On the Stability of Rational, Heterogeneous Interdomain Route Selection

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 (ABD1, AE2D2) whenever possible, otherwise select (AG1G2D1,AE1D2)

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 = { ri | i  V } • Specify the route chosen by each AS • Paths in a state may be inconsistent • Preferences of ASes • Utility function ui(r), for each i  V • Dependency on r, not just ri: 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 ri is overwhelmed by ri’ if • Whenever ri is available, so is ri’ • Choosing ri’ 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. General Instability of RRS networks • A necessary condition to establish general instability • If no such (NE) route selection exists, the network is unstable under any RRS algorithms 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