Policy-Compliant Path Diversity and Bisection Bandwidth

Transcription

1 Policy-Compliant Path Diversity and Bisection Bandwidth Rowan Klöti1, Vasileios Kotronis1, Bernhard Ager1, Xenofontas Dimitropoulos2,1 1 ETH Zurich, Switzerland 2 University of Crete / FORTH, Greece 1

2 Assume that you are a network domain admin èhow resilient is my AS-level connection to a remote AS? The other guy èwhat limits the path diversity between me and the remote AS? My multi-homing degree? The Internet topology at large? Poor connectivity on the local/remote upstream ISPs side? Me *Picture from: / 2

3 Consider an example network topology 3

4 We can perform a min-cut between S and D 4

5 We can calculate the maximum S-D flow 5

6 We can calculate the edge-disjoint S-D paths 6

7 Basic mechanism: min-cuts Generalized problem: max-flow / min-cut Basic theorem was proven back in 1956 J Menger s theorem Ł path diversity = min-cut, for unitary edge capacities Well-known algorithms available Ł Well, then everything is already solved, right? 7

8 Networks are governed by policies Motivation Security considerations Routing optimization techniques Financial agreements, SLAs, p2p Peak Example 1: the valley-free AS-level Internet Peers, providers, customers: p2p, p2c, c2p links Example 2: (negative) waypoint routing Force traffic into waypoints Avoid certain nodes/links along the way 8

9 Challenge: policies restrict path selection Ł Assume trivial regex policy: ( )* ( )+ ( )* 9

10 Challenge: policies restrict path selection Ł Only two edge-disjoint paths are now valid (min-cut=2) 10

11 Our contribution: estimating policy-compliant min-cuts General methodology Assumption: network policies as regular expressions Graph transformation algorithm Transformed graph contains only policy-compliant paths Min-cut values should not be distorted by the transform Min-cut calculations Complex on original graph (no straightforward method) Simple on transformed graph No modification required on classic graph algorithms 11

12 How we represent graphs and policies Network graph: Network policy: Valley-free example: Ł Graph = AS-level Internet Ł Policy = c2p*p2p?p2c* 12

13 Core of transformation: tensor product ŁIntuition: move between G nodes and NFA states concurrently ŁShould yield valid, policy-compliant paths 13

14 Does this process preserve the min-cut? Ł Intuition: the min-cut paths between any 2 node sets in G should traverse at most the same number of edges as in G 14

15 Idea: properly add aggregation states 15

16 Are all cases fully aggregatable? Aggregatable NFA cases Non-aggregatable NFA cases One-to-One One-to-Many Not a complete bipartite graph! Many-to-One Many-to-Many Min-cut is inflated by a factor of 2 Maximal biclique finding problem 16

17 Remember our initial motivation èhow resilient is my AS-level connection to a remote AS? The other guy èwhat limits the path diversity between me and the remote AS? My multi-homing degree? The Internet topology at large? Poor connectivity on the local/remote upstream ISPs side? + POLICIES! Me *Picture from: / 17

18 Example I: Policies and AS-level path diversity p2p Peak p2p p2p Plateau Classic Valley-Free (VF) vs Multi-Peering Links (MPL) Graph based on CAIDA s AS relationship dataset (+/- open p2p links from PeeringDB) 18

19 Example II: Effect of depeering events Simulated depeering between two tier-ones Examined the effect on their exclusive customer cones Valley-free Multi-p2p links significant loss of path diversity negligible loss Policy relaxation seems to be beneficial Inter-domain policy scenario Loss in mean path diversity after depeering(%) Valley-free Open Links 7.02 Multiple Peering Links Open Links

20 Summary and Contributions Estimating policy-compliant min-cuts on network graphs Network policies as regular expressions Graph transformation algorithm Exact values or approximations depending on NFA form Min-cut calculations Complex on original graph Simple on transformed graph No modification required on classic graph algorithms Large variety of use cases out there AS-level path diversity under diverse policy models MPTCP, multipath routing, flow routing applications 20

21 Questions? POLICY- COMPLIANT MIN-CUTS AS-level Internet 21

22 BACKUP 22

23 Assume that you are a datacenter operator How resilient is my switched topology to link failures? What is the bisection bandwidth of my datacenter? Picture from: 23

24 Min-cuts are the answer to many more questions What is the max feasible bandwidth for a MPTCP transfer between two of my server clusters? What is the bisection bandwidth of my datacenter? How resilient is my switched topology to link failures? How much edge capacity should be depleted for a successful DDoS link-flooding attack against my network? What limits the AS-level path diversity between my domain and another remote domain? My multi-homing degree? The Internet topology at large? Poor connectivity on the local/remote upstream providers side? 24

25 Complexity of the graph transform process In space: Ł V = O ( V ( Q + Δ ) Ł E = O ( Δ ( V + E ) In time: Ł t = O ( V Q + Δ ( V + E + Q )) + t dec In practice, the total running time is dominated by the mincut calculation on the transformed graph 25

26 Related Work Tensor products Soule et al. use tensor products in a different context (bandwidth allocation policies) Network resilience Research on resilient networks Network are not simply geographical maps Policy-compliance framework is very important Min-cuts with policies Connectivity discovered by RV protocols by Sobrinho et al., valley-free s-t paths/cuts Ł Our main contribution: graph transformation without changing classic algorithms (can also be extended for finding the shortest valid paths), generic method 26

27 Inter-domain Routing Policy NFAs 27

28 NFA vs DFA (With Steps MPL scenario) 28