Abstract:
In this thesis, we study a novel hierarchical wireless networking approach in which some of the nodes are more capable than others. In such networks, the more capable nodes can serve as Mobile Backbone Nodes and provide a backbone over which end-to-end communication can take place. The main design problem considered in this thesis is that of how to (i) Construct such Mobile Backbone Networks so as to optimize a network performance metric, and (ii) Maintain such networks under node mobility. In the first part of the thesis, our approach consists of controlling the mobility of the Mobile Backbone Nodes (MBNs) in order to maintain network connectivity for the Regular Nodes (RNs). We formulate this problem subject to minimizing the number of MBNs and refer to it as the Connected Disk Cover (CDC) problem. We show that it can be decomposed into the Geometric Disk Cover (GDC) problem and the Steiner Tree Problem with Minimum Number of Steiner Points (STP-MSP). We prove that if these subproblems are solved separately by y- and 5-approximation algorithms, the approximation ratio of the joint solution is y1+6. Then, we focus on the two subproblems and present a number of distributed approximation algorithms that maintain a solution to the GDC problem under mobility. A new approach to the solution of the STP-MSP is also described. We show that this approach can be extended in order to obtain a joint approximate solution to the CDC problem. Finally, we evaluate the performance of the algorithms via simulation and show that the proposed GDC algorithms perform very well under mobility and that the new approach for the joint solution can significantly reduce the number of Mobile Backbone Nodes.(cont.) In the second part of the thesis, we address the the joint problem of placing a fixed number K MBNs in the plane, and assigning each RN to exactly one MBN. In particular, we formulate and solve two problems under a general communications model. The first is the Maximum Fair Placement and Assignment (MFPA) problem in which the objective is to maximize the throughput of the minimum throughput RN. The second is the Maximum Throughput Placement and Assignment (MTPA) problem, in which the objective is to maximize the aggregate throughput of the RNs. Due to the change in model (e.g. fixed number of MBNs,general communications model) from the first part of the thesis, the problems of this part of the thesis require a significantly different approach and solution methodology. Our main result is a novel optimal polynomial time algorithm for the MFPA problem for fixed K. For a restricted version of the MTPA problem, we develop an optimal polynomial time algorithm for K < 2. We also develop two heuristic algorithms for both problems, including an approximation algorithm for which we bound the worst case performance loss. Finally, we present simulation results comparing the performance of the various algorithms developed in the paper. In the third part of the thesis, we consider the problem of placing the Mobile Backbone Nodes over a finite time horizon. In particular, we assume complete a-priori knowledge of each of the RNs' trajectories over a finite time interval, and consider the problem of determining the optimal MBN path over that time interval. We consider the path planning of a single MBN and aim to maximize the time-average system throughput. We also assume that the velocity of the MBN factors into the performance objective (e.g. as a constraint/penalty).(cont.) Our first approach is a discrete one, for which our main result is a dynamic programming based approximation algorithm for the path planning problem. We provide worst case analysis of the performance of the algorithm. Additionally, we develop an optimal algorithm for the 1-step velocity constrained path planning problem. Using this as a sub-routine, we develop a greedy heuristic algorithm for the overall path planning problem. Next, we approach the path-planning problem from a continuous perspective. We formulate the problem as an optimal control problem, and develop interesting insights into the structure of the optimal solution. Finally, we discuss extensions of the base discrete and continuous formulations and compare the various developed approaches via simulation.
Description:
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2007.; Includes bibliographical references (p. 181-189).