1. Fernando Paganini ORT University, Uruguay (on leave from UCLA) Congestion control with adaptive multipath routing based on optimization Collaborator: Enrique Mallada, ORT University, Uruguay.

2. [Kelly-Maulloo-Tan ’98, Low-Lapsley ’99, many others] Book by Srikant, 2004. Source rate x(t) Optimization on the demand side: congestion control Price feedback

3. Optimization on the supply side

4. Combining demand and supply?

5. Difficulties with the path formulation An exponential number of paths! How do we limit size? Sources do not have the path information, nor is it reasonable to add all this complexity to them. Overlay with the edge router doing rate control? but even routers don’t know end-to-end paths.

6. A better set of control variables.

7. More detailed notation :

8. Price information : LINKS SOURCES

9. Adaptation of router traffic splits LINKS SOURCES Traffic splitting Node price recursion Adapt splits

10. Primal congestion control under adaptive multipath routing :

11. Dual congestion control under fixed multipath routing :

12. Dual congestion control under adaptive multipath routing :

13. EXAMPLE Source 1 Source 2 Destination Links in light blue have very high capacity.

14. EXAMPLE (cont) Fluid-flow simulation Using SCILAB

15. Implementation issues

16. Conclusions We presented natural optimization problems that combine multipath routing with elastic demands, using variables which are local to sources and routers. We introduced congestion prices for nodes that use multipath routing, and a slow adaptation of traffic split ratios at routers. Combined with standard congestion control, this strategy yields decentralized solutions to the optimization problems. The algorithms fit with the TCP/IP philosophy (end-to-end control of source rate, local control of routing based on neighbor information). Open question: what happens if we remove time-scale separations? We are starting to look at implementation issues, in particular combining explicit and implicit methods to propagate prices.