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
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 TMbased 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
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 TMbased Route Selection
TM-based route selection
using greedy strategy may
lead to persistent route
oscillations
An RRS algorithm works if
only one AS uses TMbased 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
r is stable route
selection for a
network with
RRS algorithms
r satisfies
conditions similar
to a Nash
Equilibrium (NE)
If no such (NE) route selection exists, the
network is unstable under any RRS
algorithms
Potential Instability of TMbased Route Selection
B
A
AD
BD
{S}AD
{}BD
BFD
{S}AD
{}BFD
AED
A
B
A
{}AED
{S}BD
B
{S}AED
{}BFD
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