Wei Dong* Swati Rallapalli* Lili Qiu* K.K. Ramakrishnan+ Yin Zhang**The University of Texas at Austin +Rutgers University

Swati Rallapalli

IEEE INFOCOM 2014April 30, 2014

Double Auctions for Dynamic Spectrum Allocation

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Calls for efficient spectrum usage!

Static Spectrum allocation

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Almost nothing remaining

—Centralized auction and static allocation: no sharing—Unpredictable demand

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Seller 1: Channel 1, Price: $

Seller 2: Channel 2, Price: $

Seller n: Channel n, Price: $

Buyers

Decision: Winning buyers, sellers and payments

Our Approach: DA2

Double-Auction for Dynamic Allocation of Spectrum

Auctioneer

Asks Bids

AskBid: <Price, Location, Range>

Obtain spectrum only to support typical demands Buy additional spectrum on-demand Sell spare spectrum for profit

Generate conflict graph

Desired properties

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TruthfulnessNo buyer/seller can lie to improve self utility

Individual rationalityParticipants get non-negative utilities

Budget balanceAuctioneer should not lose moneyAmount paid to sellers ≤ Amount charged to buyers

Good performanceHigh efficiency: buyers’ valuation - sellers’ valuation highHigh revenue: incentive for sellers to participateHigh utilization: higher spectrum reuse

ConsiderationsSpectrum is spatially reusableDifferent buyers can use same channel simultaneouslyComplex competition patterns: conflict graph

Nodes: buyers Edges: interference

Double auction: truthfulness is hard to achieveSuppose with fixed N: seller and buyer side truthfulPossible to manipulate N i.e. number of goods traded

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D:$7

A:$3

B:$3 C:$3

D is best!

A + B + C is best!

Existing solution: TRUST

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Step 1: Group non-conflicting buyers randomlyStep 2: Group bid = Size of group * lowest bid in groupStep 3: Match lowest asking sellers with highest bidding groupsStep 4: Sacrifice last pair where bid ≥ ask, use the bid to charge

winning groups and the ask to pay winning sellers Split payment equally within a group Outcome: Seller a wins receives 2, Group A wins pays 2/3 each

$99Group A: Bid 3*10= $30

Group B: Bid 2*1= $2

Buyer Conflict GraphSeller x: $1

Sellers

Seller y: $2Seller x: $1

Seller y: $2Sacrificed

• Joint design of buyer side and seller side

• Random Grouping of buyers

• Inefficient: $99, $99 could have won!

$10 $10

$1 $99

$99

$99

Existing solutionsSmall, Spring, TDSA improve on TRUST: but similar in spiritApply classic McAfee’s double auction design

Jointly compute the buyer/seller allocation and pricing Limited design space, not able to capture the unique properties

Group non-conflicting buyers to form virtual buyers Groups are formed randomly Buyers in a group share same fate

Win and lose together Uniform pricing within a group

Low efficiency and revenue Unfair

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Key features of our designDecouple buyer side and seller side designLarger design space: captures different properties of two sidesTheorem: A spectrum double auction is truthful if

both seller side and buyer side auctions are truthful when N, the number of channels that are sold, is fixed

no seller or buyer can improve self utility by unilaterally modifying own bid and causing N to change

Buyer side: divide and conquer for better grouping of buyersCreate partitions Compute allocation and pricing within partition Combine results from all partitions

Seller side: simple uniform price auctionSellers have exclusive right on channel no conflict graph9

Benefit of our idea

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$99

$1 $99

$10 $10

Partition A Partition B

Win!

Win!

DA2 outcome: • Efficiency 99 + 99 = $198 • Revenue 1+20 = $21

$99

$1 $99

$10 $10

TRUST Outcome: • Efficiency 99+10+10 = $119• Revenue = $2

Recollect: Group A won

Buyer Conflict Graph Group Bid = $20

Group Bid = $2

Buyer Conflict Graph

Design questions

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How to partition the conflict graph? Need toPreserve economic properties, andAchieve good performance

How to allocate spectrum in a partition?

How to deal with conflicts while combining the results?

What makes a good partition?

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Few conflicts across partitionsMost edges within partitions and few edges across partitionsEdges across partitions some winners may be dropped

when merging partitions

A partition should not be too smallRevenue of a partition comes from the losing buyers

0 revenue if partition is too small and all buyers win

Partition algorithm

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Partition objective:Normalized cut (NCut): normalizes the weights of the edges

on the cut by the sum of node degrees in each partitionCaptures our goal of finding balanced cuts while minimizing

the number of edges on the cutSpectral clustering: well-known for approximate solutionsMeila-Shi algorithmAutomatically finds # of clusters

Allocation in a partition

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Construct groups within the partition

We use improved group bid proposed in TDSA: Allows a subset of group to win A group won’t lose because it has a few very low bids

If N channels sell, the top N groups win and they pay the N+1th group’s group bid

Merge Procedure

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3

1

2

4 5

7 6

c1

c2

c1

c1

c2

c2 3

1

2

4 5

7 6

c1

c2

c1

c1

c2

c2

3

1

2

4 5

7 6

c1

c2

c2

c2

c1

c1

3

1

2

4 5

7 6c2

c2

c2

c1

c1

After allocation within each partition

1. Add removed edges2. Detect conflicts

Re-order to resolve conflicts

If no re-ordering,drop node with highest degree

Final allocation

Pair-wise merge: low computation cost, easily parallalizable!

Combining seller side and buyer side

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Find N (# of channels) that satisfies budget balance

1. Start by allocating all the channels

2. Run the buyer side auction and seller side auction

3. Compare amount received from buyers R and paid to sellers P

4. If R≥P, end, else N = N - 1 and go to step 2

Economic properties

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DA2 is truthfulOur buyer/seller side design is truthful with a given NOur buyer/seller side design, when applied to double

auctions, does not allow a buyer/seller to unilaterally manipulate N and gain

DA2 is individually rational

DA2 is budget balanced

Addressing Practical Issues

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Buyer/Seller quality:Sellers: quality of channel, Buyers: communication rangeReputation score accounted for in bids and asksPreserves economic properties

Leveraging prior-knowledge:Compute sets based on expected group bids formulated as

MWIS: Max Weight Independent set

Avoid starvation:Drop randomly with probability proportional to node-degree

in the merge procedure

Evaluation setup

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Conflict graphs generated from real cell tower locations Three cities: San Francisco, Chicago and NYC An auction area of size around 5km by 5km

Two buyers conflict if distance less than 500m Also vary the value from 250m to 750m

Bids generated uniformly between 0 to 100

Asks generated uniformly between 0 to 2500 The area a seller is selling can cover as many as 25 buyers Also scaled from 0.5 to 1.5 times the default value

Performance at different locations

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NYC SF Chicago0

500

1000

1500

2000

2500

TRUST TDSA DA2

Effici

ency

NYC SF Chicago0

200400600800

1000120014001600

TRUST TDSA DA2Re

venu

e— DA2 significantly outperforms existing schemes in all locations

— Divide & Conquer: helps form better groups— Better groups higher revenue easier to satisfy sellers ask

prices more channels sold— DA2 revenue upto 126x of TRUST and 115% of TDSA

Impact of number of sellers

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3 4 5 6 70

50010001500200025003000

TRUST TDSA DA2

# of sellers

Effici

ency

3 4 5 6 70

400

800

1200

1600

TRUST TDSA DA2

# of sellers

Reve

nue

— More sellers: higher probability of a seller asking for low price— DA2 gives maximum benefit under challenging case with fewest

sellers: 3x times the performance of TDSA

ConclusionDA2 is a truthful double auction to dynamically allocate spectrum

Explicitly de-coupled buyer and seller side to capture different properties of the two sides

Using real cell tower topology traces show that DA2 out-performs existing schemes by up to 62x in efficiency, 126x in revenue and 65x in utilization

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Q&A

Thank youwdong86@cs.utexas.edu

swati@cs.utexas.edu

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Our Approach: Dynamic spectrum allocationA double-sided market for spectrum resource

Service providers with excess spectrum at a particular time & area submit asks to sell their spectrum

Service providers in need of spectrum bid to buy spectrum24

Impact of network density

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0.25 0.5 0.750

10002000300040005000

TRUST TDSA DA2

Buyer communication range (km)

Effici

ency

0.25 0.5 0.750

500

1000

1500

2000

TRUST TDSA DA2

Buyer communication range (km)

Reve

nue

— Long range less re-use of channel challenging auction design— DA2 out-performs TDSA by 152% in efficiency and 172% in revenue

at 0.75 km

Impact of bid distribution

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0.5 0.8 1 1.2 1.50

500100015002000250030003500

TRUST TDSA DA2

Scale of ask price

Effici

ency

0.5 0.8 1 1.2 1.50

500

1000

1500

2000

TRUST TDSA DA2

Scale of ask price

Effici

ency

— A higher asking price: challenging to the auction design— Benefit of our scheme is higher when the asking price is high

Static Spectrum allocation

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One reason for crisis: Static allocation, dynamic demandDifferent providers overload at different time/locations

Existing solution: TRUST

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Two sellers a and b ask for 1 and 2 respectivelyBuyers form the following conflict graph:

Step 1: group non-conflicting buyers randomlyStep 2: compute group bid

Size of group * lowest bid in group

99

1 99

1 199 1 1 Group bid:

3*1= 3Group bid: 2*1= 2

Existing solution: TRUST

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Two sellers a and b asking for 1 and 2 respectivelyBuyers form the following conflict graph:

Step 3: Match lowest asking sellers with highest bidding groupsStep 4: Sacrifice the last pair where bid≥ask, use the bid to charge

winning groups and the ask to pay winning sellers Split equally within a group Outcome: seller a wins and receives 2, (99, 1, 1) win, pay 2/3 each

99

1 99

1 199 1 1 Group bid: 3

Group bid: 2

Seller a

Seller bSacrificed

Combining results from partitions

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Consider a pair of partitions A and B1. Add back removed edges, if there’s no conflict, terminate2. Try to find a reordering function f(x) of the channel

assignments in A, such that the conflicts are resolved E.g. f(1)=2 means all buyers currently assigned channel 1 are

now assigned channel 23. If no reordering can be found, drop a buyer on the cut

with the highest degree and go to step 2

Pairwise: low computation cost, easily parallelizable

The world is going wireless1 billion smart mobile devices today

Mobile services part of everyday life

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Wireless traffic is growing fast

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Wireless traffic to grow 2.7x in 5 yearsBy 2017 majority of IP traffic is expected to be wireless

[Data from Cisco Forecast]2012 2013 2014 2015 2016 20170

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80Growth in Wireless Traffic

Exab

ytes

per

Mon

th

Seller side design

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Seller side does not involve the conflict graphSeller has exclusive right to the channel

A traditional uniform price designIf N channels sell, the top N lowest asking sellers winSellers are paid at the N+1th lowest asking price

Example: N=3, sellers ask for 1, 2, 3, 4, 5First 3 sellers win and each get paid 4

Overview of buyer side design

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Divide and conquer approachPartition the conflict graph into smaller partitionsCompute allocation and pricing in each partitionCombine results from all partitions