Truthful Spectrum Auction Truthful Spectrum Auction Design for Secondary Design for Secondary

NetworksNetworks

Yuefei ZhuYuefei Zhu∗∗, Baochun Li, Baochun Li∗∗ and Zongpeng Li and Zongpeng Li††

∗ ∗ Electrical and Computer Engineering, University of TorontoElectrical and Computer Engineering, University of Toronto†† Computer Science, University of CalgaryComputer Science, University of Calgary

Spectrum scarcitySpectrum scarcity

There is a There is a spectrum shortagespectrum shortage

AT&T: U.S. is quickly running out of AT&T: U.S. is quickly running out of spectrum (February 2012)spectrum (February 2012)

Solutions such as secondary access Solutions such as secondary access mitigate the problemmitigate the problem

Secondary spectrum auctionsSecondary spectrum auctions

Need for multi-hop Need for multi-hop supportsupport

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Multi-hop transmissionMulti-hop transmission

What are the difficulties What are the difficulties for multi-hop supported for multi-hop supported

auctions?auctions?

ChallengesChallenges

UnawarenessUnawareness: unknown of the # of : unknown of the # of channels to bid for.channels to bid for.

InterferenceInterference: more complicated: more complicated

TruthfulnessTruthfulness: desirable but difficult : desirable but difficult to achieveto achieve

ContributionsContributionsA heuristic auctionA heuristic auction

guarantees truthfulness guarantees truthfulness

provides winning SNs with interference-provides winning SNs with interference-free end-to-end multi-hop pathsfree end-to-end multi-hop paths

A randomized auctionA randomized auction

truthful in expectationtruthful in expectation

provably approximately-optimal in social provably approximately-optimal in social welfarewelfare

A heuristic truthful A heuristic truthful auctionauction

Our idea: Channel Our idea: Channel assignmentassignment

Virtual bid Virtual bid for SN for SN ii: :

SortSort SNs: SNs:

GreedilyGreedily assignassign channels to channels to shortest paths as long as there are shortest paths as long as there are channels feasible for assignmentchannels feasible for assignment

•

InterferencInterference e consideredconsidered

Our idea: PaymentOur idea: PaymentGet a winner Get a winner ii ’’s s ““critical bidcritical bid””::

Set Set bbii to 0, run the greedy assignment. to 0, run the greedy assignment. The first bidder that makes it infeasible The first bidder that makes it infeasible to accommodate to accommodate i i along its path is along its path is ii ’’s s ““critical biddercritical bidder””. .

This This ““critical biddercritical bidder”” submits a submits a ““critical critical bidbid”” of of ii

PaymentPayment: :

Payment:Payment:

A toy exampleA toy example

TruthfulnessTruthfulnessLemma: The heuristic auction is individually rational.

is always no larger than

Theorem: The heuristic auction is truthful.

Proof of truthfulness is based on:

1.monotonic winner determination

2.bid-independent pricing

• (Myerson’s characterization (1981))

A randomized auctionA randomized auction

Problem formulationProblem formulationAn integer program:An integer program:

• Winner determination to weighted Winner determination to weighted max-flowmax-flow

Social Social welfarewelfare

s.t.s.t.

DecompositionDecompositionRelaxRelax the variables to the variables to [0,1][0,1], getting , getting a linear program (LPR)a linear program (LPR)

If the integrality gap between the If the integrality gap between the integer program (IP) and the LPR is integer program (IP) and the LPR is at most , we can at most , we can decomposedecompose the optimal solution asthe optimal solution as

feasible feasible assignmeassignmentnt

Decomposition (contDecomposition (cont’’d)d)

, we can view , we can view this decomposition as this decomposition as a probability a probability distributiondistribution over the integer over the integer solutions, where a feasible channel solutions, where a feasible channel assignment is selected with assignment is selected with probability probability

Randomized channel Randomized channel assignment: assignment: done!done!

Payment?Payment?

PaymentPaymentA A VCG-likeVCG-like payment is used for payment is used for ensuring truthfulness (in ensuring truthfulness (in expectation) and approximately expectation) and approximately maximizing social welfare: maximizing social welfare:

ResultsResultsTheorem: Theorem: The randomized auction The randomized auction is truthful in expectation.is truthful in expectation.

Theorem: Theorem: The randomized auction The randomized auction achieves optimal social welfare achieves optimal social welfare in expectation.in expectation.

Simulation resultsSimulation results

Auction efficiency with Auction efficiency with different numbers of SNs different numbers of SNs

enrolledenrolled

Auction efficiency with Auction efficiency with different sizes of SNsdifferent sizes of SNs

Auction efficiency with Auction efficiency with different auction settingsdifferent auction settings

ConclusionsConclusionsGeneralizedGeneralized secondary users secondary users

ProvableProvable truthfulness truthfulness

Performance-guaranteedPerformance-guaranteed social social welfarewelfare

ImprovedImproved spectrum utilization spectrum utilization

Thank YouThank You

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