Communication Networks

Slides:

Advertisements

Similar presentations

Mission-based Joint Optimal Resource Allocation in Wireless Multicast Sensor Networks Yun Hou Prof Kin K. Leung Archan Misra.

Advertisements

Distributed Rate Assignments for Broadband CDMA Networks Tara Javidi Electrical & Computer Engineering University of California, San Diego.

Costas Busch Louisiana State University CCW08. Becomes an issue when designing algorithms The output of the algorithms may affect the energy efficiency.

Network Economics -- Lecture 1: Pricing of communication services Patrick Loiseau EURECOM Fall 2012.

Maximum Flow and Minimum Cut Problems In this handout: Duality theory Upper bounds for maximum flow value Minimum Cut Problem Relationship between Maximum.

Capacity Allocation in Networks Under Noncooperative Elastic Users Instructor: Ishai Menache Eliron Amir Winter 2006.

Simultaneous Routing and Resource Allocation in Wireless Networks Mikael Johansson Signals, Sensors and Systems, KTH Joint work with Lin Xiao and Stephen.

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

1 LP Duality Lecture 13: Feb Min-Max Theorems In bipartite graph, Maximum matching = Minimum Vertex Cover In every graph, Maximum Flow = Minimum.

1 Advancing Supercomputer Performance Through Interconnection Topology Synthesis Yi Zhu, Michael Taylor, Scott B. Baden and Chung-Kuan Cheng Department.

Convex Optimization Chapter 1 Introduction. What, Why and How  What is convex optimization  Why study convex optimization  How to study convex optimization.

1 EL736 Communications Networks II: Design and Algorithms Class8: Networks with Shortest-Path Routing Yong Liu 10/31/2007.

Decomposable Optimisation Methods LCA Reading Group, 12/04/2011 Dan-Cristian Tomozei.

Communication Networks A Second Course Jean Walrand Department of EECS University of California at Berkeley.

Yashar Ganjali Computer Systems Laboratory Stanford University February 13, 2003 Optimal Routing in the Internet.

Introduction to Linear and Integer Programming Lecture 7: Feb 1.

Charge-Sensitive TCP and Rate Control Richard J. La Department of EECS UC Berkeley November 22, 1999.

Dual Problem of Linear Program subject to Primal LP Dual LP subject to ※ All duality theorems hold and work perfectly!

The Widrow-Hoff Algorithm (Primal Form) Repeat: Until convergence criterion satisfied return: Given a training set and learning rate Initial:  Minimize.

EMGT 501 HW # (b) (c) 6.1-4, Due Day: Sep. 21.

ADCN MURI Tools for the Analysis and Design of Complex Multi-Scale Networks Review September 9, 2009 Protocols for Wireless Networks Libin Jiang, Jiwoong.

Communication Networks A Second Course Jean Walrand Department of EECS University of California at Berkeley.

Rethinking Internet Traffic Management: From Multiple Decompositions to a Practical Protocol Jiayue He Princeton University Joint work with Martin Suchara,

Linear Programming – Max Flow – Min Cut Orgad Keller.

Optimization Theory Primal Optimization Problem subject to: Primal Optimal Value:

Trading Convexity for Scalability Marco A. Alvarez CS7680 Department of Computer Science Utah State University.

Data Envelopment Analysis. Weights Optimization Primal – Dual Relations.

By: Gang Zhou Computer Science Department University of Virginia 1 A Game-Theoretic Framework for Congestion Control in General Topology Networks SYS793.

DaVinci: Dynamically Adaptive Virtual Networks for a Customized Internet Jennifer Rexford Princeton University With Jiayue He, Rui Zhang-Shen, Ying Li,

1 ESI 6417 Linear Programming and Network Optimization Fall 2003 Ravindra K. Ahuja 370 Weil Hall, Dept. of ISE

1 Unveiling Anomalies in Large-scale Networks via Sparsity and Low Rank Morteza Mardani, Gonzalo Mateos and Georgios Giannakis ECE Department, University.

1 Chapter-4: Network Flow Modeling & Optimization Deep Medhi and Karthik Ramasamy August © D. Medhi & K. Ramasamy, 2007.

Mazumdar Ne X tworking’03 June 23-25,2003, Chania, Crete, Greece The First COST-IST(EU)-NSF(USA) Workshop on EXCHANGES & TRENDS IN N ETWORKING 1 Non-convex.

Logical Topology Design

Congestion Control in CSMA-Based Networks with Inconsistent Channel State V. Gambiroza and E. Knightly Rice Networks Group

Minimax Open Shortest Path First (OSPF) Routing Algorithms in Networks Supporting the SMDS Service Frank Yeong-Sung Lin ( 林永松 ) Information Management.

Jean Walrand – NSF – April 24-25, 20031/5 Economic Mechanisms Grand Challenge: Design economic mechanisms that provide incentives for increasing the utility.

Machine Learning Weak 4 Lecture 2. Hand in Data It is online Only around 6000 images!!! Deadline is one week. Next Thursday lecture will be only one hour.

DaVinci: Dynamically Adaptive Virtual Networks for a Customized Internet Jiayue He, Rui Zhang-Shen, Ying Li, Cheng-Yen Lee, Jennifer Rexford, and Mung.

Use Cases for High Bandwidth Query and Control of Core Networks Greg Bernstein, Grotto Networking Young Lee, Huawei draft-bernstein-alto-large-bandwidth-cases-00.txt.

1 Slides by Yong Liu 1, Deep Medhi 2, and Michał Pióro 3 1 Polytechnic University, New York, USA 2 University of Missouri-Kansas City, USA 3 Warsaw University.

Sebastian Max Radio and Frequency Assignment in Multi-Radio Multi-Channel Wireless Mesh Networks Radio and Frequency Assignment in Multi-Radio Multi-Channel.

1 Traffic Engineering By Kavitha Ganapa. 2 Introduction Traffic engineering is concerned with the issue of performance evaluation and optimization of.

Internet Traffic Engineering Motivation: –The Fish problem, congested links. –Two properties of IP routing Destination based Local optimization TE: optimizing.

Optimization-based Cross-Layer Design in Networked Control Systems Jia Bai, Emeka P. Eyisi Yuan Xue and Xenofon D. Koutsoukos.

1 Transport Bandwidth Allocation 3/29/2012. Admin. r Exam 1 m Max: 65 m Avg: 52 r Any questions on programming assignment 2 2.

Architecture and Algorithms for an IEEE 802

Introduction to Linear Programs

LECTURE DAY 3 Timo Laukkanen.

Multi-channel, multi-radio wireless networks

ENGM 535 Optimization Networks

ME 521 Computer Aided Design 15-Optimization

Cross layer design is wireless multi-hop network

Frank Yeong-Sung Lin (林永松) Information Management Department

Wireless Networks - Energy, Security

The Simplex Method: Standard Minimization Problems

Topological Ordering Algorithm: Example

Uncooperative Flow Control

Communication Networks

Structural Optimization Design ( Structural Analysis & Optimization )

Topological Ordering Algorithm: Example

Frank Yeong-Sung Lin (林永松) Information Management Department

Topological Ordering Algorithm: Example

EEL 6935 Wireless Ad Hoc Networks

CS5321 Numerical Optimization

Power Efficient Communication ----Joint Routing, Scheduling and Power Control Design Presenter: Rui Cao.

Communication Networks

Horizon: Balancing TCP over multiple paths in wireless mesh networks

ACHIEVEMENT DESCRIPTION

Topological Ordering Algorithm: Example

Presentation transcript:

Communication Networks A Second Course Jean Walrand Department of EECS University of California at Berkeley

Optimization Motivation Convex Programming Optimization of networks Mathematics Convex Programming Convexity Network Provisioning Duality Congestion Control Kuhn-Tucker Algorithms

Motivation Optimization of networks Network provisioning Routing MAC Topology: How many nodes; Interconnections Capacity Routing Load balancing Energy-efficient routing MAC Minimize power Transport Maximize user utility Incentives Pricing, peering, services

Motivation … Mathematics Convex Programs Linear or Quadratic Programs Mathematical Programming Integer Linear Programming Geometric and Semidefinite Programs Algorithms (directions, step sizes, stopping)

Convexity Non convex: Local conditions don’t say anything about optimality Convex: Local conditions suffice for optimality

Convexity

Convexity

Convexity

Convexity

Convexity

Convexity Another look:

Convexity  PRIMAL  DUAL

Convexity  PRIMAL  DUAL Valid under convexity assumptions, … see later.

Network Provisioning l1 l2 x1 x2

Network Provisioning l1 l2 x1 x2

Network Provisioning l1 l2 x1 x2

Network Provisioning l1 l2 x1 x2 Summary:

Network Provisioning l1 l2 x1 x2

Duality

Duality

Congestion Control

Congestion Control