1. On the Stability of Rational, Heterogeneous Interdomain Route Selection Hao Wang Yale University Joint work with Haiyong Xie, Y. Richard Yang, Avi Silberschatz, Yale University Li Erran Li, Bell-labs Yanbin Liu, UT Austin ICNP 2005

2. Outline  Motivation  Rational route selection (RRS) framework  Applications of the RRS framework  Stability of RSS networks  Potential instability of traffic demand matrix (TM)-based route selection  Summary

3. Interdomain Routing Stability ASes adopt local policies to select routes, e.g.:  To maximize revenue  To load-balance interdomain traffic Interaction of route selection policies can lead to instability  Persistent route oscillation even though the network topology is stable Routing instability can greatly disrupt network operations

4. Previous Work on Stability Conditions for stability in general networks, e.g.:  “ Dispute wheel ” [Griffin et al. ’ 02]  “ Dispute ring ” [ Feamster et al. ’ 05] ISP business considerations tend to stabilize the Internet, e.g. [Gao & Rexford ‘ 01]  Can be generalized, e.g: Class-based routing [Jaggard & Ramachandran 04] Proposals to guarantee stability, e.g.:  SPVP3 [Griffin & Wilfong ‘ 00]

5. What ’ s missing Stability of BGP networks with heterogeneous route selection algorithms  Greedy route selection (SPVP) is not always a good choice  Different ASes in a network may run different route selection algorithms

6. Beyond Greedy Route Selection Optimal route selection for AS A Greedy route selection for AS A Optimal route selection for AS A: select (ABD 1, AE 2 D 2 ) whenever possible, otherwise select (AG 1 G 2 D 1,AE 1 D 2 )

7. What ’ s missing (cont ’ ) Traffic demand matrix-based route selection  Traffic engineering may require local policies of ASes to involve both egress routes and traffic demand  Traffic demand may change with the chosen egress routes

8. TM-based Route Selection {S}BFD: S is sending traffic to D using B’s route BFD B chooses route depending on inbound-traffic volume

9. RRS Framework – Basic Ideas Do not specify in any details how ASes select routes  Achieve generality Focus on sequences of network states over time  Generated by a set of route selection algorithms, one per AS Identify general properties satisfied by these sequences  Inspired by work on adaptive learning [Milgrom & Roberts ‘ 91] and learning on the Internet [ Friedman & Shenker ‘ 97]  Have to deal with dependency among route selections: routes available to an AS are exported by its neighbors

10. Model AS level routing  Network topology: a simple, undirected graph G = (V,E)  V: set of ASes  E: set of interdomain links Network state (network route selection)  A set of path r = { r i | i  V }  Specify the route chosen by each AS  Paths in a state may be inconsistent Preferences of ASes  Utility function u i (r), for each i  V  Dependency on r, not just r i : can model multiple destinations and/or TM- based route selection Network dynamics  A sequence of states { r(t) | t  T }  T = { 0, 1, … } : indices of the sequence of physical times at which state changes  Can evolve in arbitrary way

11. RRS Algorithms / RRS Networks Overwhelmed route selections  Route selection r i is overwhelmed by r i ’ if  Whenever r i is available, so is r i ’  Choosing r i ’ always yields strictly better outcome RRS algorithms  Asymptotically, overwhelmed route selections are no longer chosen (more general than “best-response”)  Allows arbitrary transient behavior  Network-specific: whether an algorithm belongs to RRS depends on the network, esp. preferences of ASes RRS networks  Networks with ASes running RRS algorithms  E.g.: A network running BGP greedy route selection (SPVP) is an RSS network under certain assumptions

12. Outline  Motivation  Rational route selection (RRS) framework  Applications of the RRS framework  Stability of RRS networks  Potential instability of traffic demand matrix (TM)-based route selection  Summary

13. Stability of RRS Networks The sequence { r(t) } asymptotically lie in a set, U   The sequence { r(t) } generated by RRS algorithms belongs to a sequence of monotonic decreasing sets  The set U  depends only on network topology and preferences of ASes, but not protocol dynamics If U  is a singleton, stability is guaranteed

14. An Application of the Stability Results Sequential Dominant Route Selection (SDRS)  A partial order of ASes  The destination AS is the first  An AS can decide its strictly dominant route selection given route selections of ASes precedes it U  is singleton for a network with SDRS  “ No dispute wheel ” conditions guarantee stability for any RRS network

15. Outline  Motivation  Rational route selection (RRS) algorithms framework  Applications of the RRS framework  Stability of RSS networks  Potential instability of traffic demand matrix (TM)-based route selection  Summary

16. Potential Instability of TM- based Route Selection TM-based route selection using greedy strategy may lead to persistent route oscillations An RRS algorithm works if only one AS uses TM- based route selection  Do experimentations for a period of time to learn the consequence of each choice {}BD -> {S}BD -> {S} BFD -> {} BFD -> {} BD -> …

17. A necessary condition to establish general instability If no such (NE) route selection exists, the network is unstable under any RRS algorithms General Instability of RRS networks r is stable route selection for a network with RRS algorithms r satisfies conditions similar to a Nash Equilibrium (NE)

18. Potential Instability of TM- based Route Selection This network is unstable under any RRS algorithms

19. Summary Rational route selection framework  Accommodate heterogeneity  Incorporate rationality A sufficient condition to guarantee routing stability of RSS networks A necessary condition to establish general instability of RSS networks

20. Thank you!

21. Backup Slides

22. An Example BGP greedy route selection (SPVP) is an instance of RSS algorithm if  The ranking of an AS depends on egress routes only  BGP messages are reliably delivered in FIFO order w/ bounded delay  BGP messages are processed immediately (can be relaxed)  Update messages are sent in bounded time after an route change