Distributed Association Control in Shared Wireless Networks
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Distributed Association Control in Shared Wireless Networks
Krishna C. Garikipati and Kang G. ShinUniversity of Michigan-Ann Arbor
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Shared Wireless Networks
Modes of operation
Advantages• Improves network coverage and capacity• Under-utilized APs put to use
Peer-to-peer sharing Public sharing
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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
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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
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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
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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
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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
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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:
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Randomized Approach
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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
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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
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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
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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
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Distributed Update Process New Update rule
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Distributed Update Process New Update rule
• User can obtain locally through scanning
Current AssociationProbing AP
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Distributed Update Process New Update rule
• User can obtain locally through scanning
Current AssociationProbing AP
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Distributed Update Process New Update rule
• User makes a decision on switching
Current Association
Selects next association with
prob. distribution
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Distributed Update Process New Update rule
Completely distributed and asynchronous
• User initiates reassociation with selected AP
Old AssociationNew Association
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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
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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
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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
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Greedy Approach
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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
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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
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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
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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
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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
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Simulation
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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
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Simulation Comparison with other distributed policies
Best Association gives the highest fairness
• Slight reduction in throughput due to PF fairness
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Conclusion Association control in shared WLANs
• Greedy heuristic performs close to optimal• Achievable using a distributed mechanism
Extendable to Heterogeneous Networks ?