Combining Multipath Routing and Congestion Control for Robustness Peter Key.
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Transcript of Combining Multipath Routing and Congestion Control for Robustness Peter Key.
Combining Multipath Routing and Combining Multipath Routing and Congestion Control for RobustnessCongestion Control for Robustness
Peter KeyPeter Key
Motivation
• Performance of Internet /overlays unpredictable – and hard to manage
• Multiple ownership / policies (eg BGP) can exacerbate performance problems
• … but diversity increasing– Multihoming– Mesh
• So why not harness the diversity?
Outline
• Motivation• Framework• Resource Pooling
– 2 resources– the function– Cutset dimensioning
• Multipath – Coordinated control– Fluid dynamics
• Route choices & architectures• Concluding remarks
Framework
• Network: capacited graph – G=[X,J]
• Edges have capacity Cj
• Routes s S , sets of edges
• Demands type r, associated source –destination, can use a set of routes
• Link-route incidence matrix A,
route flow incidence matrix B
Framework
• File Transfers– Arrival rate – Mean file size
– Nr in progress
• Streaming – Arrival rate
– Mean holding time
– Mr in progress
• Rate allocation : – xr to both types (fair share): exact rate depends on utility
function
rload r
rr
1r rF
r1
r
lrlr
rrr CxMN :
)(
Resource sharing
Fixed Routing
Dynamic Routing
Fixed Proportions
FMean transf er time
C-
Capacity C
2
F
2p
1-p
1 FTransf er time
2 C-
p 1-pTransf er time F
C-2 C-2 (1 )p p
2 max( ,1 )Stable C p p
F
– Assume performance measure
– non-decreasing in 1st arg., non-increasing in second
– Dimensioning means
– Eg
Performance : the function
( , )C
( , ) some measurable C D D
( , ) =(- ,0)C C , D1( , ) ( )C C
( , )C
Take a cutset C of the Graph G
Under resource pooling, necessary performance conditions are
Becomes interesting when related to sufficiency
Cutset Dimensioning
,j r
j
r jjC
C
D
C
C
Node cutsets:
(Keslassy et al)
• Symmetric case; – Valiant load balancing, – Dynamic routing
Mesh Network Example
6
1
5 4
2
3
and ij j ij j
r r
2 per link suffi cient traffi c matrices
rN
1r
N 2r
N
Multipath Routing: Utility functions
• Utility function associated with type r flow
• increasing, strictly concave etc– Eg TCP,
– Putting w=k/(RTT)2 implies familiar
( )rU x
( )U x w x
1 1 TCP f air:
( )r
r
xT p r
Cost functions
• Now require “cost” convex, and
• True for packet marking etc • with “prices” pj,:
• is prob of drop/marking at j when load is yj,
• Eg small buffer model
( , )j C
0
( , ) /jy
j j j j jy C p z C dz
( ; ) ( ; )L z C Lz LC
j j jp y C
min 1,j j
j j
by yC Cjp
Multipath
Maximise
;r r sr sr j r j s sr sr jr s j r s
N U B x N A B x C
over
• Coordinated
• Single utility function across possible routes flow can choose– Single dependence on RTT
0srx
Fluid Dynamics
• Scale arrival rates and capacities by large number L and take limits
• Gives limiting ODE (FLLN)
1
, 1
rrrr ML
mNL
n
( ) ( ) ( ) ( );
( ) ' ( )r r r r r
r r r r
n t n t x n t mt C
m t m t
Limit Theorems
• Theorem:– Under multipath routing, there is a unique
invariant point– System in Lyapunov stable (under mild
conditions on )– Allocation is only non-zero to routes s for
which “prices” on route are equal– When no streaming, offered load is split
optimally, independent of utility functions
ˆ ˆˆ,r r r r r rm n x
j
Remarks
• Prices on route s are
• Unless “prices” are equal on different routes, only one route is used
• Coordinated multipath chooses load fractions to minimise total “cost”– if no streaming traffic present, fractions
independent of utility functions
ˆ' ( ; )j s j j jj
A y C
rs
Remarks
• Coordinated multipath chooses load fractions to minimise total “cost”rs
,
ˆ ;rrj j s sr sr sr j
j s r
A B x C
Route Choices
• How to search for low cost paths?– Use 2 per nominal route, (eg “direct” +1)– Periodically add new route at random– Probe to chose which route to drop
• Cf “Sticky Random” DAR– “Power of 2”, Mitzenmacher
• Theorem: Under random path resampling, mulitpath routing will find an optimal feasible load split, if one exists
Architecture
• Need path diversity– Dual homing– Multiple addresses (eg IPv6)
• For overlays, wireless, or the Internet?
• Need coordinated congestion control, uncoordinated, parallel, inefficient (see Laurent’s talk …)– at transport or application layer
Summary: Multipath routing/multi-access
• Source /edge routing
• Halve delay (processor sharing)
• Resilience • Simpler dimensioning (cutsets)
C
C
C
C
22 vs 2p p
1 1
vs 2 2 ) ( )C C
• Robust routing provides robustness to– Traffic variations /uncertainty– Routing / BGP / Network operators
• Need to combine multipath routing with congestion control
• Challenges: – Time-scales for route adaptation– Removing RTT bias of TCP?
Summary
References
• Fluid models of integrated traffic and multipath routing, Peter Key & Laurent Massoulié, QUESTA, June 2006
• Network Programming methods for loss networks, Gibbens and Kelly, JSAC 1995
• Stability of end-to-end algorithms for joint routing and rate control, Kelly and Voice, CCR, 2005
• Dynamic Alternative Routing, Gibbens, Kelly and Key, ITC, 1989.