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

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
We would like to avoid instability if possible

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]
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.

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
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

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 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

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