Distributed Association Control in Shared Wireless Networks

Distributed Association Control in Shared Wireless Networks

Krishna C. Garikipati and Kang G. ShinUniversity of Michigan-Ann Arbor

Shared Wireless Networks

Modes of operation

Advantages• Improves network coverage and capacity• Under-utilized APs put to use

Peer-to-peer sharing Public sharing

Key Features Uncoordinated Access Points

• Ad-hoc deployment• No global policy

Backhaul Limited• Wireless capacity > wired capacity

Throughput Inefficiency• RSSI based AP selection• Unfairness + low bandwidth utilization

Internet

User

AP

ADSL

Association Control An important problem1

• Control of user associations to prevent overloading and/or starvation of users

A B A B

BA

CB

AC

Throughput Throughput

• Crucial for the success of sharing

1“Seven Ways that HetNets are a Cellular Paradigm Shift”, IEEE Communications Magazine, March 2013

Setup Variables

• Set of users,

Throughput

• Set of APs, • Association of user is • Association vector, where • Set of users connected to AP is

Backhaul capacity

MAC overhead

MCSRate

Airtime fraction

• Equal for all users connected to same AP

Association Control Problem Balancing throughput via user associations

where

is defined as the proportional fair utility

How to solve it without a central controller ?

• Utility Maximization

• NP-hard => intractable for large search space

Related Work

None of them achieve PF in a distributed way

Utility based approaches

Work Fairness Coordination

[A. Kumar and V. Kumar 05]Optimal association of stations and APs

[Bejarano et al. 03]Load-balancing of APs

[Li et al. 08]Approx. algo. for Multi-Rate WLANs

Centralizedmax-min

[Kauffmann et al. 07]Self Organization of WLANs

proportional

delay

proportional

Centralized

Distributed

Centralized

This Work Feasibility of association control without global coordination

Optimal randomized solution with probabilistic associations

Sub-optimal greedy approach with performance bounds • Dense networks:

• Backhaul limited:

• Concept of Marginal utility

• Steady state distribution:

Randomized Approach

Randomized Approach User associates with APs probabilistically

Desired steady state distribution

Lemma : For every , is an increasing function in . Moreover, as ,

• Connects for a random duration, scans and switches• Generated Markov Chain:

where is a fixed parameter

Update Process Poisson clock

Discretization

• Users have i.i.d clocks with inter-tick duration • Scan is triggered at a clock tick

• Equivalent DTMC is where is the global poisson clock

T1 time

User update process

T2 T3 T4

Scanning Association

Update Process, e.g., Gibbs sampler

• Association prob. of user at a clock tick

• Markov Chain is aperiodic, irreducible • is the steady state distribution

Not distributed as user requires global information to compute

• One-step transition probability is

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

Distributed Update Process New Update rule

Distributed Update Process New Update rule

• User can obtain locally through scanning

Current AssociationProbing AP

Distributed Update Process New Update rule

• User can obtain locally through scanning

Current AssociationProbing AP

Distributed Update Process New Update rule

• User makes a decision on switching

Current Association

Selects next association with

prob. distribution

Distributed Update Process New Update rule

Completely distributed and asynchronous

• User initiates reassociation with selected AP

Old AssociationNew Association

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 AssociationProbing AP

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 1 The generated Markov chain has steady state distribution

where

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 1 The generated Markov chain has steady state distribution

where

Theorem 2 The expected utility in steady state satisfies

where and

Greedy Approach

Best Association User associates in a deterministic way

• Greedy approach to randomization• At clock tick, user chooses AP

Theorem 3 The Best Association converges almost surely. Every optimal association is an equilibrium association.

• Results in Nash Equilibrium which satisfies the property

for all and all

Best Association User associates in a deterministic way

• Greedy approach to randomization• At clock tick, user chooses AP

Theorem 3 The Best Association converges almost surely. Every optimal association is an equilibrium association.

• Results in Nash Equilibrium which satisfies the property

for all and all

Equilibrium state is not easy to find

Best Association Two scenarios

Dense (collocated) Network Backhaul limited

• Users connect to same set of APs and at same PHY rate

• All APs are backhaul limited and wireless settings are irrelevant

Dense Networks User index can be dropped

• Number of users associated with each AP,

Theorem 4 Every equilibrium association is globally optimal, that is

• Utility of AP where , are constants

Theorem 5 It takes at most N re-associations to reach equilibrium; each user switches at most once

Concave

Backhaul limited Wireless parameters can be ignored

• Number of users associated with each AP,

Theorem 6 Every equilibrium association satisfies the lower bound,

• Each user has different neighborhood

Concave

• Utility of AP , assume

Simulation

Simulation Performance in random topology

Greedy approach converges to almost optimal solution

• Association control performs significantly better than RSSI approach

• Partial scanning leads to slower convergence

Simulation Comparison with other distributed policies

Best Association gives the highest fairness

• Slight reduction in throughput due to PF fairness

Conclusion Association control in shared WLANs

• Greedy heuristic performs close to optimal• Achievable using a distributed mechanism

Extendable to Heterogeneous Networks ?

Thank youKrishna C. Garikipati

[email protected]