MAP: Multi-Auctioneer Progressive Auction in Dynamic Spectrum Access Lin Gao, Youyun Xu, Xinbing Wang Shanghai Jiaotong University

MAP: Multi-Auctioneer Progressive Auction in Dynamic Spectrum Access 2 Outline Introduction  Motivations  Objectives System Model and Problem Formulation Centralized Channel Assignment Auction-based Channel Assignment Simulations and Conclusions

MAP: Multi-Auctioneer Progressive Auction in Dynamic Spectrum Access 3 Motivation  Currently, wireless systems suffer from the inefficiency in spectrum usage. Dynamic spectrum access (DSA) is a promising paradigm to achieve efficient utilization of the spectrum resource.  The primary spectrum owners (POs) may lease their excess spectrum bands (residual channels) to the secondary users (SUs) for enhanced profit.  The essential problem: (i) Efficiency: how to assign the residual channels among the SUs with the highest spectrum utilization, and (ii) Incentive: what is the motivation for each PO and SU accepting such an assignment.

MAP: Multi-Auctioneer Progressive Auction in Dynamic Spectrum Access 4 Objectives -- How to Solve the Problem?  Centralized algorithms:  Linear-programming-based branch-and-bound algorithm [14]  Graph-theory-based optimal matching algorithm [16]  In this paper, we propose an auction-based spectrum bands assignment framework, named as MAP, which works in a totally distributed manner.  We show analytically that MAP achieves the efficient (optimal) spectrum assignment compared to the centralized algorithm (efficiency). We further show that, through the inherent profit transfer process in auction mechanism, both POs and SUs are willing to accept the assignment of MAP (incentive).

MAP: Multi-Auctioneer Progressive Auction in Dynamic Spectrum Access 5 Outline Introduction System Model and Problem Formulation  System Model  Problem Formulation Centralized Channel Assignment Auction-based Channel Assignment Simulations and Conclusions

MAP: Multi-Auctioneer Progressive Auction in Dynamic Spectrum Access 6 System Model  We consider an DSA network consisting of POs and SUs. Each POs owns residual channels which can be used by SUs.  We consider an DSA network consisting of M POs and N SUs. Each POs i owns m i residual channels which can be used by SUs.  Each channel can only be used by one SU, and each SU can only use one channel.  Different SUs may have different valuations () on the same channel and different channels may have different values to the same SU.  Different SUs may have different valuations ( v ij ) on the same channel and different channels may have different values to the same SU. An example of DSA network with M=3 POs and N=6 SUs.

MAP: Multi-Auctioneer Progressive Auction in Dynamic Spectrum Access 7 System Model  Valuation () is defined as the the income of SU by using the channel of PO. The valuation is often related to the channel capacity and channel quality (typically the signal-to-noise ratio (SNR)).  Valuation ( v ij ) is defined as the the income of SU i by using the channel of PO j. The valuation is often related to the channel capacity and channel quality (typically the signal-to-noise ratio (SNR)).  Valuation Matrix: An example of valuation matrix with M=4 POs and N=6 SUs.

MAP: Multi-Auctioneer Progressive Auction in Dynamic Spectrum Access 8 Problem Formulation  The optimal channel assignment problem is defined as follows:

MAP: Multi-Auctioneer Progressive Auction in Dynamic Spectrum Access 9 Problem Formulation  An example of optimal channel assignment with,, and :  An example of optimal channel assignment with M=4, N=6, and m i =2 :

MAP: Multi-Auctioneer Progressive Auction in Dynamic Spectrum Access 10 Outline Introduction System Model and Problem Formulation Centralized Channel Assignment  Optimal matching algorithm Auction-based Channel Assignment Simulations and Conclusions

MAP: Multi-Auctioneer Progressive Auction in Dynamic Spectrum Access 11  The original optimization problem can be transformed into the following problem in graph: find a set of edges with maximum weight, subjecting to for each SU and for each PO  The original optimization problem can be transformed into the following problem in graph: find a set of edges with maximum weight, subjecting to ρ j ≤ 1 for each SU j ∈ N and ρ i ≤ m i for each PO i ∈ M. Optimal matching algorithm A graph representation for the optimization problem with and. A graph representation for the optimization problem with M=2 and N=6.

MAP: Multi-Auctioneer Progressive Auction in Dynamic Spectrum Access 12  Using the splitting graph, the optimization problem in previous page can be transformed into the classical optimal matching problem in graph theory. Optimal matching algorithm A splitting graph representation for the example in previous page. Kuhn-Munkres algorithm 1957

MAP: Multi-Auctioneer Progressive Auction in Dynamic Spectrum Access 13 Outline Introduction System Model and Problem Formulation Centralized Channel Assignment Auction-based Channel Assignment  Mechanism of MAP  Equilibrium of MAP Simulations and Conclusions

MAP: Multi-Auctioneer Progressive Auction in Dynamic Spectrum Access 14 Mechanism of MAP  Centralized channel assignment algorithm is not practical for DSA networks, thus we propose an auction-based channel assignment framework.  The essential elements for the auction:  Auctioneer – all POs  Bidders – all SUs  Auctioned Objects – the residual channels owned by all POs  Strategy of POs – each PO i specifies the price of channel p i  Strategy of SUs – each SU j selects an PO for buying, i.e., x j =i.  Utility of POs – each PO i obtains the utility (p i -c i ) * d i, where d i is the demand of SUs for the channel of PO i.  Utility of SUs – each SU j obtains the utility v ji -p i

MAP: Multi-Auctioneer Progressive Auction in Dynamic Spectrum Access 15 Mechanism of MAP  We propose MAP, a multi-auctioneer progressive auction for the channel assignment problem. The basic idea for MAP is that: Each auctioneer systematically adjusts the price and each bidder subsequently chooses the best auctioneer for bidding.  Due to the progressive nature of MAP, we define MAP as a round- based distributed process that works as follows:  (i) Asking: In the first stage of each round, each PO elicits( 抽出 ) the demands of SUs and judges whether it is in demanded surplus. If so, the PO raises his price by a given number and announces the new price.  (ii) Bidding: In the second stage of each round, each SU chooses the best PO which maximize his utility and competes for the channel from that PO.

MAP: Multi-Auctioneer Progressive Auction in Dynamic Spectrum Access 16 Mechanism of MAP  The mechanism of MAP:

MAP: Multi-Auctioneer Progressive Auction in Dynamic Spectrum Access 17 Mechanism of MAP  An example of MAP with,, and  An example of MAP with M=2, N=2, and m i =1 :

MAP: Multi-Auctioneer Progressive Auction in Dynamic Spectrum Access 18 Equilibrium of MAP  Weak Equilibrium: Weak equilibrium is defined as a status in which the demand for channels owned by each PO does not exceed the supply, i.e.,, for each PO  Weak Equilibrium: Weak equilibrium is defined as a status in which the demand for channels owned by each PO i does not exceed the supply, i.e., d i ≤ m i, for each PO i ∈ M.  Strong Equilibrium: Strong equilibrium is defined as a status in which (i) the demand for channels owned by each PO does not exceed the supply, i.e.,, for each PO, and (ii) if the demand for channels owned by PO is less than the supply, i.e.,, then the price of PO equals its reservation price, i.e.,.  Strong Equilibrium: Strong equilibrium is defined as a status in which (i) the demand for channels owned by each PO i does not exceed the supply, i.e., d i ≤ m i, for each PO i ∈ M, and (ii) if the demand for channels owned by PO i is less than the supply, i.e., d i < m i, then the price of PO i equals its reservation price, i.e., p i = c i.

MAP: Multi-Auctioneer Progressive Auction in Dynamic Spectrum Access 19 Equilibrium of MAP  An example of weak equilibrium and strong equilibrium.

MAP: Multi-Auctioneer Progressive Auction in Dynamic Spectrum Access 20 Equilibrium of MAP  Convergence: (Lemma 1) MAP converges to a weak equilibrium.  Convergence: (Lemma 2) MAP converges to a strong equilibrium, if the step size  is small enough.  Efficiency: (Lemma 3) The channel assignment of MAP is optimal, if step size  is small enough.  Incentive: both POs and SUs have incentives to follow the mechanism of MAP.

MAP: Multi-Auctioneer Progressive Auction in Dynamic Spectrum Access 21 Outline Introduction System Model and Problem Formulation Centralized Channel Assignment Auction-based Channel Assignment Simulations and Conclusions  Simulation Results  Conclusions

MAP: Multi-Auctioneer Progressive Auction in Dynamic Spectrum Access 22 Simulation Results  Simulation Setup  We assume that the simulation network contains of M POs and N SUs, distributed in a square area of 1000m*1000m;  The duration of one Round in MAP is 10ms. Number of POs: Number of SUs: Number of CHs: Number of POs: M=5, Number of SUs: N=50, Number of CHs: m i =6.

MAP: Multi-Auctioneer Progressive Auction in Dynamic Spectrum Access 23 Simulation Results  Convergence  MAP Converges in 1.5 seconds. Number of POs: Number of SUs: Number of CHs: Step size: Number of POs: M=5, Number of SUs: N=50, Number of CHs: m i =6, Step size:  =10.

MAP: Multi-Auctioneer Progressive Auction in Dynamic Spectrum Access 24 Simulation Results  Convergence Speed and Efficiency vs Step size  Converging speed rapidly increases with respect to step size;  Even at the largest step size, the degradation of throughput of MAP is less than 1% compared to the centralized algorithm.  Even at the largest step size  =100, the degradation of throughput of MAP is less than 1% compared to the centralized algorithm. Number of POs: Number of CHs: Number of POs: M=5, Number of CHs: m i =6.

MAP: Multi-Auctioneer Progressive Auction in Dynamic Spectrum Access 25 Simulation Results  Prices of POs  The price of POs increases with the number of SUs (i.e., the demand). Number of POs: Number of CHs: Step size: Number of POs: M=5, Number of CHs: m i =6, Step size:  =10.

MAP: Multi-Auctioneer Progressive Auction in Dynamic Spectrum Access 26 Simulation Results  Profit Transfer  The profit of POs increases with the number of SUs (i.e., demand). Number of POs: Number of CHs: Step size: Number of POs: M=5, Number of CHs: m i =6, Step size:  =10.

MAP: Multi-Auctioneer Progressive Auction in Dynamic Spectrum Access 27 Simulation Results  Incentive Compatible  SUs will truthfully reveal their preference among different POs, so that different types of SUs can be directed to their interested POs automatically. Number of POs: Number of SUs: Number of CHs: Step size: SUs type: Pos type: Number of POs: M=5, Number of SUs: N=50, Number of CHs: m i =6, Step size:  =10, SUs type: {voice, data} Pos type: {GSM, WLAN}

MAP: Multi-Auctioneer Progressive Auction in Dynamic Spectrum Access 28 Conclusions  In this paper, we study the problem of spectrum band (channel) allocation in DSA networks with multiple primary spectrum owners and multiple second users.  We propose MAP, a multi-auctioneer progressive auction mechanism, in which each auctioneer systematically raises the price and each bidder subsequently chooses one auctioneer for bidding.  We show analytically that MAP converges to a equilibrium state and it achieves the efficient spectrum assignment compared to the centralized optimal assignment.  We further investigate the inherent profit transfer process in auction mechanism, and show that both POs and SUs are willing to accept the assignment.

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