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
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