Simplicity in Complex Networks Mung Chiang Electrical Engineering - PowerPoint PPT Presentation

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 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

1. From Descriptive to Explanatory Reverse engineer backoff MAC as a non-cooperative game 0.5 0.4 0.3 p l 0.2 Best response 0.1 Gradient Stochastic subgradient 0 0 20 40 60 80 100 time 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

2. From Homogeneous to Heterogeneous Steering heterogeneous congestion control to desirable equilibria 0.25 0.24 0.23 0.22 0.21 0.2 p 2 0.19 0.18 0.17 0.16 0.15 0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2 p 1 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

3. Architecture Plant CPU Control Input Output Processing Sensor Actuator Memory Controller Application IO� CO� Presentation CO� VHO� VHO� IO� Session CO� SAI� VHO� VHO� Transport SAI� SAI� VHO� IO� IO� Network 10 Gbps� CO� CO� CO� 1 Gbps� Link SAI� SAI� SAI� 100 Mbps� Physical

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

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

4. Robustness: Stochastic NUM Stochastic dynamics at session, packet, and constraint levels rate region stability region for small α maximum stability region stability region for large α φ 2 φ 2 φ 2 φ 1 φ 1 φ 1 (c) time-varying (a) convex rate region (b) nonconvex rate region 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

4. Robustness: Availability Provisioning Quantify tradeoff: normal-time throughput and down-time availability 4 x 10 7 a=0.7 varing a (b=1) 6.5 varing b (a=1.7) 6 b=3 a=1.7 b=2 5.5 b=1 Throughput 5 4.5 4 a=2.7 3.5 3 2.5 96.84% 99.00% 99.68% 99.90% 99.97% Weighted Average Service Availability D. Xu, Y. Li, M. Chiang, and A. R. Calderbank, “Elastic service availability: Utility framework and optimal provisioning”, IEEE INFOCOM , 2007

5. Tradeoff with Complexity 3D throughput-delay-complexity tradeoff in a parameterized framework Complexity O( 2 L ) TORA-MW TORA-GREEDY O( 2 L ) Delay TORA-( 1, ξ,χ ) TORA-( 1/ Θ , ξ , χ ) 1 TORA-PC ( γ =1, δ ~ 1/2 L ) Stability stretching Y. Yi, A. Proutiere, and M. Chiang, “Complexity-stability-delay tradeoff in scheduling over wireless networks”, ACM Mobihoc , May 2008

6. Optimizability Design for optimizability assumption� formulation� solution� restrictive� intractable� non-scalable� relaxation� tractable� scalable� J. He, J. Rexford, and M. Chiang, “Don’t optimize existing protocols, design optimizable protocols”, ACM Sigcomm Computer Communications Review , Aug. 2007

6. DFO At Work Simple distributed routing achieves optimal Internet traffic engineering Optimal TE DEFT l� OSPF DEFT� a� MPLS� m� i� t� Capacity Utilization 1 p� o� 0.8 OSPF� 0.6 0.4 0.2 simple� 0 abilene hier50a hier50b rand50 rand50a rand100 Network D. Xu, M. Chiang, and J. Rexford, “Link-state routing with hop-by-hop forwarding achieves optimal traffic engineering”, IEEE INFOCOM , 2008

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.

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

Application: Wireline Broadband Access Power allocation over multi-carrier interference channel of DSL 2 1.8 1.6 User 1 achievable rate (Mbps) 1.4 1.2 1 0.8 Optimal Spectrum Balancing Iterative Spectrum Balancing 0.6 Autonomous Spectrum Balancing Iterative Waterfilling 0.4 0 1 2 3 4 5 6 7 8 User 4 achievable rate (Mbps) R. Cendrillon, J. Huang, M. Chiang, and M. Moonen, “Autonomous Spectrum Balancing for Digital Subscriber Lines”, IEEE Transactions on Signal Processing , Aug. 2007

Application: Wireless Broadband Access Maximize: utility function of powers and SIR assignments Subject to: SIR assignments feasible Variables: transmit powers and SIR assignments 12 Utility Level Curves 10 8 QoS 2 6 4 2 0 0 1 2 3 4 5 6 7 8 9 10 QoS 1 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

Application: Virtual Network Embedding Multipath support in substrate to enable more efficient virtualization Virtual networks experiment gaming Substrate network 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

Application: P2P Content Sharing Fundamental bounds on how much can P2P help in streaming p2p live streaming system single multiple full mesh graph ? full mesh graph ? yes no yes no number of sessions degree bounded? degree bounded? degree bounded? degree bounded? no yes no yes no yes no yes with helper? with helper? with helper? with helper? with helper? with helper? with helper? with helper? no yes no yes no yes no yes no yes no yes no yes no yes 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 S. Liu, R. Zhang-Shen, W. Jiang, J. Rexford, and M. Chiang, “Performance bounds for peer-assisted live streaming”, ACM Sigmetrics , 2008

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