1. 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)

2. Outline Introduction Network Model Economic Model Problem Formulation Blocking Probabilities Characterization of Prices Comparison between Pricing Techniques Conclusion 2

3. 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/.

4. 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

5. 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.

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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

13. 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

14. 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

15. 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

16. 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

17. Blocking Probabilities(3/5) － Experiment Accuracy of the Reduced Load Approximation: 17

18. 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

19. Blocking Probabilities(5/5) － Experiment 19

20. 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

21. 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.

22. Characterization of Prices(3/3) － Experiment 22

23. 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

24. Comparison between Pricing Techniques(2/2) Another simplistic approach of pricing: ◦ To use space guard bands. 24

25. 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

26. 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