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Double Auctions for Dynamic Spectrum Allocation

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  1. Double Auctions for Dynamic Spectrum Allocation Wei Dong* Swati Rallapalli* Lili Qiu* K.K. Ramakrishnan+ Yin Zhang* *The University of Texas at Austin +Rutgers University Swati Rallapalli IEEE INFOCOM 2014 April 30, 2014

  2. Calls for efficient spectrum usage!

  3. Static Spectrum allocation Almost nothing remaining • Centralized auction and static allocation: no sharing • Unpredictable demand

  4. Our Approach: DA2 Double-Auction for Dynamic Allocation of Spectrum Decision: Winning buyers, sellers and payments Generate conflict graph Auctioneer Ask Bid: <Price, Location, Range> Seller 1: Channel 1, Price: $ Seller 2: Channel 2, Price: $ Asks Bids • Obtain spectrum only to support typical demands • Buy additional spectrum on-demand • Sell spare spectrum for profit Seller n: Channel n, Price: $ Buyers

  5. Desired properties Truthfulness • No buyer/seller can lie to improve self utility Individual rationality • Participants get non-negative utilities Budget balance • Auctioneer should not lose money • Amount paid to sellers ≤ Amount charged to buyers Good performance • High efficiency: buyers’ valuation - sellers’ valuation  high • High revenue: incentive for sellers to participate • High utilization: higher spectrum reuse

  6. Considerations Spectrum is spatially reusable • Different buyers can use same channel simultaneously • Complex competition patterns: conflict graph • Nodes: buyers • Edges: interference Double auction: truthfulness is hard to achieve • Suppose with fixed N: seller and buyer side truthful • Possible to manipulate N i.e. number of goods traded A:$3 A + B + C is best! D is best! D:$7 B:$3 C:$3

  7. Existing solution: TRUST Sellers Buyer Conflict Graph Group A: Bid 3*10= $30 $10 $10 Seller x: $1 $99 $99 • Step 1: Group non-conflicting buyers randomly • Step 2: Group bid = Size of group * lowest bid in group • Step 3: Match lowest asking sellers with highest bidding groups • Step 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 awins receives 2, Group A wins pays 2/3 each Seller x: $1 Seller y: $2 $1 $99 $99 Group B: Bid 2*1= $2 Seller y: $2 Sacrificed • Joint design of buyer side and seller side • Random Grouping of buyers • Inefficient: $99, $99 could have won!

  8. Existing solutions Small, Spring, TDSA improve on TRUST:but similar in spirit • Apply 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

  9. Key features of our design Decouple buyer side and seller side design • Larger design space: captures different properties of two sides • Theorem: 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 buyers • Create partitions • Compute allocation and pricing within partition • Combine results from all partitions Seller side: simple uniform price auction • Sellers have exclusive right on channel  no conflict graph

  10. Benefit of our idea Buyer Conflict Graph Buyer Conflict Graph Group Bid = $20 Recollect: Group A won $10 $10 $10 $99 $10 Win! $99 $1 $99  Win! $1 $99 Partition A Partition B Group Bid = $2 • DA2 outcome: • Efficiency 99 + 99 = $198 • Revenue 1+20 = $21 • TRUST Outcome: • Efficiency 99+10+10 = $119 • Revenue = $2

  11. Design questions How to partition the conflict graph? Need to • Preserve economic properties, and • Achieve good performance How to allocate spectrum in a partition? How to deal with conflicts while combining the results?

  12. What makes a good partition? Few conflicts across partitions • Most edges within partitions and few edges across partitions • Edges across partitions some winners may be dropped when merging partitions A partition should not be too small • Revenue of a partition comes from the losing buyers • 0 revenue if partition is too small and all buyers win

  13. Partition algorithm Partition objective: • Normalized cut (NCut): normalizes the weights of the edges on the cut by the sum of node degrees in each partition • Captures our goal of finding balanced cuts while minimizing the number of edges on the cut Spectral clustering: well-known for approximate solutions • Meila-Shi algorithm • Automatically finds # of clusters

  14. Allocation in a partition • 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

  15. Merge Procedure After allocation within each partition c1 c1 c1 c2 c1 c2 3 4 5 3 4 5 1. Add removed edges 2. Detect conflicts 1 1 2 7 6 2 7 6 c2 c2 c1 c2 c2 c1 Re-order to resolve conflicts Final allocation c2 c2 c1 c1 c1 3 4 5 3 4 5 Pair-wise merge: low computation cost, easily parallalizable! 1 1 If no re-ordering, drop node with highest degree 2 2 7 6 7 6 c2 c1 c2 c1 c2 c2

  16. Combining seller side and buyer side Find N (# of channels) that satisfies budget balance • Start by allocating all the channels • Run the buyer side auction and seller side auction • Compare amount received from buyers R and paid to sellers P • If R≥P, end, else N = N - 1 and go to step 2

  17. Economic properties DA2 is truthful • Our buyer/seller side design is truthful with a given N • Our buyer/seller side design, when applied to double auctions, does not allow a buyer/seller to unilaterally manipulate Nand gain DA2 is individually rational DA2 is budget balanced

  18. Addressing Practical Issues Buyer/Seller quality: • Sellers: quality of channel, Buyers: communication range • Reputation score accounted for in bids and asks • Preserves 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

  19. Evaluation setup • 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

  20. Performance at different locations • DA2 significantly outperforms existing schemes in alllocations • Divide & Conquer: helps form better groups • Better groups  higher revenue  easier to satisfy sellers ask prices  more channels sold • DA2revenue upto 126x of TRUST and 115% of TDSA

  21. Impactof number of sellers • 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

  22. Conclusion DA2 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

  23. Q&A Thank you wdong86@cs.utexas.eduswati@cs.utexas.edu

  24. Our Approach: Dynamic spectrum allocation A 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 spectrum

  25. Impact of network density • 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

  26. Impact of bid distribution • A higher asking price: challenging to the auction design • Benefit of our scheme is higher when the asking price is high

  27. Static Spectrum allocation One reason for crisis: Static allocation,dynamic demand • Different providers overload at different time/locations

  28. Existing solution: TRUST • Two sellers a and b ask for 1 and 2 respectively • Buyers form the following conflict graph: • Step 1: group non-conflicting buyers randomly • Step 2: compute group bid • Size of group * lowest bid in group 99 99 1 1 1 1 Group bid: 3*1= 3 1 99 Group bid: 2*1= 2

  29. Existing solution: TRUST • Two sellers a and b asking for 1 and 2 respectively • Buyers form the following conflict graph: • Step 3: Match lowest asking sellers with highest bidding groups • Step 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 99 1 1 1 1 Seller a Group bid: 3 1 99 Group bid: 2 Seller b Sacrificed

  30. Combining results from partitions Consider a pair of partitions A and B • Add back removed edges, if there’s no conflict, terminate • 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 2 • 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

  31. The world is going wireless 1 billion smart mobile devices today Mobile services part of everyday life

  32. Wireless traffic is growing fast • Wireless traffic to grow 2.7xin 5 years • By 2017 majority of IP traffic is expected to be wireless [Data from Cisco Forecast]

  33. Seller side design Seller side does not involve the conflict graph • Seller has exclusive right to the channel A traditional uniform price design • If N channels sell, the top N lowest asking sellers win • Sellers are paid at the N+1th lowest asking price Example: N=3, sellers ask for 1, 2, 3, 4, 5 • First 3 sellers win and each get paid 4

  34. Overview of buyer side design Divide and conquer approach • Partition the conflict graph into smaller partitions • Compute allocation and pricing in each partition • Combine results from all partitions