Abstract. We study an online buffer management problem for networks supporting Quality-of-Service (QoS) applications. Packets with different QoS values arrive at a network switch and are to be sent along an outgoing link. Due to overloading conditions, some packets have to be dropped. The objective is to maximize the total value of packets that are sent. We formulate this as an online scheduling problem for unit-length jobs, where each job is specified by its release time, deadline, and a nonnegative weight (QoS value). The goal is to maximize the weighted throughput, that is the total weight of scheduled jobs. We first give a randomized algorithm RMix with competitive ratio of e/(e − 1) ≈ 1.582. This is the first algorithm for this problem with competitive ratio smaller than 2. Then we consider s-bounded instances where the span of each job (deadline minus release time) is at most s. We give a 1.25-competitive randomized algorithm for 2-bounded instances, matching the known lower bound. We give a deterministic algorithm Edfα, whose competitive ratio on s-bounded instances is at most 2 − 2/s + o(1/s). For 3-bounded instances its ratio is φ ≈ 1.618, matching the lower bound. Previously, an upper bound of φ was known for 2-bounded instances, and our work extends this result. Next, we consider 2-uniform instances, where the span of each job is exactly 2. We prove a lower bound of 4 − 2 √ 2 ≈ 1.172 for randomized algorithms. For deterministic memoryless algorithms, we prove a lower bound of √ 2 ≈ 1.414, matching a known upper bound. Finally, we consider the multiprocessor case and give an 1/(1 − ( M M+1)M)-competitive algorithm for M processors. We also show improved lower bounds for the general and 2-uniform cases. 1

We study the problem of scheduling a set of preemptive tasks, where each task j is specified by its release time r j , deadline d j , processing time p j , and weight w j representing its profit rate.

This thesis describes a web-based, responsive, zooming and panning visualization system for a full-featured geographic description of the United States. Current web-based map servers provide, from a visualization standpoint, little more than one static image per page, with hyperlinks for navigation; continuous zooming and panning requires locally stored data. Our primary contribution is a multi-threaded, scalable and responsive client-server architecture that responds to user requests as naturally and quickly as possible, regardless of network bandwidth reliability. This architecture can be generalized for use in other applications, including non-geographic ones. To this we add a scalable and exible user interface for navigation of multi-scale geographic data, with intuitive zooming and panning, pop-up feature labels, and a user controlled tree-hierarchy of windows. We build software tools and algorithms for translating the U.S. Census Bureau's TIGER data into a format designed for speedy database retrieval and network delivery, and for generalizing the data into multiple levels of detail. Because of anomalies in the TIGER data, this processing requires some human intervention. v vi Contents Acknowledgments iii Abstract v List of Figures xi List of Tables xiii 1

This thesis describes a web-based, responsive, zooming and panning visualization system for a full-featured geographic description of the United States. Current web-based map servers provide, from a visualization standpoint, little more than one static image per page, with hyperlinks for navigation; continuous zooming and panning requires locally stored data. Our primary contribution is a multi-threaded, scalable and responsive client-server architecture that responds to user requests as naturally and quickly as possible, regardless of network bandwidth reliability. This architecture can be generalized for use in other applications, including non-geographic ones. To this we add a scalable and flexible user interface for navigation of multi-scale geographic data, with intuitive zooming and panning, pop-up feature labels, and a user controlled tree-hierarchy of windows. We build software tools and algorithms for translating the U.S. Census Bureau’s TIGER data into a format designed for speedy database retrieval and network delivery, and for generalizing the data into multiple levels of detail. Because of anomalies in the TIGER data, this processing requires some human intervention.