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Simplicity in Complex Networks Mung Chiang Electrical Engineering Department, Princeton COS 561 November 25, 2008 Six Viewpoints on Complex Networks Simple Description: From Descriptive to Explanatory Models From Homogeneous to

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Simplicity in Complex Networks

Mung Chiang Electrical Engineering Department, Princeton COS 561 November 25, 2008

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Six Viewpoints on Complex Networks

Simple Description:

  • From Descriptive to Explanatory Models
  • From Homogeneous to Heterogeneous Models

Simple Conceptual Framework:

  • From Describing to Deriving Architectures
  • Robustness to Network Dynamics

Simple Protocols:

  • Tradeoff with Complexity
  • Design for Optimizability

Making a difference in large-scale operational networks

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  • 1. From Descriptive to Explanatory

Reverse engineer backoff MAC as a non-cooperative game

20 40 60 80 100 0.1 0.2 0.3 0.4 0.5 time pl Best response Gradient Stochastic subgradient

  • J. W. Lee, A. Tang, J. Huang, M. Chiang, and A. R. Calderbank, “Reverse engineering MAC: A

game-theoretic model”, IEEE Journal of Selected Areas in Communication, Jul. 2007

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  • 2. From Homogeneous to Heterogeneous

Steering heterogeneous congestion control to desirable equilibria

0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2 0.15 0.16 0.17 0.18 0.19 0.2 0.21 0.22 0.23 0.24 0.25 p1 p2

  • A. Tang, J. Wang, S. H. Low, and M. Chiang, “Equilibrium of heterogeneous congestion control

protocols: Existence and Uniqueness”, IEEE/ACM Transactions on Networking, Jul. 2007

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  • 3. Architecture

Plant Sensor Controller Actuator

CPU

Input Output Memory Control Processing

Application Presentation Session Transport Network Link Physical

CO IO SAI SAI SAI

100 Mbps

CO CO IO

10 Gbps 1 Gbps

VHO VHO VHO VHO VHO CO IO SAI SAI SAI CO CO IO

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  • 3. Math Foundation for Network Architecture

Who should do what and how to connect them

  • M. Chiang, S. H. Low, A. R. Calderbank, and J. C. Doyle, “Layering as optimization decomposition: A

mathematical theory of network architectures”, Proceedings of the IEEE, Jan. 2007

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  • 3. Layering As Optimization Decomposition

Network: Generalized NUM Layering architecture: Decomposition scheme Layers: Decomposed subproblems Interfaces: Functions of primal or dual variables Horizontal and vertical decompositions through

  • implicit message passing (e.g., queuing delay, SIR)
  • explicit message passing (local or global)

3 Steps: G.NUM ⇒ A solution architecture ⇒ Alternative architectures

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  • 4. Robustness: Stochastic NUM

Stochastic dynamics at session, packet, and constraint levels

φ1 φ2 φ1 φ1 φ2 φ2 (a) convex rate region (b) nonconvex rate region rate region maximum stability region stability region for small α stability region for large α (c) time-varying rate regions

  • Y. Yi and M. Chiang, “Stochastic network utility maximization: A tribute to Kelly’s paper published in

this journal a decade ago”, European Transactions on Telecommunications, March 2008

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  • 4. Robustness: Availability Provisioning

Quantify tradeoff: normal-time throughput and down-time availability

96.84% 99.00% 99.68% 99.90% 99.97% 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 x 10

4

Weighted Average Service Availability Throughput b=1 b=3 a=0.7 a=2.7 a=1.7 b=2 varing a (b=1) varing b (a=1.7)

  • D. Xu, Y. Li, M. Chiang, and A. R. Calderbank, “Elastic service availability: Utility framework and
  • ptimal provisioning”, IEEE INFOCOM, 2007
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  • 5. Tradeoff with Complexity

3D throughput-delay-complexity tradeoff in a parameterized framework

Stability Delay Complexity O(2L) O(2L) 1 TORA-(1,ξ,χ) TORA-(1/Θ,ξ,χ) TORA-MW TORA-PC (γ=1,δ ~ 1/2L) TORA-GREEDY stretching

  • Y. Yi, A. Proutiere, and M. Chiang, “Complexity-stability-delay tradeoff in scheduling over wireless

networks”, ACM Mobihoc, May 2008

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  • 6. Optimizability

Design for optimizability

restrictive relaxation non-scalable scalable

solution assumption formulation

intractable tractable

  • J. He, J. Rexford, and M. Chiang, “Don’t optimize existing protocols, design optimizable protocols”,

ACM Sigcomm Computer Communications Review, Aug. 2007

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  • 6. DFO At Work

Simple distributed routing achieves optimal Internet traffic engineering

abilene hier50a hier50b rand50 rand50a rand100 0.2 0.4 0.6 0.8 1

Network Capacity Utilization Optimal TE DEFT OSPF

simple

  • p

t i m a l

MPLS OSPF DEFT

  • D. Xu, M. Chiang, and J. Rexford, “Link-state routing with hop-by-hop forwarding achieves optimal

traffic engineering”, IEEE INFOCOM, 2008

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Geometry of Simplicity

Around, Through, or Above Nonconvexity

1 2 3

  • M. Chiang, “Nonconvex optimization of communication systems”, Advances in Mechanics and

Mathematics, Special Volumn on G. Strang’s 70th Birthday, Ed., D. Gao and H. Sherali, Springer, 2008.

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Applications to Operational Networks

  • Wireline Broadband Access

FAST Copper Project: With AT&T and Marvell

  • Wireless Broadband Access

Load-spillage power control: With Qualcomm and Siemens-Nokia

  • Internet Management and Virtualization

DEFT and Adaptive Virtualization: With AT&T and Cisco

  • Content Distribution and P2P

Achieving streaming capacity of P2P: With Microsoft and Motorola

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Application: Wireline Broadband Access

Power allocation over multi-carrier interference channel of DSL

1 2 3 4 5 6 7 8 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 User 4 achievable rate (Mbps) User 1 achievable rate (Mbps) Optimal Spectrum Balancing Iterative Spectrum Balancing Autonomous Spectrum Balancing Iterative Waterfilling

  • R. Cendrillon, J. Huang, M. Chiang, and M. Moonen, “Autonomous Spectrum Balancing for Digital

Subscriber Lines”, IEEE Transactions on Signal Processing, Aug. 2007

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Application: Wireless Broadband Access

Maximize: utility function of powers and SIR assignments Subject to: SIR assignments feasible Variables: transmit powers and SIR assignments

1 2 3 4 5 6 7 8 9 10 2 4 6 8 10 12

QoS 1 QoS 2 Utility Level Curves

  • P. Hande, S. Rangan, M. Chiang, and X. Wu, “Distributed uplink power control for optimal SIR

assignment in cellular data networks”, IEEE/ACM Transactions on Networking, 2008

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Application: Virtual Network Embedding

Multipath support in substrate to enable more efficient virtualization

Virtual networks Substrate network

gaming experiment

  • M. Yu, Y. Yi, J. Rexford, and M. Chiang, “Rethinking virtual network embedding: Support of path

splitting and migration”, ACM Computer Communication Review, April 2008

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Application: P2P Content Sharing

Fundamental bounds on how much can P2P help in streaming

12 with helper? no yes with helper? no yes degree bounded? no yes with helper? no yes with helper? no yes degree bounded? no yes full mesh graph ? yes no with helper? no yes with helper? no yes degree bounded? no yes with helper? no yes with helper? no yes degree bounded? no yes full mesh graph ? yes no 1 2 3 4 5 6 7 8 9 10 11 13 14 15 16 number of sessions p2p live streaming system multiple single

  • S. Liu, R. Zhang-Shen, W. Jiang, J. Rexford, and M. Chiang, “Performance bounds for peer-assisted

live streaming”, ACM Sigmetrics, 2008

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Contacts

chiangm@princeton.edu www.princeton.edu/∼chiangm