Internet%20Protocols

1
Internet Protocols

• Steven Low
• CS/EE
• netlab.CALTECH.edu
• October 2004
• with J. Doyle, L. Li, A. Tang, J. Wang

2
Internet Protocols
Selects user criteria, web layout, utility
Application
TCP/AQM IP
Selects source transmission rates
Selects paths from sources to dests
Link
Selects topology, capacities, power,
3
Internet Protocols

• 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

Application
TCP/AQM IP
Link
4
Internet Protocols

• 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

Need to reverse engineer to forward engineer
new large networks
Application
TCP/AQM IP
Link
5
Internet Protocols

• 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

Need to reverse engineer much easier than
biology with full specs
Application
TCP/AQM IP
Link
6
Internet Protocols
Minimize response time (web layout)
Application
TCP/AQM IP
Maximize utility (TCP/AQM)
Minimize path costs (IP)
Link
Minimize SIR, max capacities,
7
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

8
Outline
Chiang X-ities??
General Approach 1) Understand a single layer
in isolation and assume other layers are designed
nearly optimally. 2) Understand interactions
across layers 3) Incorporate additional layers,
with the ultimate goal of viewing entire
protocol stack as solving one giant optimization
problem (where individual layers are solving
parts of it).
Utility maximization
Utility maximization
Chiang Wireless issues ??
9
Outline
Applications
TCP/ AQM

• Utility maximization
• Some implications

IP
10
Network model
11
Network model - example
TCP Reno currently deployed TCP
AI
MD
TailDrop
12
Network model - example
TCP FAST high speed version of Vegas
13
Duality model

• Flow control problem (Kelly, Malloo, Tan 98)

• Primal-dual algorithm

• TCP/AQM
• Maximize utility ( solve Dual) with different
  utility functions
• (L 03) (x,p) primal-dual optimal iff

14
Duality model

• Historically
• Packet level implemented first
• Flow level understood as after-thought
• But flow level design determines
• performance, fairness, stability

(Mo Walrand 00)
15
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
16
Protocol decomposition
Applications
TCP/ AQM
IP

• TCP-AQM
• TCP algorithms maximize utility with different
  utility functions

Congestion prices coordinate across protocol
layers
17
Protocol decomposition
Applications
IP
TCP/ AQM
IP

• 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
18
Protocol decomposition
Applications
IP
TCP/ AQM
IP

• 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
19
Protocol decomposition
Applications
Link
IP
IP
TCP/ AQM
IP

• TCP/IP with optimal c
• With optimal provisioning, static routing is
  optimal using provisioning cost a as link costs

TCP/IP with static routing in well-designed
network
20
Outline
Applications
TCP/ AQM

• Utility maximization
• Some implications

IP
21
Implications

• Is fair allocation always inefficient ?
• Does raising capacity always
• increase throughput ?

Intricate and surprising interactions in
large-scale networks unlike at single link
22
Implications

• Is fair allocation always inefficient
• Does raising capacity always
• increase throughput

23
Fairness
(Mo, Walrand 00)

• Identify allocation with a
• An allocation is fairer if its a is larger

24
Fairness
(Mo, Walrand 00)

• a 0 maximum throughput
• a 1 proportional fairness
• a 2 min delay fairness (Reno)
• a infinity maxmin fairness

25
Efficiency

• Unique optimal rate x(a)
• An allocation is efficient if T(a) is large

26
Conjecture
Conjecture T(a) is nonincreasing i.e. a fair
allocation is always inefficient
27
Example 1
Conjecture T(a) is nonincreasing i.e. a fair
allocation is always inefficient
28
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

29
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

30
Counter-example

• There exists a network such that
• dT/da gt 0 for almost all agt0
• Intuition
• Large a favors expensive flows
• Long flows may not be expensive
• Max-min may be more efficient than proportional
  fairness

long
expensive
31
Counter-example

• Theorem Given any a0gt0, there exists network
  where
• Compact example

32
Implications

• Is fair allocation always inefficient ?
• Does raising capacity always
• increase throughput ?

Intricate and surprising interactions in
large-scale networks unlike at single link
33
Throughput capacity

• Intuition Increasing link capacities always
  raises throughput T
• Theorem Necessary sufficient condition for
  general networks (R, c)
• Corollary For all a, increasing
• a links capacity can reduce T
• all links capacities equally can reduce T
• all links capacities proportionally raises T

34
Protocol decomposition
Link
IP

• 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 a as link costs

Congestion prices coordinate across protocol
layers
35
Some implications

• 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