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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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