1. Benefits of coordination in multipath flow control Laurent Massoulié & Peter Key Microsoft Research Cambridge

2. Multipath data transfers Already a large fraction of current Internet traffic (P2P file sharing); A necessary feature for efficient mesh and ad hoc networking.

3. Question: What coordination between flow control on component paths needed? Extreme scenario: no coordination; e.g., individual TCP connections on each path, transferring disjoint data items. Is it good enough?

4. Methodology: Focus on flow-level system models; Assess performance from: Schedulable region; Equilibrium costs.

5. Network model: Flows of types s 2 S; Each type s has an associated set of routes, r 2 R(s) Total rate sent along each route r:  r Network cost is where  : convex, increasing cost function Ex:

6. Coordinated (fair) flow control: N s : number of type s-flows; each sends at rate  r /N s over route r, where  r solves: maximise where: (alpha-fairness: [Mo-Walrand]; multipath version: [Kelly-Maulloo-Tan]; [Mo-Walrand]; [HSHST])

7. Uncoordinated (fair) flow control: N s : number of type s-flows; each sends at rate  r /N s over route r, where  r solves: maximise where: Suitable for modelling uncoordinated TCP flows on each path

8. “Fluid” dynamics: Arrival rate of type s transfers: s ; Mean volume of type s transfers:  s. Consider dynamics: “drift” of stochastic process where flow arrivals at instants of Poisson process (intensity s ) and volumes exponentially distributed (parameter  s ) Interpretation: describes behaviour of stochastic system after joint rescaling of arrival rates and service capacities

9. Performance metrics: Schedulable region: Set of demand vectors (  s = s /  s ) s  S for which fluid dynamics asymptotically stable. Equilibrium cost: For demand vector (  s ) s  S in schedulable region, network cost  ({  r (N * )} r  R ) at equilibrium point N *.

10. Performance under coordination: 1)Schedulable region contains any vector (  s ) s  S such that: there exists a vector of route loads (  r ) r  R  int(dom(  )) verifying (eg, for sharp capacity constraints: ) 2) Given (  s ) s  S, equilibrium cost achieves minimum of  ((  r ) r  R ) over all such (  r ) r  R irrespective of alpha-fairness criterion used.

11. Bad performance without coordination: Example network: sharp link capacity constraints Schedulable region with coordination: C a bc 2C a b c  b +  c < 2C,  a +  c < 2C,  b +  a < 2C.

12. Bad performance (ctd) Schedulable region without coordination: Assume alpha-fair sharing with identical weights w. Symmetric load vector (  a =  b =  c =  schedulable iff:  < C[1+2 -1/  ]/[1+2 1-1/  ] With coordination: iff  < C. e.g. for  =2, a loss of 29% efficiency. C a bc

13. Beyond the triangle network grids cliques a d c b

14. Network: links l, capacity C l. Routes: single link. Then schedulable region (with or without coordination): However uncoordinated multipath produces higher equilibrium cost, sensitive to fairness criterion. e.g., for network: At equilibrium load split into The case of 1-hop routes abc 1324 a 2 1

15. Flow-level models can help select fairness objective of congestion control. Previously proposed coordination optimal in terms of both schedulable region and equilibrium cost. Open problems: route selection? Concluding remarks