLVABILITY/UNSOLVABILITY –The existence of final state –SOLVABILITY/UBSOLVABILITY(sd) a single destination case TRAPED –The existence of trap.

14. Sept. 28 200Internet routing seminar (Fall 2000) BGP converge problems (Cont.) K-Robust –Will solvable S remain solvable under any k links failure Unique –Uniqueness of final state Multiple –Whether a solvable S has more than one solution

15. Sept. 28 200Internet routing seminar (Fall 2000) Complexity results REACHABILITY is NP-complete ASYMETRY is NP-complete SOLVABILITY(SD) is NP-complete; UNSOLVABILITY(SD), SOLVABILITY, and UNSOLVABILITY are NP-hard TRAPPED is NP-hard K- ROBUST is NP-hard UNIQUE(SD), UNIQUE are NP-hard MULTIPLE(SD) is NP-complete, MULTIPLE is NP- hard

16. Sept. 28 200Internet routing seminar (Fall 2000) Abstract Model and Real BGP Model capture the most of routing behavior –Complexity results is valid for real BGP Model might disagree with real BGP 1 0 2 Disagree Bad Gadget 1Bad Gadget 2 d 1,d 2

17. Sept. 28 200Internet routing seminar (Fall 2000) Conclusion and future work Static analysis can not really solve the problem –No global policy available –NP-hard or NP-complete Extend BGP to deal with policy conflicts –A challenge to be scalable, robust and compatible to address aggregation Characterize BGP policy inconsistencies