Communication Networks

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Communication Networks

• A Second Course

Jean Walrand Department of EECS University of
California at Berkeley
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Optimization

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

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Motivation

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

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Motivation

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

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Convexity
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Convexity
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Convexity
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Convexity
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Convexity
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Convexity
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Convexity
Another look
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Convexity
? PRIMAL
? DUAL
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Convexity
? PRIMAL
? DUAL
Valid under convexity assumptions, see later.
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Network Provisioning
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Network Provisioning
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Network Provisioning
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Network Provisioning
Summary
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Network Provisioning
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Duality
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Duality
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Congestion Control
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Congestion Control