Ashraf Al Daoud

A stackelberg game for pricing uplink power in wide-band cognitive radio networks

We study the problem of pricing uplink power in wide-band cognitive radio networks under the objective of revenue maximization for the service provider and while ensuring incentive compatibility for the users. User utility is modeled as a concave function of the signal-to-noise ratio (SNR) at the base station, and the problem is formulated as a Stackelberg game. Namely, the service provider imposes differentiated prices per unit of transmitting power and the users consequently update their power levels to maximize their net utilities. We devise a pricing policy and give conditions for its optimality when all the users are to be accommodated in the network. We show that there exist infinitely many Nash equilibrium points that reward the service provider with the same revenue. The pricing policy charges more from users that have better channel conditions and more willingness to pay for the provided service. We then study properties of the optimal revenue with respect to different parameters in the network. We show that for regimes with symmetric users who share the same level of willingness to pay, the optimal revenue is concave and increasing in the number of users in the network. We analytically obtain achievable SNRs for this special case, and finally present a numerical study in support of our results.

Secondary Pricing of Spectrum in Cellular CDMA Networks

We study secondary pricing of spectrum in wireless cellular networks employing CDMA at the physical layer. We consider a primary license holder who aims to lease its spectrum within a certain geographic subregion of its own network. Such a transaction has two contrasting economic implications for the seller: On the one hand the seller obtains a revenue due to the exercised price, or rent, of the region. On the other hand, the seller incurs a cost due to (i) reduced spatial coverage of its network and (ii) possible interference from the leased region into the retained portion of its network. We formulate an optimization problem with the objective of profit maximization, and characterize its solutions based on a reduced load approximation that can be shown to be asymptotically exact. The form of optimal prices suggests charging the buyer per admitted call, in proportion with the interference it generates. The charged amount balances the corresponding loss of revenue incurred by the seller due to the influence of an admitted call. We numerically argue that this pricing approach yields better profit compared to some other simplistic techniques.

Pricing strategies for spectrum lease in secondary markets

We develop analytical models to characterize pricing of spectrum rights in cellular CDMA networks. Specifically, we consider a primary license holder that aims to lease its spectrum within a certain geographic subregion of its network. Such a transaction has two contrasting economic implications: On the one hand the lessor obtains a revenue due to the exercised price of the region. On the other hand, it incurs a cost due to: 1) reduced spatial coverage of its network; and 2) possible interference from the leased region into the retained portion of its network, leading to increased call blocking. We formulate this tradeoff as an optimization problem, with the objective of profit maximization. We consider a range of pricing philosophies and derive near-optimal solutions that are based on a reduced load approximation (RLA) for estimating blocking probabilities. The form of these prices suggests charging the lessee in proportion to the fraction of admitted calls.We also exploit the special structure of the solutions to devise an efficient iterative procedure for computing prices. We present numerical results that demonstrate superiority of the proposed strategy over several alternative strategies. The results emphasize importance of effective pricing strategies in bringing secondary markets to full realization.

Joint channel allocation and user association for heterogeneous wireless cellular networks

We study the engineering of heterogeneous cellular networks composed of a macrocell and some picocells by investigating the interplay of different network processes and parameters such as channel allocation, user association and reuse pattern (to control inter-cell interference between picocells). We formulate a joint association, channel allocation, and inter-cell interference management problem that relies on very few assumptions. This problem turns out to be an Integer Non-Linear program that is NP-hard. However, its structure is such that we can solve it exactly for relatively large size systems. We use optimal solutions as benchmarks to understand how different simple association schemes perform. Our results show the critical impact of the association rules on system performance and shows the interplay of the different processes and parameters. We believe that these insights will help design online association schemes in the future.

Profitability of dynamic spectrum provision for secondary use

We characterize policies and prices for secondary spectrum provision whose profitability is insensitive to the demand curve. In more explicit terms, the paper provides a critical price value such that if secondary access is priced above that value then allowing secondary access is profitable for the licensee as long as the price generates secondary demand. Conversely, if the price does not generate demand then the licensee does not incur any operational cost due to secondary service. Hence such characterization serves as a guarantee that a spectrum licensee can strictly avoid revenue loss due to participation in spectrum trading.

Brief announcement: cloud computing games: pricing services of large data centers

Organizations opt to reduce costs by contracting their day-to-day computing needs to service providers who offer large-scale data centers and cloud computing services. Like other computing commodities, data centers provide paid services that require careful pricing. Using a Stackelberg game formulation, we present a demand-based pricing model for maximizing revenue of data center providers that serve clients who aim to maximize their utilities.

Reservation policies for revenue maximization from secondary spectrum access in cellular networks

We consider the problem of providing opportunistic spectrum access to secondary users in wireless cellular networks. From the standpoint of spectrum license holders, achieving benefits of secondary access entails balancing the revenue from such access and its impact on the primary service of the license holder. While dynamic optimization is a natural framework to pursue such a balance, spatial constraints due to interference and uncertain demand characteristics render exact solutions difficult. In this paper, we study guiding principles for spectrum license holders to accommodate secondary users via reservation-based admission policies. Using notions of dynamic optimization, we first develop the concept of average implied cost for establishing a connection in an isolated locality. The formula of the cost provides an explicit characterization of the value of spectrum access. We then generalize this concept to arbitrary topologies of interference relations and show that the generalization is justified under an analogue of the reduced load approximation judiciously adapted from the wireline to the wireless setting. An explicit characterization of this quantity demonstrates the localized nature of the relationship between overall network revenue and reservation parameters. Based on this relationship, we develop an online distributed algorithm for computing optimal reservation parameters. The performance of the algorithm is verified through a numerical study.

On Pricing of Spectrum in Secondary Markets

Optimal price of spectrum in secondary markets is studied. We consider a primary license holder who aims to lease the right to provide service in a given subset of its coverage area. Such a transaction has two contrasting economic implications for the seller: on the one hand the seller obtains a revenue due to the exercised price of the region. On the other hand, the seller incurs a cost due to (i) reduced spatial coverage of its network and (ii) possible interference from the leased region into the retained portion of its network. We formulate an optimization problem with the objective of profit maximization, and characterize its solutions based on a reduced load approximation. The form of optimal price suggests charging each admitted call in proportion to the attendant revenue loss due to the generated interference.

On spectrum sharing in narrowband cellular wireless networks

We study secondary spectrum sharing in narrowband cellular networks in which calls in neighboring cells need to be assigned different channels. Analysis of such networks are in general difficult due to large state spaces and lack of closed form expressions. Here we consider linear topologies and show that they lend themselves to exact analysis. We analyze four sharing policies where equilibrium distribution of cell occupancies is a Markov random field. For each policy we derive closed form expressions for the equilibrium distributions in the form of a product of certain stochastic matrices. This characterization leads to tractable computation of equilibrium distributions and blocking probabilities. We use the obtained results to compare the policies in terms of (i) maximum revenue, and (ii) secondary price-demand pairs that lead to positive profit for the network service provider.

Profit-robust policies for dynamic sharing of radio spectrum

We investigate profitability from secondary spectrum provision under unknown relationships between price charged for spectrum use and demand drawn at the given price. We show that profitability is governed by the applied admission policy and the price charged to secondary users. We explicitly identify a critical price (market entry price) such that if secondary demand is charged below that price, the licensee endures losses from spectrum provision, regardless of the applied admission policy. Furthermore, we show that an admission policy that admits secondary demand only when no channel is occupied is profitable for any price that exceeds the critical price. We prove that this policy is profit-robust to variations in secondary demand, i.e., if the policy is profitable for a certain price, it will be profitable for any secondary demand that the price generates, as long as the price generates demand. We also investigate profitability from a set of policies that allow more secondary users to access spectrum by defining the number of users that can be concurrently served. Our results demonstrate profit-robustness of these policies and explicitly characterize profitable prices. We provide a numerical study to verify our theoretical findings.