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• W2520032020 abstract "In this thesis, we have studied a variety of optimal set partition problems that arise in communication networks. Based on the results of these studies, novel algorithms are proposed and evaluated to solve the underlying problems. In Chapter 1, the classical optimal sequential paging scheme, which minimizes the average paging cost to find the location of a mobile user in a cellular network is presented and an efficient algorithm is proposed to solve the associated optimal set partition problem. In addition, the first known bound of the reduction of average paging cost is derived. The bound is independent of the probabilistic information about the location of a mobile user and therefore is applicable in all cases. In Chapter 2, concurrent paging schemes in cellular networks are proposed to further reduce the average paging delay and these schemes are evaluated. Unlike the optimal sequential paging scheme in Chapter 1 that searches for mobile users one by one, concurrent paging schemes look for multiple mobile users simultaneously whenever possible. We study concurrent paging schemes from the viewpoint of queueing theory, but do not make any assumptions on the arrival process or the distribution of the service time. Novel scheduling algorithms based on controlled out-of-order service are proposed to improve average delay without increasing delay of any mobile user or increasing paging cost. Specifically, according to our simulations, one of the above scheduling algorithms is able to support up to ten times higher traffic load. Furthermore, the scheduling algorithm requires low computational complexity and therefore is feasible in practice. In Chapter 3, multicast flow control schemes that are applicable in, but not limited to, the Internet are analyzed. The multicast flow control problem is formulated as the list partition problem, in which receivers are optimally partitioned into multiple subgroups. The notion of normalized throughput is introduced to study the impact of receiver capacities on the system throughput. It is proved that the optimal sequential paging problem is a special case of the list partition problem. Based on the result, it is shown that when two subgroups are formed, the limit of the normalized throughput is always nonzero. This is in spite of the fact that when a single subgroup is used, the normalized throughput approaches zero as the total number of receivers increase. Our results provide a quantitative and analytical support to the usage of multiple subgroups in the multicast flow control schemes. Chapter 4 extends the work presented in Chapter 3. A multicast flow control problem in which the throughput is dominated by both the receiver with the largest round trip time and the receiver with the smallest buffer size is studied. In this case, the multicast flow control problem is formulated as a two-dimensional set partition problem. It is proved that when the round trip times and the buffer sizes are correlated, the two-dimensional set partition problem becomes the list partition problem and therefore is polynomial solvable. For a general case, there are no known polynomial-time algorithms to solve the problem and therefore upper bounds and lower bounds of the throughput are derived." @default.
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• W2520032020 date "2001-01-01" @default.
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• W2520032020 title "Optimal set partition problems in communication networks" @default.
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