1. Combining Multipath Routing and Congestion Control for Robustness Peter Key

2. Motivation Performance of Internet /overlays unpredictable –and hard to manage Multiple ownership / policies (eg BGP) can exacerbate performance problems … but diversity increasing –Multihoming –Mesh So why not harness the diversity?

3. Outline Motivation Framework Resource Pooling –2 resources –the  function –Cutset dimensioning Multipath –Coordinated control –Fluid dynamics Route choices & architectures Concluding remarks

4. Framework Network: capacited graph –G=[X,J] Edges have capacity C j Routes s  S, sets of edges Demands type r, associated source – destination, can use a set of routes Link-route incidence matrix A, route flow incidence matrix B

5. Framework File Transfers –Arrival rate –Mean file size –N r in progress Streaming –Arrival rate –Mean holding time –Mr in progress Rate allocation : –x r to both types (fair share): exact rate depends on utility function

6. Resource sharing Fixed Routing Dynamic Routing Fixed Proportions Capacity C p 1-p

7. –Assume performance measure – non-decreasing in 1 st arg., non- increasing in second –Dimensioning means –Eg Performance : the  function

8. Take a cutset C of the Graph G Under resource pooling, necessary performance conditions are Becomes interesting when related to sufficiency Cutset Dimensioning

9. Node cutsets: (Keslassy et al) Symmetric case; –Valiant load balancing, –Dynamic routing Mesh Network Example 6 1 54 2 3

10. Multipath Routing: Utility functions Utility function associated with type r flow increasing, strictly concave etc –Eg TCP, –Putting w=k/(RTT) 2 implies familiar

11. Cost functions  Now require “cost” convex, and True for packet marking etc with “prices” p j,: is prob of drop/marking at j when load is y j, Eg small buffer model

12. Multipath over Coordinated Single utility function across possible routes flow can choose –Single dependence on RTT

13. Fluid Dynamics Scale arrival rates and capacities by large number L and take limits Gives limiting ODE (FLLN)

14. Limit Theorems Theorem: –Under multipath routing, there is a unique invariant point –System in Lyapunov stable (under mild conditions on ) –Allocation is only non-zero to routes s for which “prices” on route are equal –When no streaming, offered load is split optimally, independent of utility functions

15. Remarks Prices on route s are Unless “prices” are equal on different routes, only one route is used Coordinated multipath chooses load fractions to minimise total “cost” –if no streaming traffic present, fractions independent of utility functions

16. Remarks Coordinated multipath chooses load fractions to minimise total “cost”

17. Route Choices How to search for low cost paths? –Use 2 per nominal route, (eg “direct” +1) –Periodically add new route at random –Probe to chose which route to drop Cf “Sticky Random” DAR –“Power of 2”, Mitzenmacher Theorem: Under random path resampling, mulitpath routing will find an optimal feasible load split, if one exists

18. Architecture Need path diversity –Dual homing –Multiple addresses (eg IPv6) For overlays, wireless, or the Internet? Need coordinated congestion control, uncoordinated, parallel, inefficient (see Laurent’s talk …) –at transport or application layer

19. Summary: Multipath routing/multi-access Source /edge routing Halve delay (processor sharing) Resilience Simpler dimensioning (cutsets) C C C C

20. Robust routing provides robustness to –Traffic variations /uncertainty –Routing / BGP / Network operators Need to combine multipath routing with congestion control Challenges: –Time-scales for route adaptation –Removing RTT bias of TCP? Summary

21. References Fluid models of integrated traffic and multipath routing, Peter Key & Laurent Massoulié, QUESTA, June 2006 Network Programming methods for loss networks, Gibbens and Kelly, JSAC 1995 Stability of end-to-end algorithms for joint routing and rate control, Kelly and Voice, CCR, 2005 Dynamic Alternative Routing, Gibbens, Kelly and Key, ITC, 1989.