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Communication Networks

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Presentation on theme: "Communication Networks"— Presentation transcript:

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

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

3 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

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

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

6 Convexity

7 Convexity

8 Convexity

9 Convexity

10 Convexity

11 Convexity Another look:

12 Convexity  PRIMAL  DUAL

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

14 Network Provisioning l1 l2 x1 x2

15 Network Provisioning l1 l2 x1 x2

16 Network Provisioning l1 l2 x1 x2

17 Network Provisioning l1 l2 x1 x2 Summary:

18 Network Provisioning l1 l2 x1 x2

19 Duality

20 Duality

21 Congestion Control

22 Congestion Control

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