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Distributed Association Control in Shared Wireless Networks

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### Distributed Association Control in Shared Wireless Networks

Krishna C. Garikipatiand Kang G. Shin

University of Michigan-Ann Arbor

- Advantages

•Improves network coverage andcapacity

• Under-utilized APs put to use

- Modes of operation

Peer-to-peer sharing

Public sharing

- 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

- 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

- 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

- 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 ?

- 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

- 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:

- 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 ,

- 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

- 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

- 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

- New Update rule

- New Update rule

•User can obtain locally through scanning

Current Association

Probing AP

- New Update rule

•User can obtain locally through scanning

Current Association

Probing AP

- New Update rule

•User makes a decision on switching

Current Association

Selects next association with prob. distribution

- New Update rule

•User initiates reassociation with selected AP

Old Association

New Association

Completely distributedand asynchronous

- 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

- 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

- 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

- 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.

- 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

- 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

- 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

- 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,

- 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

- Comparison with other distributed policies

•Slight reduction in throughput due to PF fairness

Best Association gives the highestfairness

- Association control in shared WLANs

•Greedy heuristic performs close to optimal

• Achievable using a distributed mechanism

- Extendable to Heterogeneous Networks ?

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