MAP: Multi-Auctioneer Progressive Auction in Dynamic Spectrum Access Lin Gao, Youyun Xu, Xinbing...

MAP: Multi-Auctioneer Progressive MAP: Multi-Auctioneer Progressive Auction in Dynamic Spectrum AccessAuction in Dynamic Spectrum Access

Lin Gao, Youyun Xu, Xinbing Wang

Shanghai Jiaotong University

MAP: Multi-Auctioneer Progressive Auction in Dynamic Spectrum Access 2

OutlineOutline

IntroductionIntroduction MotivationsMotivations ObjectivesObjectives

System Model and Problem FormulationSystem Model and Problem Formulation

Centralized Channel AssignmentCentralized Channel Assignment

Auction-based Channel AssignmentAuction-based Channel Assignment

Simulations and ConclusionsSimulations and Conclusions


MotivationMotivation

Currently, wireless systems suffer from the Currently, wireless systems suffer from the inefficiencyinefficiency in spectrum in spectrum usage. Dynamic spectrum access (DSA) is a promising paradigm to usage. Dynamic spectrum access (DSA) is a promising paradigm to achieve efficient utilization of the spectrum resource. achieve efficient utilization of the spectrum resource.

The primary spectrum owners (POs) may The primary spectrum owners (POs) may leaselease their excess spectrum their excess spectrum bands (residual channels) to the secondary users (SUs) for enhanced bands (residual channels) to the secondary users (SUs) for enhanced profit.profit.

The essential problem:The essential problem: (i) (i) EfficiencyEfficiency: how to assign the residual : how to assign the residual channels among the SUs with the highest spectrum utilization, and (ii) channels among the SUs with the highest spectrum utilization, and (ii) IncentiveIncentive: what is the motivation for each PO and SU accepting such : what is the motivation for each PO and SU accepting such an assignment.an assignment.


Objectives --Objectives -- How to Solve the Problem? How to Solve the Problem?

Centralized algorithms: Centralized algorithms: Linear-programming-based Linear-programming-based branch-and-boundbranch-and-bound algorithm [14] algorithm [14] Graph-theory-based Graph-theory-based optimal matchingoptimal matching algorithm [16] algorithm [16]

In this paper, we propose an In this paper, we propose an auction-basedauction-based spectrum bands spectrum bands assignment framework, named as MAP, which works in a totally assignment framework, named as MAP, which works in a totally distributed manner. distributed manner.

We show analytically that MAP achieves the efficient (optimal) We show analytically that MAP achieves the efficient (optimal) spectrum assignment compared to the centralized algorithm spectrum assignment compared to the centralized algorithm ((efficiencyefficiency). We further show that, through the inherent profit transfer ). We further show that, through the inherent profit transfer process in auction mechanism, both POs and SUs are willing to process in auction mechanism, both POs and SUs are willing to accept the assignment of MAP (accept the assignment of MAP (incentiveincentive).).


OutlineOutline

IntroductionIntroduction

System Model and Problem FormulationSystem Model and Problem Formulation System ModelSystem Model Problem FormulationProblem Formulation





System ModelSystem Model

We consider an DSA network consisting ofWe consider an DSA network consisting of M POs and POs and N SUs. Each SUs. Each POs POs i owns owns mi residual channels which can be used by SUs.residual channels which can be used by SUs.

Each channel can only be used by Each channel can only be used by oneone SU, and each SU can only use SU, and each SU can only use oneone channel. channel.

Different SUs may have different Different SUs may have different valuationsvaluations ( (vij) on the same channel ) on the same channel

and different channels may have different values to the same SU.and different channels may have different values to the same SU.

An example of An example of DSA network DSA network with with M=3M=3 POs POs and and N=6N=6 SUs. SUs.

s1s2 s3 s4 s5

a1 a2

900MHz band 2.4GHz band

frequency

: idle spectrum band: busy spectrum band

a3

5GHz band

s6v12 v13v11


System ModelSystem Model

11 12 13 14

21 22 23 24

31 32 33 34

41 42 43 44

51 52 53 54

61 62 63 64

v v v v

v v v v

v v v v

v v v v

v v v v

v v v v

V

ValuationValuation ( (vij) is defined as the the income of SU ) is defined as the the income of SU i by using the by using the

channel of PO channel of PO j. The valuation is often related to the channel capacity . The valuation is often related to the channel capacity and channel quality (typically the signal-to-noise ratio (SNR)).and channel quality (typically the signal-to-noise ratio (SNR)).

Valuation MatrixValuation Matrix::

An example of An example of valuation matrix valuation matrix with with M=4M=4 POs POs and and N=6N=6 SUs. SUs.


Problem FormulationProblem Formulation

*

=1 .

arg max

. . ( ) 1,

( ) ,

( ) {0,1}, ,

ji

ji jij N i M

jii M

ji ij N

ji

where r denotes PO i assigns a channel to SU j

r v

s t i r j N

ii r m i M

iii r i M j N

R

R

The The optimal channel assignmentoptimal channel assignment problem is defined as follows: problem is defined as follows:


Problem FormulationProblem Formulation

An example of An example of optimal channel assignmentoptimal channel assignment with with M=4, , N=6, and , and mi=2 ::

1 3 0 1 0 1 0 02 1 5 0 0 0 1 0

4 1 0 2 1 0 0 0

0 0 1 01 1 5 20 0 0 11 3 3 50 1 0 0

0 2 3 1

assignmentmatrix

1jii

r

ji ij

r m


OutlineOutline



Centralized Channel AssignmentCentralized Channel Assignment Optimal matching algorithmOptimal matching algorithm




The original optimization problem can be transformed into the The original optimization problem can be transformed into the following problem in graph: following problem in graph: find a set of edges with maximum weight, find a set of edges with maximum weight, subjecting tosubjecting to ρj≤ 1 for each SUfor each SU j ∈ N andand ρi≤ mi for each POfor each PO i ∈ M.

Optimal matching algorithmOptimal matching algorithm

A graph representation for the optimization problem A graph representation for the optimization problem with with M=2 and and N=6..

POs

s1

SUss2

s3 s4 s5 s6

a1 a2

5

ma1=3 ma2=4

71 2 3 64 7

5

2 11


Using the Using the splitting graphsplitting graph, the optimization problem in previous page , the optimization problem in previous page can be transformed into the classical can be transformed into the classical optimal matching problemoptimal matching problem in in graph theory.graph theory.

Optimal matching algorithmOptimal matching algorithm

A splitting graph representation for the example in A splitting graph representation for the example in previous page.previous page.

POs

s1

SUss2

5

a1: ma1=3

71 255 5

111 77 222

s2s3 s4 s5 s6

3 64 7

5

11

33 222 1111

4 44 666 777

5 5 5

a2: ma2=4

Kuhn-Munkres Kuhn-Munkres algorithm 1957algorithm 1957


OutlineOutline




Auction-based Channel AssignmentAuction-based Channel Assignment Mechanism of MAPMechanism of MAP Equilibrium of MAPEquilibrium of MAP



Mechanism of MAPMechanism of MAP

Centralized channel assignment algorithm is not practical for DSA Centralized channel assignment algorithm is not practical for DSA networks, thus we propose an auction-based channel assignment networks, thus we propose an auction-based channel assignment framework. framework.

The essential elements for the auction:The essential elements for the auction: Auctioneer Auctioneer –– all POs all POs Bidders Bidders –– all SUs all SUs Auctioned Objects Auctioned Objects –– the residual channels owned by the residual channels owned by

all POsall POs Strategy of POs Strategy of POs –– each PO each PO ii specifies the price specifies the price of of

channel channel ppi i

Strategy of SUs Strategy of SUs –– each SU each SU j j selects an PO for buying, selects an PO for buying, i.e., i.e., xxjj=i=i..

Utility of POs Utility of POs –– each PO each PO ii obtains the utility obtains the utility ((ppii-c-cii) ) * d* di i , , where where d dii is the demand of SUs for the channel of PO is the demand of SUs for the channel of PO ii..

Utility of SUs Utility of SUs –– each SU each SU jj obtains the utility obtains the utility vvjiji-p-pii



We propose We propose MAPMAP, a , a multi-auctioneer progressive auctionmulti-auctioneer progressive auction for the for the channel assignment problem. The basic idea for MAP is that: channel assignment problem. The basic idea for MAP is that: Each Each auctioneer systematically adjusts the price and each bidder auctioneer systematically adjusts the price and each bidder subsequently chooses the best auctioneer for bidding.subsequently chooses the best auctioneer for bidding.

Due to the progressive nature of MAP, we define MAP as Due to the progressive nature of MAP, we define MAP as a a round-round-basedbased distributed process that works as follows: distributed process that works as follows: (i) (i) AskingAsking: In the first stage of each round, each PO : In the first stage of each round, each PO

elicits(elicits( 抽出抽出 )) the demands of SUs and judges the demands of SUs and judges whether it is in whether it is in demanded surplusdemanded surplus. If so, the PO . If so, the PO raises his price by a given number and announces raises his price by a given number and announces the new price.the new price.

(ii) (ii) BiddingBidding: In the second stage of each round, : In the second stage of each round, each SU chooses the best PO which maximize his each SU chooses the best PO which maximize his utility and competes for the channel from that PO.utility and competes for the channel from that PO.



The mechanism of MAP:The mechanism of MAP:



An example of MAP with An example of MAP with M=2, , N=2, and , and mi=1 :

p1=0

POs

SUs

p2=0

8.3 5.47.0 2.1

a1

s2s1

a2

Round 1

p1=1 p2=0

8.3 5.47.0 2.1

a1

s2s1

a2

Round 2

p1=2 p2=0

8.3 5.47.0 2.1

a1

s2s1

a2

Round 3

Round 2Round 1 Round 3 Round 4

a1: p1=0

a2: p2=0

s1: x1=a1

s2: x2=a1

a1: p1=1

a2: p2=0

s1: x1=a1

s2: x2=a1

a1: p1=2

a2: p2=0

s1: x1=a2

s2: x2=a1Auction Ends


Equilibrium of MAPEquilibrium of MAP

Weak EquilibriumWeak Equilibrium: Weak equilibrium is defined as a status in which : Weak equilibrium is defined as a status in which the demand for channels owned by each PO the demand for channels owned by each PO i does not exceed the does not exceed the

supply, i.e.,supply, i.e., di ≤ mi, for each PO, for each PO i M.∈

Strong EquilibriumStrong Equilibrium: Strong equilibrium is defined as a status in which : Strong equilibrium is defined as a status in which (i) the demand for channels owned by each PO (i) the demand for channels owned by each PO i does not exceed the does not exceed the

supply, i.e.,supply, i.e., di ≤ mi, for each PO, for each PO i M∈ , and (ii) if the demand for , and (ii) if the demand for

channels owned by PO channels owned by PO i is less than the supply, i.e., is less than the supply, i.e., di < mi, then the , then the

price of PO price of PO i equals its reservation price, i.e., equals its reservation price, i.e., pi = ci..



An example of weak equilibrium and strong equilibrium.An example of weak equilibrium and strong equilibrium.

p1=6c1=0

POs

SUs

p2=4c2=0

(a)

8 57 2

a1

s2s1

a2

p1=6c1=6

p2=4c2=2

(b)

8 57 2

a1

s2s1

a2

p1=0c1=0

p2=2c2=0

(b*)

2 -15 0

a1

s2s1

a2

weak strong



ConvergenceConvergence: (Lemma 1) MAP converges to a weak equilibrium.: (Lemma 1) MAP converges to a weak equilibrium.

ConvergenceConvergence: (Lemma 2) MAP converges to a strong equilibrium, if : (Lemma 2) MAP converges to a strong equilibrium, if the step size the step size is small enough. is small enough.

EfficiencyEfficiency:: ( (Lemma 3)Lemma 3) The channel assignment of MAP is optimal, if The channel assignment of MAP is optimal, if step size step size is small enough. is small enough.

IncentiveIncentive: both POs and SUs have incentives to follow the mechanism : both POs and SUs have incentives to follow the mechanism of MAP.of MAP.


OutlineOutline





Simulations and ConclusionsSimulations and Conclusions Simulation ResultsSimulation Results ConclusionsConclusions


Simulation ResultsSimulation Results

Simulation SetupSimulation Setup We assume that the simulation network contains of We assume that the simulation network contains of

M POs and N SUs, distributed in a square area of M POs and N SUs, distributed in a square area of 1000m*1000m;1000m*1000m;

The duration of one Round in MAP is 10ms.The duration of one Round in MAP is 10ms.

Number of POs: Number of POs: M=5,Number of SUs: Number of SUs: N=50,Number of CHs: Number of CHs: mi=6.



ConvergenceConvergence MAP Converges in 1.5 seconds.MAP Converges in 1.5 seconds.

Number of POs: Number of POs: M=5,Number of SUs: Number of SUs: N=50,Number of CHs: Number of CHs: mi=6,

Step size:Step size: =10.



Convergence Speed and Efficiency vs Step sizeConvergence Speed and Efficiency vs Step size Converging speed rapidly increases with respect to Converging speed rapidly increases with respect to

step size;step size; Even at the largest step sizeEven at the largest step size =100 , the , the

degradation of throughput of MAP is less than 1% degradation of throughput of MAP is less than 1% compared to the centralized algorithm.compared to the centralized algorithm.

Number of POs: Number of POs: M=5, Number of CHs: Number of CHs: mi=6.



Prices of POsPrices of POs The price of POs increases with the number of SUs The price of POs increases with the number of SUs

(i.e., the demand).(i.e., the demand).

Number of POs: Number of POs: M=5,Number of CHs: Number of CHs: mi=6,




Profit TransferProfit Transfer The profit of POs increases with the number of SUs The profit of POs increases with the number of SUs

(i.e., demand).(i.e., demand).

Number of POs: Number of POs: M=5,Number of CHs: Number of CHs: mi=6,




Incentive CompatibleIncentive Compatible SUs will truthfully reveal their preference among SUs will truthfully reveal their preference among

different POs, so that different types of SUs can be different POs, so that different types of SUs can be directed to their interested POs automatically.directed to their interested POs automatically.

Number of POs: Number of POs: M=5,

Number of SUs:Number of SUs: N=50,

Number of CHs: Number of CHs: mi=6,

Step size:Step size: =10,

SUs type: SUs type: {voice, data}Pos type:Pos type: {GSM, WLAN}


ConclusionsConclusions

In this paper, we study the problem of spectrum band (channel) In this paper, we study the problem of spectrum band (channel) allocation in DSA networks with multiple primary spectrum owners and allocation in DSA networks with multiple primary spectrum owners and multiple second users.multiple second users.

We propose MAP, a multi-auctioneer progressive auction mechanism, We propose MAP, a multi-auctioneer progressive auction mechanism, in which each auctioneer systematically raises the price and each in which each auctioneer systematically raises the price and each bidder subsequently chooses one auctioneer for bidding.bidder subsequently chooses one auctioneer for bidding.

We show analytically that MAP converges to a equilibrium state and it We show analytically that MAP converges to a equilibrium state and it achieves the efficient spectrum assignment compared to the achieves the efficient spectrum assignment compared to the centralized optimal assignment.centralized optimal assignment.

We further investigate the inherent profit transfer process in auction We further investigate the inherent profit transfer process in auction mechanism, and show that both POs and SUs are willing to accept the mechanism, and show that both POs and SUs are willing to accept the assignment.assignment.

Thank you !Thank you !

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MAP: Multi-Auctioneer Progressive Auction in Dynamic Spectrum Access Lin Gao, Youyun Xu, Xinbing...

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