On the Stability of Rational, Heterogeneous Interdomain Route Selection

Hao WangYale University

Joint work with

Haiyong Xie, Y. Richard Yang, Avi Silberschatz, Yale University

Li Erran Li, Bell-labsYanbin 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

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

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]

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

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 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 selectionNetwork 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

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 -> …

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)

Potential Instability of TM-based Route Selection

{S}AED

{}BFD

{S}AD

{}BFDBFD

{}AED

{S}BD

{S}AD

{}BDBD

AEDAD

{S}AED

{}BFD

{S}AD

{}BFDBFD

{}AED

{S}BD

{S}AD

{}BDBD

AEDADA

BAB

AA

BBAABB

AB

AB

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