Distributed Association Control in Shared Wireless Networks

1. Distributed Association Control in Shared Wireless Networks Krishna C. Garikipatiand Kang G. Shin University of Michigan-Ann Arbor

2. Shared Wireless Networks • Advantages •Improves network coverage andcapacity • Under-utilized APs put to use • Modes of operation Peer-to-peer sharing Public sharing

3. Key Features • Uncoordinated Access Points Internet •Ad-hoc deployment • No global policy ADSL • Backhaul Limited •Wireless capacity > wired capacity User • Throughput Inefficiency •RSSI based AP selection AP • • Unfairness+ low bandwidth utilization

4. Association Control • An important problem1 • •Control of user associations to prevent overloading and/or starvation of users • •Crucial for the success of sharing A A C C B B Throughput Throughput A B A B • 1“Seven Ways that HetNetsare a Cellular Paradigm Shift”, IEEE Communications Magazine, March 2013

5. Setup • Variables •Set of users, •Set of APs, •Association of user is •Association vector, where •Set of users connected to AP is • Throughput Backhaul capacity •Equal for all users connected to same AP Airtime fraction MAC overhead MCSRate

6. Association Control Problem • Balancing throughput via user associations • Utility Maximization where is defined as the proportional fair utility •NP-hard=> intractable for large search space • How to solve it without a central controller ?

7. Related Work • Utility based approaches • [Bejaranoet al. 03] • Load-balancing of APs max-min Centralized • [A. Kumar and V. Kumar 05] • Optimal association of stations and APs proportional Centralized • [Kauffmann et al. 07] • Self Organization of WLANs delay Distributed • [Li et al.08] • Approx. algo. for Multi-Rate WLANs Centralized proportional None of them achieve PF in a distributed way

8. This Work • Feasibility of association control without global coordination •Concept of Marginal utility • Optimal randomized solution with probabilistic associations •Steady state distribution: • Sub-optimal greedyapproach with performance bounds •Dense networks: •Backhaul limited:

9. Randomized Approach

10. Randomized Approach • User associates with APs probabilistically •Connects for a random duration, scans and switches •Generated Markov Chain: • Desiredsteady state distribution whereis a fixed parameter Lemma: For every , is an increasing function in . Moreover, as ,

11. Update Process • Poisson clock • Users have i.i.d clocks with inter-tick duration • Scan is triggered at a clock tick User update process Scanning Association T1 T2 T3 T4 time • Discretization •Equivalent DTMC is where is the global poisson clock

12. Update Process, e.g., • Gibbs sampler •Association prob. of user at a clock tick • One-step transition probability is • Markov Chain is aperiodic, irreducible • is the steady state distribution Not distributed as user requires global information to compute

13. Distributed Update Process • Objective function separation where utility of AP is defined as • Define Marginal Utility for each AP w.r.t user where is set of users connected to AP except

14. Distributed Update Process • New Update rule

15. Distributed Update Process • New Update rule •User can obtain locally through scanning Current Association Probing AP

16. Distributed Update Process • New Update rule •User can obtain locally through scanning Current Association Probing AP

17. Distributed Update Process • New Update rule •User makes a decision on switching Current Association Selects next association with prob. distribution

18. Distributed Update Process • New Update rule •User initiates reassociation with selected AP Old Association New Association Completely distributedand asynchronous

19. Partial Information • Marginal utility from subset of APs is known •Due to partial scanning or probe frame losses •Probability of knowing utility from AP is Current Association Probing AP

20. Partial Information • Marginal utility from subset of APs is known •Due to partial scanning or probe frame losses •Probability of knowing utility from AP is Theorem 1The generated Markov chain has steady state distribution where

21. Partial Information • Marginal utility from subset of APs is known •Due to partial scanning or probe frame losses •Probability of knowing utility from AP is Theorem 1The generated Markov chain has steady state distribution where Theorem 2The expected utility in steady state satisfies where and

22. Greedy Approach

23. Best Association • User associates in a deterministic way •Greedy approach to randomization •At clock tick, user chooses AP •Results in Nash Equilibriumwhich satisfies the property for all and all Theorem 3The Best Association converges almost surely. Every optimal association is an equilibrium association.

24. Best Association • User associates in a deterministic way •Greedy approach to randomization •At clock tick, user chooses AP •Results in Nash Equilibriumwhich satisfies the property for all and all Theorem 3The Best Association converges almost surely. Every optimal association is an equilibrium association. Equilibriumstate is not easy to find

25. Best Association • Two scenarios •Users connect to same set of APs and at same PHY rate •All APs are backhaul limited and wireless settings are irrelevant Dense (collocated) Network Backhaul limited

26. Dense Networks • User index can be dropped •Number of users associated with each AP, •Utilityof AP where , are constants Concave Theorem 4Every equilibrium association is globally optimal, that is Theorem 5It takes at most N re-associations to reach equilibrium; each user switches at most once

27. Backhaul limited • Wireless parameters can be ignored •Number of users associated with each AP, •Each user has different neighborhood •Utilityof AP , assume Concave Theorem 6Every equilibrium association satisfies the lower bound,

28. Simulation

29. Simulation • Performance in random topology •Association control performs significantly better than RSSI approach •Partial scanning leads to slower convergence Greedy approach converges to almost optimal solution

30. Simulation • Comparison with other distributed policies •Slight reduction in throughput due to PF fairness Best Association gives the highestfairness

31. Conclusion • Association control in shared WLANs •Greedy heuristic performs close to optimal • Achievable using a distributed mechanism • Extendable to Heterogeneous Networks ?

32. Thank you Krishna C. Garikipati gkchai@eecs.umich.edu