An Economic Framework for Dynamic Spectrum Access and Service Pricing

Shamik Sengupta Department of Electrical and Computer Engineering, Stevens Institute of Technology, Hoboken, NJMainak Chatterjee School of Electrical Engineering and Computer Science, University of Central Florida, Orlando, FL1An Economic Framework for Dynamic Spectrum Access and Service PricingIEEE/ACM TRANSACTIONS ON NETWORKING, VOL. 17, NO. 4, AUGUST 2009Outline2IntroductionRelated WorkSpectrum Allocation Through AuctionsService Provisioning Using GamesEstimating the Demand for BandwidthChannel Threshold Based Provider SelectionNumerical ResultConclusion & CommentsIntroduction3Introduction4Wireless Service Providers (WSPs) buy spectrum from the spectrum owner and use it for providing services to the end users. It is called static spectrum allocationHowever, the current practice of static spectrum allocation often leads to low spectrum utilization and results in fragmentation of the spectrum creating white space (unused thin bands). Therefore, the concept of Dynamic Spectrum Allocation (DSA) is being investigated. Introduction: Economic Paradigm Shift5

White SpaceIntroduction: Cyclic Dependency6Two problems in the trading systemDynamic spectrum allocation (upper half of Fig. 1)WSPs use spectrum to service end users (lower half of Fig. 1)Cyclic Dependency (typical supply-demand scenario)Estimation of the demand for bandwidth and the expected revenue drive the WSPs strategiesService pricing in turn affect the demand by the users

Introduction: Distribution of This Work7We answer the following questions:How the spectrum will be allocated from the coordinated access band (CAB, a common pool of open spectrum) to the service providersHow service providers will determine the price of their servicesHow are the above two inter-relatedRelated Work8Related Work9Auction TheorySingle-unit auction [33]Multi-unit multiple winners [1]Second-price auction [19]Real-time auction framework and piecewise linear demand curve [8]Collusion issue [12][1] B. Aazhang, J. Lilleberg, and G. Middleton, Spectrum sharing in a cellular system, in IEEE Symp. Spread Spectrum Techniques and Applications, 2004, pp. 355359.[8] S. Gandhi, C. Buragohain, L. Cao, H. Zheng, and S. Suri, A general framework for wireless spectrum auctions, in Proc. IEEE DySpan, 2007, pp. 2233.[12] Z. Ji and K. J. R. Liu, Collusion-resistant dynamic spectrum allocation for wireless networks via pricing, in Proc. IEEE DySpan, 2007, pp. 187190[19] P. Maille and B. Tuffin, Multibid auctions for bandwidth allocation in communication networks, in Proc. IEEE INFOCOM, 2004, ol. 1, pp. 5465[33] W.Vickrey, Counterspeculation, auctions, and competitive sealed tenders, J. Finance, vol. 16, no. 1, pp. 837, Mar. 1961Related Work (contd)10Game TheoryOverview and application to networking and communication [35]Network services have been studied with the help of stability and fairness [13]Service admission control using game theory [17]

[13] F. P. Kelly, A. K. Maulluo, and D. K. H. Tan, Rate control in communication networks: Shadow prices, proportional fairness and stability, J. Oper. Res. Soc., vol. 49, pp. 237252, 1998[17] H. Lin, M. Chatterjee, S. K. Das, and K. Basu, ARC: An integrated admission and rate control framework for CDMA data networks based on non-cooperative games, in Proc. MobiCom, 2003, pp. 326338.[35] W. Wang and B. Li, Market-driven bandwidth allocation in selfish overlay networks, in Proc. IEEE INFOCOM, 2005, vol. 4, pp.25782589.Spectrum Allocation Through Auctions11Spectrum Allocation Through Auctions12The interaction between the spectrum broker and the WSPs. Auction is invoked only when the total demand of spectrums exceeds the total spectrum available in the CAB. Auction should be conducted on a periodic basis and on a small time granularity (e.g., every 1, 12, 24 hours). Synchronous auctions will allow the spectrum brokers maximize revenueAsynchronous auctions (WSPs can make requests at any point of time) make it possible for lower bidders win the auctions before higher bidders come and thus spectrum might be unavailable when higher bidders come. Auction Issues13Spectrum auctions are multi-unit auctions (bidders bid for different amount of spectrum)We assume that total spectrum is homogeneous and thus no band is superior or inferior than any other bandRoles in auctionsThe spectrum broker seller/auctioneerThe WSPs buyer/bidderImportant issuesHow to maximize the revenue generated from bidders.How to maximize the spectrum usage.How to entice bidders by increasing their probability of winning. (in simulation section)How to prevent collusion among providers. (in simulation section)Auction Rules14We assume that the WSPs need at least the spectrum amount requested (minimum requirement). A WSP would get negative utility if he/she obtain spectrum less than the minimum requirement. It is necessary to make the small companies interested in the auctions (encourage competition). The problem is close to the classical knapsack problemThe sack represents the finite capacity of spectrum. The items weight and value represent WSPs requested amount and bid. We propose the Winning Determining Sealed Bid Knapsack Auction.Auction Rules (contd)15There are L WSPs competing for a total spectrum W in a particular geographic regionAll the WSPs submit their demands at the same time in a sealed mannerSealed bid auction has shown to be perform well in all-at-a-time bidding and has the tendency to prevent collusion [26]Each WSP has no knowledge about others bidding quantity and priceStrategy adopted by service provider i: qi = {wi, xi}. Amount of spectrum requested: wi Corresponding price that the WSP is willing to pay: xi Auction Rules (contd)16The optimization problem would be

Note that a more realistic approach would have been a multiple-choice knapsack formulation with each bidder submit a continuous demand curve. However, optimizations with continuous demand is hard.

Solving the Optimization Problem17We assume thatBids can take only integer values. The number of bidders is typically of the order of 10. Thus the problem can be solved through dynamic programming with reasonably low computationP.S. Unbounded knapsack problem using dynamic programming

m[W] is the solution

Bidders Strategies18Denote the optimal allocation as M, which is the set of all the winning demand tuples qi The aggregate bid

Consider a particular bidder j who was all allocated spectrum. Then the aggregate bid without that bidder j is

Next consider if that bidder doesnt exist, then the optimal allocation change from M to M*, and the aggregate bid is

Bidders Strategies (contd)19Therefore, minimum winning bid of bidder j must be at least greater than

Bidder j will be granted the request if xj > Xj not granted the request if xj < Xj indifferent between winning and losing if xj = Xj This implies that if bidder j knows the bids of other bidders, he/she could govern the auctions.

Bidders Strategies (contd)20However, the auction is conducted in a sealed bid manner and thus bidder j would have no idea about Xj. We want to find if there exists any Nash equilibrium strategy of the bidders.Nash equilibrium: no player in the game finds it beneficial to change his/her strategyTwo different schemes under the knapsack auction are studied two corresponding lemmas are presented First price scheme: winning bidders pay their bidSecond price scheme: winning bidders pay the second highest bidBidders Reservation Price21Definition: Bidders reservation price is the maximum price a bidder would be willing to pay. WSP buys spectrum from the spectrum broker, and then sell in the form of services to end usersThe revenue thus generated helps the provider to pay the cost of spectrum statically allocated and dynamically allocated. Let the total revenue generated be R, and Rstatic goes towards the static cost, then the difference, Rdynamic, is the maximum amount that the provider can afford for the extra spectrum from CAB, i.e.,

Note that Rdynamic is not the bidders reservation price but is a prime factor that governs this reservation price

Bidders Strategies: Second Price Scheme22Lemma 1: In the second price knapsack auction, the dominant strategy of the bidder is to bid bidders reservation price.Proof Assume that the jth bidder has the demand tuple qj = {wj, xj}.Its reservation price for that amount wj is rj.The request will be granted and consequently belong to optimal allocation M only if the bid is at least Xj. And the jth bidder will pay the second price, which is Xj. (?)Then the payoff obtained by the bidder is

Bidders Strategies: Second Price Scheme (contd)23Assume that the jth bidder does not bid its true evaluation, i.e., xj rj.

OptionsCasesWin?Expected payoffxj < rj rj > xj > Xj O(rj Xj) rj > Xj > xj X0Xj > rj > xj X0xj > rj xj > rj > Xj O(rj Xj)xj > Xj > rj O(rj Xj) < 0 (*)Xj > xj > rj X0Bidders Strategies: Second Price Scheme (contd)24If bidder j wins, then the maximum expected payoff is given by Ej = rj Xj. And bidding any other (higher or lower) than its reservation price rj will not increase payoff. Thus the dominant strategy of a bidder in second price bidding under knapsack model is to bid its reservation price. Bidders Strategies: First Price Scheme25Lemma 2: In first price bidding, reservation price is the upper bidding threshold.Proof The expected payoff can be given by, Ej = rj xj. To keep Ej > 0, xj must be less than rj. Then the weak dominant strategy for the bidder in first price auction is to bid less than the reservation price. Service Provisioning Using Games26Service Provisioning Using Games27In this section, we consider the model between WSPs and end users as shown in the lower half of Fig. 2, where any user can access any WSP.

Goalinvestigate whether there exists any strategy that will help the users and providers to reach an equilibrium in the gameTo reach the goal wecharacterize the utility functions of the users and providersand then analyze the utility functionsAt last we find a pricing threshold helping both sides to reach the (Nash) equilibrium

Utility Function of Users28We consider L service providers that cater to a common pool of N users. Let the unit price advertised by the service provider j, 1jL, at time t be pj(t). Let bij(t) be the resource consumed by user i, 1iN, served by provider j. The total resource (capacity) of provider j is Cj. Utility Function of Users (contd)29The utility obtained by user i under provider j is

Where aij is a positive parameter that indicates the relative importance of benefit and acts as a weightage factor. We chose the log function since it is analytically convenient, increasing, strictly concave and continuously differentiable. The first cost component: direct cost paid to the provider for obtaining bij(t) amount of resource, that is

Utility Function of Users (contd)30The second cost component: queuing delay, assuming the queuing process to be M/M/1 at the links, and thus the delay cost component is

The third cost component: channel condition.Assume that Qj denotes the wireless channel quality received from the base station of the jth provider and thus the third cost component is

P.S. Expected waiting time in M/M/1 is 1/(-), : service rate, : arrival rateUtility Function of Users (contd)31Combining all the components in (9), (10), (11) and (12), we get the net utility as

Utility Function of Service Providers32The utility of service provider j at time t is

Where Kj is the cost incurred to provider j for maintaining network resources, and is assumed to be constant for simplicity

Strategy Analysis33To simplify the analysis, we assume that all the users maintain a channel quality threshold. We combine the cost components in (11) and (12), i.e.,

where

We assume that bij(t) in () captures the behavior of channel quality.

Strategy Analysis: Users maximize their utility34Differentiating (15) with respect to bij(t),

Similarly, the second derivative is

If we assume the last term in (42) is positive, then Uij(t) Q2 =>

Channel Threshold Based Provider Selection (contd)49Case 1: Q1 < Q2 =>

Thus, a user cannot increase his gain by unilaterally changing his/her strategy. As a result, a channel quality threshold exists for the users and maintaining this threshold will help the users to reach Nash Equilibrium.

Numerical Result50Goal51In this section, we want to Simulate our auction modelShow how our model outperforms the classical highest bid auction modelsModel the interaction between WSPs and usersNumerical Result: Spectrum Auctioning52Parameter settingTotal amount of spectrum in CAB: 100 units. Minimum and maximum amount of spectrum requested by each bidder: 11 and 50 units. (!) Minimum bid per unit of spectrum: 25 units. Number of bidders: 10. Models comparedKnapsack auction v.s. Classical highest bid auction (!)Knapsack synchronous v.s. Knapsack asynchronous (!)Numerical Result: Spectrum Auctioning (contd)53Fig. 3(a) and (b) compares revenue and spectrum usage for knapsack synchronous and classical highest bid strategies for each auction round

Numerical Result: Spectrum Auctioning (contd)54In Fig. 4(a) and (b) we compare revenue and spectrum usage for both the synchronous and asynchronous strategies

Numerical Result: Spectrum Auctioning (contd)55Figs. 5(a), (b) and 6(a), (b) show the average revenue and spectrum usage with varying number of bidders for both comparisons

Numerical Result: Spectrum Auctioning (contd)56Fig. 7(a) and (b) show that the proposed Knapsack auction model encourages the low potential bidders

Numerical Result: Spectrum Auctioning (contd)57Fig. 8(a), (b) and Fig. 9 show that the proposed auction model discourages the presence of collusion.

Numerical Result: Pricing58How the pricing strategies proposed for WSP and end users interaction work as incentives for bothWe consider two cases:Fixed number of usersConsider the equal weightage factor aij = 1.5 and Cj varies from 1 to 100Increasing number of usersConsider the ratio of aIj and Cj is fixed and Cj varies form 1 to 100

Numerical Result: Pricing (fixed)59Fig. 10 shows how the provider must decrease the price per unit of resource if the total amount of resources increases with the same user base

Numerical Result: Pricing (fixed) (contd)60With the number of users fixed, we observe that the total profit of the provider increases till a certain resource and then decreasesAllow us to estimate the maximum point

Numerical Result: Pricing (fixed) (contd)61More resources is an incentive of users

Numerical Result: Pricing (increasing)62The resource is initially scarce (raising high price) and slightly decreasing after a certain point

Numerical Result: Pricing (increasing) (contd)63With users increasing proportionally with resources, the total profit is always increasing which presents an incentive for the providers

Numerical Result: Pricing (increasing) (contd)64The net utility increases with increasing resources; thus providing incentive for the users (but it saturates earlier than the case of fixed number of users)

Conclusion & Comments65Conclusion66We provide a framework based on auction and game theories that capture the interaction among spectrum broker, service providers, and end-users.Knapsack Auction (synchronous, second price sealed manner)Utility function of WSPs and users and Nash EquilibriumMethod for providers to estimate spectrum needed and reservation priceChannel quality thresholdSimulation result illustrating the collusion issueComments67Auction model makes bidders truly report their reservation prices which seems hard to get at first. Knapsack auction works well with the integer demand and bidding price (simply leaves to bidders)How to characterize Nash Equilibrium in mathematical equationRemind the issue of collusion

Incomplete information for setting up the simulation, e.g., How to model the behavior of bidders through auction rounds?How to model the behavior of bidders if they colludes?Etc.