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