Benefits of coordination in multipath flow control

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: Ns: number of type s-flows; each sends at rate r/Ns 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: Ns: number of type s-flows; each sends at rate r/Ns 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: ) • 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. a 2C a C c b c b Bad performance without coordination: • Example network: sharp link capacity constraints • Schedulable region with coordination: b+c < 2C, a+c < 2C, b+a < 2C.

12. a C c b 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+21-1/] With coordination: iff  < C. e.g. for =2, a loss of 29% efficiency.

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

14. a b c 1 2 3 4 1 a 2 The case of 1-hop routes Network: links l, capacity Cl. 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

15. Concluding remarks 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?