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

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 Then I’ll demonstrate the applications of ….framework using two problems

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 We would like to avoid instability if possible

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] There are also studies on stability of AS path-prepending, but we focus on route selection People begin to identify missing issue in previous studies, e.g. the probabilistic safety of BGP, but we focus on some other missing issue.

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 Previous studies assume each AS runs the same, greedy route selection algorithm BGP route selection has increasingly been used by ISPs to achieve a diverse set of interdomain traffic engineering objectives

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)

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

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

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

Model AS level routing Network state (network route selection) 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 In general, network dynamics can evolve in arbitrary ways When the evolution satisfy some general properties, we get the our notion of rational route selection

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

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

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

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

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

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 -> …

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)

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

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

Thank you!

Backup Slides

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