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

Transport and Optimization Review of Duality Examples Congestion Control AIMD Reno Vegas Dual Problem Decomposition Solving the Dual Problem

Review of Duality

Review of Duality

Review of Duality

Example of Duality: Cube

Example of Duality: Discrete N(1, s2)

Example of Duality: HOT Highly Optimized Tolerance, John Doyle, Caltech… Idea: Systems optimized for typical situations As a consequence, they are vulnerable to extreme situations We explore this effect for the WWW and other models.

Example of Duality: HOT Heavy Tails DC = length of codewords after data compression [exponential] FF = size of forest fires [heavy] WWW = file lengths

Example of Duality: HOT Power laws, Highly Optimized Tolerance and generalized source coding John Doyle, J.M. Carlson, 2000

Congestion Control: AIMD B x D E y Rates equalize  fair share

Congestion Control: AIMD B x C D E y y C Chiu and Jain, 1988 Limit rates: x = y x

Congestion Control: Reno A B x C D E y In practice (Reno): window increases at rate ~ 1/RTT Limiting window ~ 1/RTT But throughput = window/RTT Limiting throughput ~ 1/RTT2

Congestion Control: Vegas B x C D E y Adjust rates based on estimated backlog. Roughly, X ~ 1/q where q is backlog in router. Then, one can show that x ~ y. The intuition is that the flows will have similar backlogs. Two types of proof: Lyapunov Show that algorithm is a gradient projection algorithm for a convex problem [ converges if …]

Congestion Control: Dual

Congestion Control: Decomposition

Congestion Control: Decomposition

Congestion Control: Solving Dual

Congestion Control: Solving Dual

Congestion Control: Solving Dual

Optimization: Summary Convex Programming Primal  Dual; Shadow cost TCP Vegas == gradient alg. for dual HOT Minimize average cost  Events have heavy tail Congestion control Dual decomposes