Consider a cognitive overlaid network (CON) that has two tiers with different priorities: a primary tier vs. a secondary tier, which is an emerging network scenario with the advancement of cognitive radio (CR) technologies. The primary tier consists of randomly distributed primary radios (PRs) of density n, which have an absolute priority to access the spectrum. The secondary tier consists of randomly distributed CRs of density m = n^y with y greater than or equal to 1, which can only access the spectrum opportunistically to limit the interference to PRs. In this dissertation, the fundamental limits of such a network are investigated in terms of the asymptotic throughput and packet delay performance when m and n approaches infinity. The following two types of CONs are considered: 1) selfish CONs, in which neither the primary tier nor the secondary tier is willing to route the packets for the other, and 2) supportive CONs, in which the secondary tier is willing to route the packets for the primary tier while the primary tier does not. It is shown that in selfish CONs, both tiers can achieve the same throughput and delay scaling laws as a stand-alone network. In supportive CONs, the throughput and delay scaling laws of the primary tier could be significantly improved with the aid of the secondary tier, while the secondary tier can still achieve the same throughput and delay scaling laws as a stand-alone network. Finally, the throughput and packet delay of a CON with a small number of nodes are investigated. Specifically, we investigate the power and rate control schemes for multiple CR links in the same neighborhood, which operate over multiple channels (frequency bands) in the presence of PRs with a delay constraint imposed on data transmission. By further considering practical limitations in spectrum sensing, an efficient algorithm is proposed to maximize the average sum-rate of the CR links over a finite time horizon under the constraints on the CR-to-PR interference and the average transmit power for each CR link. In the proposed algorithm, the PR occupancy of each channel is modeled as a discrete-time Markov chain (DTMC). Based on such a model, a novel power and rate control strategy based on dynamic programming (DP) is derived, which is a function of the spectrum sensing output, the instantaneous channel gains for the CR links, and the remaining power budget for the CR transmitter. Simulation results show that the proposed algorithm leads to a significant performance improvement over heuristic algorithms.

The transient analysis of large-scale systems is often difficult even when the systems belong to the simplest M/M/n type of queues. To address analytical difficulties, previous studies have been conducted under various asymptotic regimes by suitably accelerating parameters, thereby establishing some useful mathematical frameworks and giving insights into important characteristics and intuitions. However, some studies show significant limitations when used to approximate real service systems: (i) they are more relevant to steady-state analysis; (ii) they emphasize proofs of convergence results rather than numerical methods to obtain system performance; and (iii) they provide only one set of limit processes regardless of actual system size. Attempting to overcome the drawbacks of previous studies, this dissertation studies the transient analysis of large-scale service systems with time-dependent parameters. The research goal is to develop a methodology that provides accurate approximations based on a technique called uniform acceleration, utilizing the theory of strong approximations. We first investigate and discuss the possible inaccuracy of limit processes obtained from employing the technique. As a solution, we propose adjusted fluid and diffusion limits that are specifically designed to approximate large, finite-sized systems. We find that the adjusted limits significantly improve the quality of approximations and hold asymptotic exactness as well. Several numerical results provide evidence of the effectiveness of the adjusted limits. We study both a call center which is a canonical example of large-scale service systems and an emerging peer-based Internet multimedia service network known as P2P. Based on our findings, we introduce a possible extension to systems which show non-Markovian behavior that is unaddressed by the uniform acceleration technique. We incorporate the denseness of phase-type distributions into the derivation of limit processes. The proposed method offers great potential to accurately approximate performance measures of non-Markovian systems with less computational burden.

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In this dissertation, the robust stability of uncertain continuous and discrete singularly perturbed systems with multiple time delays is investigated. Firstly, the asymptotic stability for a class of linear continuous singularly perturbed systems with multiple time delays is investigated. A simple estimate of an upper bound of singular perturbation parameter is proposed such that the original system is asymptotically stable for any . Moreover, a delay-dependent criterion, but -independent, is proposed to guarantee the asymptotic stability of the original system. Secondly, we consider the robust stability problem of uncertain continuous singularly perturbed systems with multiple time delays. Two delay-dependent criteria are proposed to guarantee the robust stability of a class of uncertain continuous multiple time-delay singularly perturbed systems subject to unstructured perturbations. Thirdly, the robust D-stability of nominally stable discrete uncertain systems with multiple time delays is considered. Finally, the robust stability of nominally stable uncertain discrete singularly perturbed systems with multiple time delays subject to unstructured and structured perturbations is investigated. Some criteria, delay-dependent or delay-independent, will be proposed to guarantee the robust stability of the uncertain discrete multiple time-delay singularly perturbed systems. The improvements of our results over those in recent literature are also illustrated if the comparisons are possible. Some numerical examples will also be provided to illustrate our main results.

Thesis (Ph. D.)--University of Missouri-Columbia, 1999. / Typescript. Vita. Includes bibliographical references (leaves 61-64). Also available on the Internet.

Thesis supervisor: Qihe Tang. Includes bibliographic references (p. 111-116).

Thesis (Ph. D.)--University of Missouri-Columbia, 1999. / Typescript. Vita. Includes bibliographical references (leaves 61-64). Also available on the Internet.

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In this research we develop theoretical foundations and efficient solution methods for two classes of cluster-detection problems from optimization point of view. In particular, the s-club model and the biclique model are considered due to various application areas. An analytical review of the optimization problems is followed by theoretical results and algorithmic solution methods developed in this research. The maximum s-club problem has applications in graph-based data mining and robust network design where high reachability is often considered a critical property. Massive size of real-life instances makes it necessary to devise a scalable solution method for practical purposes. Moreover, lack of heredity property in s-clubs imposes challenges in the design of optimization algorithms. Motivated by these properties, a sufficient condition for checking maximality, by inclusion, of a given s-club is proposed. The sufficient condition can be employed in the design of optimization algorithms to reduce the computational effort. A variable neighborhood search algorithm is proposed for the maximum s-club problem to facilitate the solution of large instances with reasonable computational effort. In addition, a hybrid exact algorithm has been developed for the problem. Inspired by wide usability of bipartite graphs in modeling and data mining, we consider three classes of the maximum biclique problem. Specifically, the maximum edge biclique, the maximum vertex biclique and the maximum balanced biclique problems are considered. Asymptotic lower and upper bounds on the size of these structures in uniform random graphs are developed. These bounds are insightful in understanding the evolution and growth rate of bicliques in large-scale graphs. To overcome the computational difficulty of solving large instances, a scale-reduction technique for the maximum vertex and maximum edge biclique problems, in general graphs, is proposed. The procedure shrinks the underlying network, by confirming and removing edges that cannot be in the optimal solution, thus enabling the exact solution methods to solve large-scale sparse instances to optimality. Also, a combinatorial branch-and-bound algorithm is developed that best suits to solve dense instances where scale-reduction method might be less effective. Proposed algorithms are flexible and, with small modifications, can solve the weighted versions of the problems.

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