1. Achieving End-to-End Fairness in Wireless Networks Ananth Rao Ion Stoica OASIS Retreat, Jul 2005

2. Motivation Multihop Wireless Networks are being proposed for last mile broadband connectivity  Startups – Mesh Networks, Tropos, PacketHop  Microsoft, Intel Fairness is an important issue Internet Gateway

3. Simulation Results - Fairness ns2 simulation  802.11b, 1Mbps  30 nodes, 10 simultaneous flows  RTS/CTS enabled CDF of throughput of each flow from 10 runs

4. Goals End-to-end fairness Distributed algorithm  Simple Easy to implement  Robust Reduce distriuted state  Adaptive to changes in demands Lots of short HTTP flows, low degree of statistical aggregation  Avoid non-realistic assumptions

5. Fairness in Wireless Networks A B DCE f1f1 f2f2 f3f3 f2f2 f1f1 f3f3 One constraint on allocation from each link Two flows compete only if they share a link Interference causes flows not using the same link to compete Different hops of the same flow compete

6. Overview Defining fairness Model for a wireless network Our algorithm Results

7. Max-Min Fairness n flows, Flow Allocation Vector (FAV) = (f 1,f 2,f 3,…,f n ) Max-Min Fairness  There is no pair (i,j) such that f i < f j There exist positive constants  1 and  2 such that (f 1,f 2,…,f i +  1,…,f j -  2,…,f n ) is feasible  In wire-line networks, ensuring per-link Max-min fairness ensures end-to-end fairness In wireless networks, which allocations are feasible?

8. Overview Defining fairness Model for a wireless network Our algorithm Results

9. Model for a Wireless Network Efficient, collision-free MAC Fluid flow  Will be relaxed later Pair-wise interference  Can determine if a subset of links can communicate simultaneously by examining each pair within the subset What are the constraints for feasibility of an FAV?

10. Notation & Interference Graph Nodes A,B,C… Links L 1,L 2,..., Flows f 1,f 2,… t i = total fraction of time link i is active  Time allocation Vector (TAV) = (t 1,t 2,…,t k ) Interference graph  Vertex for every link L i  Edge between L i and L j if they cannot be active simultaneously ABCDL1L1 L2L2 L3L3 L1L1 L2L2 L3L3 f1f1 f2f2 Flow Constraints t 1 = f 1 / r 1 t 2 = f 2 / r 2 t 3 = f 1 / r 3

11. Feasible Space of TAVS Given the interference graph, we can obtain necessary and sufficient linear constraints on the TAV L2L2 L1L1 L3L3 L4L4 L5L5 L7L7 L6L6 (t 1 +t 2 )  1 (t 2 +t 3 +t 4 )  1 (t 4 +t 5 +t 6 +t 7 )  1 L6L6 L1L1 L5L5 L4L4 L2L2 L3L3 (t 1 +t 2 +t 6 )  1 (t 2 +t 3 +t 6 )  1 (t 3 +t 4 +t 6 )  1 (t 4 +t 5 +t 6 )  1 (t 5 +t 1 +t 6 )  1 (t 1 +t 2 +t 3 +t 4 +t 5 +2t 6 )  2 When flow constraints are applied, we get a set of linear constraints on the flows Clique constraints For every maximal clique {L i1,L i2,…,L im } in the graph (t i1 +t i2 +…+t im )  1 Often used approximation Number of cliques may be exponential

12. Wired vs. Wireless Networks 2f 1 +f 2  r f 1 +f 3 +f 5  r f 5 +f 6  r 2f 3 +f 4  r A B DCFE G f1f1 f2f2 f3f3 f4f4 G f5f5 H f6f6 f1f1 f2f2 f3f3 f4f4 f5f5 f6f6 f 1 +f 2  c f 1 +f 3 +f 5  c f 5 +f 6  c f 3 +f 4  c

13. Overview Defining fairness Model for a wireless network Our algorithm Results

14. f-dependency Relation AIMD for Wireless Networks Theorem: The AIMD algorithm presented above converges to Max-Min fair allocation if the MAC is efficient f1f1 fnfn f2f2 f3f3 Efficient MAC No fairness guarantees x1x1 xnxn x2x2 x3x3 & & & & Flows i and j and are said to be f-dependent if both f i and f j appear in a constraint All f-dependent flows need not flow through the same node  It is hard to monitor state of non-local flows  Only one-bit of information needed for AIMD

15. Discussion There may be an exponential number of facets in the feasibility polytope  n f-dependent flows can lead to up to (2 n – 1) facets Clique Constraints  Flows f i1 and f i2 are codependent iff  links L j1 and L j2 such that f i1 uses L j1 and f i2 uses L j2 L j1 and L j2 interfere (adjacent in the interference graph) Simple, Practical Distributed Algorithm

16. Implementation TCP with drop-tail queues  Piggyback current queue length in each packet header  Monitor queues of all interfering links  Drop packets if any queue drops packets Overlay MAC Layer  MAC layer in software with support for weights  Implemented in a test-bed  Adjust “local” weights based on congestion of queues  Work in progress

17. Overview Defining fairness Model for a wireless network Our algorithm Results

18. Simulation Results ns2 simulation  Same scenario as before Interference  Assume all outgoing links from nodes within communication range interfere  Monitor using promiscuous mode

19. Conclusion and Future Work Conclusions  Increase-decrease algorithms can be adapted to wireless networks  They can significantly reduce complexity of the required distributed state  Easy to implement, adaptive and perform well Future Work  Implement both TCP and OML version in test-bed  Can we adapt other congestion control protocols for wireless RED, RIO, ECN, XFS, CSFQ  Approximation bounds when interference graph is not perfect 1.5 bound on fairness for 3 well known classes of imperfect graphs