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

2. February 13, 2002Optimal Routing2  Goal: improving performance, reducing costs  Metrics: routing delay, maximum link utilization, packet loss rate, stability, convergence time after failures, …  Load Balancing: reduces delay, maximum link utilization, etc.  Current IP-backbone:  Very limited load balancing  Slow convergence time (BGP convergence up to 30 minutes)

3. February 13, 2002Optimal Routing3 Optimal Routing Abstract Model  Given: Network G, commodities (s k, t k, d k ) and cost function D uv  Minimize  Conservation of flows  Capacity constraints s1s1 t1t1 s2s2 s3s3 v u t2t2 t3t3

4. February 13, 2002Optimal Routing4  Cost associated with each link:  Increasing  Convex  Finite Derivative u V f(uv) cost(uv)

5. February 13, 2002Optimal Routing5 Previous Results  [Cantor 74] Linear Programming  Centralized  [Gallager 77] Distributed algorithm  Network dependent  [Bertsekas et al. 97] Distributed & Fast Approximation  Single commodity  [Plotkin et al. 95] Distributed Multicommodity Flow Algorithm  Linear cost function  New method  Distributed  Fast convergence  Multicommodity  Convex cost function

6. February 13, 2002Optimal Routing6 New Method  Assumptions:  conservation of flow constraint relaxed  each commodity at each node is assigned an EXCESS  The Algorithm tries to reduce the amount of excesses  Each node divides the excesses among its adjacent links  Each link adjusts flows based on the amount of excesses  Running Time:

7. February 13, 2002Optimal Routing7 Future Work  Sensitivity and stability analysis  How sensitive the algorithm is to perturbations?  Cost function  Realistic cost function  Implementations issues  Where?  How to cooperate with current routing protocols?