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Secondary Pricing of Spectrum in Cellular CDMA Networks Ashraf Al Daoud, Murat Alanyali, and David Starobinski Department of Electrical and Computer Engineering Boston University, Boston IEEE DySPAN(2007)
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Outline Introduction Network Model Economic Model Problem Formulation Blocking Probabilities Characterization of Prices Comparison between Pricing Techniques Conclusion 2
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Introduction(1/4) Legacy regulatory frameworks of cellular wireless communications do not allow reselling spectrum license. ◦ Economists have argued against such rigid regulation [1]. ◦ The Secondary Markets Initiative of the FCC permits leasing of spectrum licenses subject to approval by FCC [3]. 3 [1] R. Coase, ”The Federal Communications Commission,” Journal of Political Economy II (2), 1959. [3] The Federal Communications Commission, Secondary Markets Initiative. http://wireless.fcc.gov/licensing/secondarymarkets/.
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Introduction(2/4) A primary license holder aims to lease its spectrum within a certain geographic subregion of its own network. ◦ Benefit: Obtains revenue due to the rent of the region. ◦ Cost: Reduced spatial coverage of its network. Possible interference. Formulate optimal pricing as an optimization problem with the objective of profit maximization. 4
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Introduction(3/4) Pricing problem can be considered within the framework of monopolistic markets in classical microeconomic theory [11]. ◦ Difficulties : complexity of network-wide consequences of interference. ◦ Inefficiency : eliminate interference by isolating the activity with guardbands [10]. 5 [10] A. Tonmukayakul and M. Weiss, ”Secondary use of radio spectrum: a feasibility analysis,” Telecommunications Policy Research Conference, 2004. [11] H. R. Varian, Microeconomic Analysis, Norton, New York, 1984.
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Introduction(4/4) In this paper, the optimal price suggests charging the buyer per admitted call that generates interference for the seller. ◦ Avoid the difficulties mentioned. ◦ Reasonable loss of modeling accuracy. Adaptation of reduced load approximation. The technical focus is on the CDMA networks. 6
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Network Model(1/3) Represent a wireless cellular network with a weighted graph G = (N,W) ◦ N refers to nodes. Each node i ∈ N represents a cell. ◦ W refers to positive edge weights. For each pair i, j of cells, the associated weight w ij ∈ W represents interference between the cells. Self-loops are allowed. (w ii >0) 7
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Network Model(2/3) Assumption: a call can be sustained only if it experiences small enough interference. (threshold) A network load n is feasible. (for all cells j) n i : the number of calls in progress at cell i. k j : certain constant. In this paper we assume that all i, j ∈ N the parameters w ij and κ j are rational numbers. 8
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Network Model(3/3) Calls arrive at each i cell according to a Poisson process of rate ν i ≥ 0. An incoming call is accepted if and only if its inclusion conserves the feasibility condition (1). R(ν) : long-term average rate of revenue generation per unit time. Denote the vector of call arrival rates by ν = (νi : i ∈ N). B i (v): probability of call blocking on cell i. 9
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Economic Model(1/3) Consider pricing of a region (a given subset L ⊂ N) of cells, from the perspective of the network provider. The original provider(seller) rents the license to potential providers(buyers) for the price(p). 10
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Economic Model(2/3) Assumed that the buyer reflects the transaction price p onto its service. ◦ p affects the demand that the buyer receives in region L. α i (p) : call arrival rate of the buyer to cell i ∈ L λ(p) : The overall network demand after a transaction at price p 11
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Economic Model(3/3) F(p) denotes an expected rate of revenue over the term of a lease signed at price p. Three kinds of form: ◦ Flat price: ◦ Price per demand: ◦ Price per honored demand: 12
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Problem Formulation(1/2) Q(λ) is a network revenue due to the service provided over the region N −L: The cost incurred by the seller in leasing region L at price p: 13
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Problem Formulation(2/2) The seller aims to find the price p to maximize its profit: Assumption: The functions F and α i, i ∈ L, are differentiable. Due to F, α i, and B i (.) are differentiable, a solution p* satisfies: 14
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Blocking Probabilities(1/5) For any set of arrival rates λ the vector of cells loads evolves according to a Markov process Equilibrium distribution: Blocking probabilities: 15 difficult to compute
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Blocking Probabilities(2/5) Reduced load approximation is useful in analysis of blocking in circuit-switched telephony [6]. We shall approximate B i (λ) by the quantity : 16 [5] F. P. Kelly, ”Routing in circuit-switched networks: Optimization, shadow prices and decentralization,” Advances in Applied Probability, vol. 20, pp. 112–144, 1988. [6] F. P. Kelly, ”Loss networks,” Annals of Applied Probability, vol. 1, pp. 319–378, 1991. Differentiable in λ [5] Erlang B Formula
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Blocking Probabilities(3/5) - Experiment Accuracy of the Reduced Load Approximation: 17
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Blocking Probabilities(4/5) - Experiment the sensitivity of optimal price to errors in the blocking probabilities due to reduced load approximation: Compute optimal price of a single cell using the reduced load approximation and also using the exact equilibrium distribution of the network process. 18
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Blocking Probabilities(5/5) - Experiment 19
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Characterization of Prices(1/3) Assumption: (Exactness of reduced load approximation) Bi(λ) = for each cell i and all call arrival rates λ = (λ i : i ∈ N) An inner solution p* of the seller’s problem satisfies 20
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Characterization of Prices(2/3) When an inner solution p* exists, properly damped versions of the recursion may be expected to converge [5]. 21 [5] F. P. Kelly, ”Routing in circuit-switched networks: Optimization, shadow prices and decentralization,” Advances in Applied Probability, vol. 20, pp. 112–144, 1988.
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Characterization of Prices(3/3) - Experiment 22
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Comparison between Pricing Techniques(1/2) Simple technique of pricing: ◦ Without counting for the cost resulting from the interference caused by the sold region. 23
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Comparison between Pricing Techniques(2/2) Another simplistic approach of pricing: ◦ To use space guard bands. 24
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Conclusion(1/2) Considered the problem of optimal pricing of spectrum in CDMA-based cellular wireless networks ◦ Cell ◦ Interference Study a model of circuit-switched network traffic ◦ Poisson call arrivals ◦ Express optimal prices by adapting reduced load approximations 25
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Conclusion(2/2) The form of optimal prices suggests that the seller should charge the buyer per accepted call in the sold region Main contribution: ◦ Global consideration of network ◦ Characterization of optimal price 26
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