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 Double Auctions for Dynamic Spectrum Allocation

2 Calls for efficient spectrum usage!

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

4 Buyers Decision: Winning buyers, sellers and payments Our Approach: DA 2 Double-Auction for Dynamic Allocation of Spectrum Auctioneer AsksBids Ask Bid: Obtain spectrum only to support typical demands Buy additional spectrum on-demand Sell spare spectrum for profit Generate conflict graph

Desired properties 5 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

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 6 D:$7 A:$3 B:$3 C:$3 D is best! A + B + C is best!

Existing solution: TRUST 7 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 a wins receives 2, Group A wins pays 2/3 each $99 Group A: Bid 3*10= $30 Group B: Bid 2*1= $2 Buyer Conflict Graph Seller x: $1 Sellers Seller y: $2 Seller x: $1 Seller y: $2 Sacrificed Joint design of buyer side and seller side Random Grouping of buyers Inefficient: $99, $99 could have won! $10 $1$99

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 8

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 9

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

Design questions 11 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?

What makes a good partition? 12 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

Partition algorithm 13 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

Allocation in a partition 14 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 c1 c2 c1 c c1 c2 c1 c c1 c2 c c2 c1 After allocation within each partition 1. Add removed edges 2. 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 16 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 17 DA 2 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 N and gain DA 2 is individually rational DA 2 is budget balanced

Addressing Practical Issues 18 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

Evaluation setup 19 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 20 —DA 2 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 —DA 2 revenue upto 126x of TRUST and 115% of TDSA

Impact of number of sellers 21 —More sellers: higher probability of a seller asking for low price —DA 2 gives maximum benefit under challenging case with fewest sellers: 3x times the performance of TDSA

Conclusion DA 2 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 DA 2 out- performs existing schemes by up to 62x in efficiency, 126x in revenue and 65x in utilization 22

Q&A Thank you 23

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 24

Impact of network density 25 —Long range  less re-use of channel  challenging auction design —DA 2 out-performs TDSA by 152% in efficiency and 172% in revenue at 0.75 km

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

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

Existing solution: TRUST 28 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 Group bid: 3*1= 3 Group bid: 2*1= 2

Existing solution: TRUST 29 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 Group bid: 3 Group bid: 2 Seller a Seller b Sacrificed

Combining results from partitions 30 Consider a pair of partitions A and B 1. Add back removed edges, if there’s no conflict, terminate 2. 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 3. 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 wireless 1 billion smart mobile devices today Mobile services part of everyday life 31

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

Seller side design 33 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

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