Download FAST v3

Internet Protocols
Steven Low
CS/EE
netlab.CALTECH.edu
October 2004
with J. Doyle, L. Li, A. Tang, J. Wang
Internet Protocols
pl(t)
xi(t)
Application
Selects user criteria, web layout, utility
TCP/AQM
Selects source transmission rates
IP
Selects paths from sources to dests
Link
Selects topology, capacities, power,…
Internet Protocols
pl(t)
xi(t)
Application
TCP/AQM
IP
Link
 Protocols determines network behavior
 Critical, yet difficult, to understand and
optimize
 Local algorithms, distributed spatially
and vertically  global behavior
 Designed separately, deployed
asynchronously, evolves independently
Internet Protocols
pl(t)
xi(t)
Application
TCP/AQM
IP
Link
 Protocols determines network behavior
Need

Critical,to
yetreverse
difficult, to engineer
understand and
optimize
 Local algorithms, distributed spatially
…and
tovertically
forward
engineer
 global
behavior

Designed
separately,
deployed
new
large
networks
asynchronously, evolves independently
Internet Protocols
pl(t)
xi(t)
Application
TCP/AQM
IP
Link
 Protocols determines network behavior
Need

Critical,to
yetreverse
difficult, to engineer
understand and
optimize
 Local algorithms, distributed spatially
…and
much
easier
than
biology
vertically
 global
behavior

Designed
with
fullseparately,
specs deployed
asynchronously, evolves independently
Internet Protocols
pl(t)
xi(t)
Application
Minimize response time (web layout)
TCP/AQM
Maximize utility (TCP/AQM)
IP
Minimize path costs (IP)
Link
Minimize SIR, max capacities, …
Internet Protocols
 Each layer is abstracted as an optimization
problem
 Operation of a layer is a distributed solution
 Results of one problem (layer) are parameters of
others
 Operate at different timescales
Application
Application
TCP/AQM
IP
Link
max
x 0
U ( x )
i
i
i
subj to Rx  c
IP
Link
Outline
Applications
General Approach:
Chiang: X-ities??
1) Understand a single layer in isolation and assume
other layers are designed nearly optimally.
Utility maximization
TCP/
AQMinteractions across layers
2) Understand
Utility
maximization
3) Incorporate
the ultimate
goal of
IP additional layers, with
viewing entire protocol stack as solving one giant
optimization problem (where individual layers are solving
parts of it).
Link
Chiang: Wireless issues ??
Outline
Applications
TCP/
AQM
IP
Link
 Utility maximization
 Some implications
Network model
x
y
R
F1
Network
TCP
G1
FN
q
AQM
GL
R
T
p
Rli  1 if source i uses link l
IP routing
x(t  1)  F ( RT p(t ), x(t ))
p(t  1)  G ( p(t ), Rx (t ))
Reno, Vegas
DT, RED, …
Network model - example
TCP Reno: currently deployed TCP
AI
xi2
1
xi (t  1)  2 
Ti
2
R
li
pl (t )
MD
l


pl (t  1)  Gl   Rli xi (t ), pl (t ) 
 i

TailDrop
Rli  1 if source i uses link l
IP routing
x(t  1)  F ( RT p(t ), x(t ))
p(t  1)  G ( p(t ), Rx (t ))
Reno, Vegas
DT, RED, …
Network model - example
TCP FAST: high speed version of Vegas
i 

xi (t  1)  xi (t )    i  xi (t ) Rli pl (t ) 
Ti 
l

1

pl (t  1)  p l (t )    Rli xi (t )  cl 
cl  i

Rli  1 if source i uses link l
IP routing
x(t  1)  F ( RT p(t ), x(t ))
p(t  1)  G ( p(t ), Rx (t ))
Reno, Vegas
DT, RED, …
Duality model
 Flow control problem (Kelly, Malloo, Tan 98)
 Primal-dual algorithm
Reno, Vegas, FAST
DT, RED, REM/PI, AVQ
 TCP/AQM
 Maximize utility (& solve Dual) with different utility functions
 (L 03): (x*,p*) primal-dual optimal iff
Duality model
Historically
 Packet level implemented first
 Flow level understood as after-thought
 But flow level design determines
 performance, fairness, stability
(Mo & Walrand 00)




  1 : Vegas, FAST, STCP
  1.2: HSTCP (homogeneous sources)
  2 : Reno (homogeneous sources)
  infinity: XCP (single link only)
Duality model
Historically
 Packet level implemented first
 Flow level understood as after-thought
 But flow level design determines
 performance, fairness, stability
Now: can forward engineer
Given (application) utility functions, can
generate provably scalable TCP algorithms
Protocol decomposition
Applications
TCP-AQM
TCP/
AQM
IP
Link
max max max
c
R
x 0
subject to
U ( x )
i
i
i
Rx  c,  c  B
T
TCP-AQM:
 TCP algorithms maximize utility with different
utility functions
Congestion prices coordinate across protocol layers
Protocol decomposition
Applications
IP
TCP/
AQM
IP
Link
TCP-AQM
max max max
c
R
x 0
subject to
U ( x )
i
i
i
Rx  c,  c  B
T
TCP/IP:
 TCP algorithms maximize utility with different
utility functions
 Shortest-path routing is optimal using congestion
prices as link costs
Congestion prices coordinate across protocol layers
Protocol decomposition
Applications
IP
TCP/
AQM
IP
Link
TCP-AQM
max max max
c
R
x 0
subject to
U ( x )
i
i
i
Rx  c,  c  B
T
TCP/IP (with fixed c):
 Equilibrium of TCP/IP exists iff zero duality gap
 NP-hard, but subclass with zero duality gap is LP
 Equilibrium, if exists, can be unstable
 Can stabilize, but with reduced utility
Inevitable tradeoff bw utility max & routing stability
Protocol decomposition
Applications
Link
TCP/
AQM
IP
Link
IP
TCP-AQM
max max max
c
R
x 0
subject to
U ( x )
i
i
i
Rx  c,  c  B
T
TCP/IP with optimal c:
 With optimal provisioning, static routing is optimal using
provisioning cost  as link costs
TCP/IP with static routing in well-designed network
Outline
Applications
TCP/
AQM
IP
Link
 Utility maximization
 Some implications
Implications
 Is fair allocation always inefficient ?
 Does raising capacity always
increase throughput ?
Intricate and surprising interactions in large-scale
networks … unlike at single link
Implications
 Is fair allocation always inefficient
 Does raising capacity always
increase throughput
Fairness
(Mo, Walrand 00)
 Identify allocation with 
 An allocation is fairer if its  is larger
Fairness
(Mo, Walrand 00)
   0: maximum throughput
   1: proportional fairness
   2: min delay fairness (Reno)
   infinity: maxmin fairness
Efficiency
 Unique optimal rate x()
 An allocation is efficient if T() is large
Conjecture
Conjecture
T() is nonincreasing
i.e. a fair allocation is always inefficient
Example 1
max
throughput
proportional
fairness
maxmin
fairness
0
1/(L+1)
1/2
1
L/L(L+1)
1/2
Conjecture
T() is nonincreasing
i.e. a fair allocation is always inefficient
Intuition
“The fundamental conflict between
achieving flow fairness and maximizing
overall system throughput….. The basic
issue is thus the trade-off between these
two conflicting criteria.”
Luo,etc.(2003), ACM MONET
Results
Theorem: Necessary & sufficient
condition for general networks (R, c)
provided every link has a 1-link flow
Corollary 1: true if N(R)=1
Counter-example
There exists a network such that
dT/d > 0 for almost all >0
Intuition
 Large  favors expensive flows
 Long flows may not be expensive
Max-min may be more efficient than
proportional fairness
expensive
long
Counter-example
 Theorem: Given any
network where
0>0, there exists
Compact example
0
Implications
 Is fair allocation always inefficient ?
 Does raising capacity always
increase throughput ?
Intricate and surprising interactions in large-scale
networks … unlike at single link
Throughput & capacity
Intuition: Increasing link capacities always
raises throughput T
Theorem: Necessary & sufficient condition
for general networks (R, c)
Corollary: For all , increasing
 a link’s capacity can reduce T
 all links’ capacities equally can reduce T
 all links’ capacities proportionally raises T
Protocol decomposition
Link
IP
TCP-AQM
max max max
c
R
x 0
subject to
U ( x )
i
i
i
Rx  c,  c  B
T
 TCP algorithms maximize utility with different
utility functions
 IP shortest path routing is optimal using congestion prices
as link costs, with given link capacities c
 With optimal provisioning, static routing is optimal using
provisioning cost  as link costs
Congestion prices coordinate across protocol layers
Some implications
TCP-AQM
max max max
c
R
x 0
subject to
U ( x )
i
i
i
Rx  c,  c  B
T
TCP/AQM:
 TCP maximizes aggregate utility (not throughput)
 Fair bandwidth allocation is not always inefficient
 Increasing capacity does not always raise throughput
Intricate network interactions  paradoxical behavior