In cognitive radio networks (CRN), primary users can lease out their unused bandwidth to secondary users in return for a fee. We study price competition in a CRN with multiple primaries and multiple secondaries in a region, where each primary tries to attract secondaries by setting a lower price for his bandwidth than other primaries. A CRN has two distinctive features, which makes the price competition very different from that in traditional commodity markets. First, in every slot, each primary may or may not have unused bandwidth available. So primaries are uncertain about the number of other primaries from whom they face competition. Second, spectrum is a commodity that allows spatial reuse: the same band can be simultaneously used at far-off locations without interference; on the other hand, simultaneous transmissions at neighboring locations on the same band interfere with each other. As a result, a primary cannot offer bandwidth at all locations, but must select an independent set of locations at which to offer it. Also, the choice of the independent set and the prices at those locations must be made jointly. We formulate price competition in a CRN as a game, taking into account both bandwidth uncertainty and spatial reuse. We analyze the game in a single slot, as well as its repeated version. In each case, we not only prove the existence of a Nash equilibrium, but also explicitly compute it. The expressions we obtain provide interesting insights into how the price competition evolves for different values of the system parameters. Moreover, for the game in a single slot, we prove the uniqueness of the Nash equilibrium in the class of symmetric equilibria.

In wireless sensor networks, a large number of sensors perform distributed sensing of a target field. A sensor cover is a subset of the set of all sensors that covers the target field. The lifetime of the network is the time from the point the network starts operation until the set of all sensors with non-zero remaining energy does not constitute a sensor cover any more. An important goal in sensor networks is to design a schedule, that is, a sequence of sensor covers to activate in every time slot, so as to maximize the lifetime of the network. In this paper, we design a polynomial-time, distributed algorithm for maximizing the lifetime of the network and prove that its lifetime is at most a factor O(log n * log nB) lower than the maximum possible lifetime, where n is the number of sensors and B is an upper bound on the initial energy of each sensor. Our algorithm does not require knowledge of the locations of nodes or directional information, which is difficult to obtain in sensor networks. Each sensor only needs to know the distances between adjacent nodes in its transmission range and their sensing radii. In every slot, the algorithm first assigns a weight to each node that is exponential in the fraction of its initial energy that has been used up so far. Then, in a distributed manner, it finds an O(log n) approximate minimum weight sensor cover, which it activates in the slot.

Cognitive radio networks are emerging as a promising technology for the efficient use of radio spectrum. In these networks, there are two categories of networks on different channels: primary networks and secondary networks. A primary network on a channel has prioritized access to the channel and secondary networks can use the channel when the primary network is not using it. The access allocation problem is to select the primary and secondary networks on each channel. We develop an auction-based framework that allows networks to bid for primary and secondary access based on their utilities and traffic demands, and uses the bids to solve the access allocation problem. We develop algorithms for the access allocation problem and show how they can be used either to maximize the auctioneer's revenue given the bids, or to maximize the social welfare of the bidding networks, while enforcing incentive compatibility. We first consider the case when the bids of a network depend on which other networks it will share channels with. When there can be only one secondary network on a channel, we design an optimal polynomial-time algorithm for the access allocation problem based on reduction to a maximum matching problem in weighted graphs. When there can be two or more secondary networks on a channel, we show that the optimal access allocation problem is NP-Complete. Next, we consider the case when the bids of a network are independent of which other networks it will share channels with. We design a polynomial-time dynamic programming algorithm to optimally solve the access allocation problem when the number of possible cardinalities of the set of secondary networks on a channel is upper-bounded. Finally, we design a polynomial-time algorithm which approximates the access allocation problem within a factor of 2 when the above upper bound does not exist.

Abstract-We address the question of optimal trading of bandwidth (service) contracts in wireless spectrum markets, for the primary spectrum providers. We propose a structured spectrum market and consider two basic types of spectrum contracts that can help attain desired flexibilities and tradeoffs in terms of service quality, spectrum usage efficiency and pricing: long-term guaranteed-bandwidth contracts, and shortterm opportunistic-access contracts. A primary provider (seller) creates and maintains a portfolio composed of an appropriate mix of these two types of contracts. The optimal contract trading question in this context amounts to how the spectrum contract portfolio of a seller in the spectrum market should be dynamically adjusted, so as to maximize return subject to meeting the bandwidth demands of its own subscribers. We formulate the optimal contract trading question as a stochastic dynamic programming problem, and obtain structural properties of the optimal dynamic trading strategy that takes into account the current market prices of the contracts and the subscriber demand process in the decision-making.

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