Parallel processing is prevalent in many manufacturing and service systems. Many manufactured products are built and assembled from several components fabricated in parallel lines. An example of this manufacturing system configuration is observed at a manufacturing facility equipped to assemble and test web servers. Characteristics of a typical web server assembly line are: multiple products, job circulation, and paralleling processing. The primary objective of this research was to develop analytical approximations to predict performance measures of manufacturing systems with job failures and parallel processing. The analytical formulations extend previous queueing models used in assembly manufacturing systems in that they can handle serial and different configurations of paralleling processing with multiple product classes, and job circulation due to random part failures. In addition, appropriate correction terms via regression analysis were added to the approximations in order to minimize the gap in the error between the analytical approximation and the simulation models. Markovian and general type manufacturing systems, with multiple product classes, job circulation due to failures, and fork and join systems to model parallel processing were studied. In the Markovian and general case, the approximations without correction terms performed quite well for one and two product problem instances. However, it was observed that the flow time error increased as the number of products and net traffic intensity increased. Therefore, correction terms for single and fork-join stations were developed via regression analysis to deal with more than two products. The numerical comparisons showed that the approximations perform remarkably well when the corrections factors were used in the approximations. In general, the average flow time error was reduced from 38.19% to 5.59% in the Markovian case, and from 26.39% to 7.23% in the general case. All the equations stated in the analytical formulations were implemented as a set of Matlab scripts. By using this set, operations managers of web server assembly lines, manufacturing or other service systems with similar characteristics can estimate different system performance measures, and make judicious decisions - especially setting delivery due dates, capacity planning, and bottleneck mitigation, among others.

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In a data streaming system, each component consumes one or several streams of data on the fly and produces one or several streams of data for other components. The entire Internet can be viewed as a giant data streaming system. Other examples include real-time exploratory data mining and high performance transaction processing. In this thesis we study several measurement and resource allocation optimization problems of data streaming systems. Measuring quantities associated with one or several data streams is often challenging because the sheer volume of data makes it impractical to store the streams in memory or ship them across the network. A data streaming algorithm processes a long stream of data in one pass using a small working memory (called a sketch). Estimation queries can then be answered from one or more such sketches. An important task is to analyze the performance guarantee of such algorithms. In this thesis we describe a tail bound problem that often occurs and present a technique for solving it using majorization and convex ordering theories. We present two algorithms that utilize our technique. The first is to store a large array of counters in DRAM while achieving the update speed of SRAM. The second is to detect global icebergs across distributed data streams. Resource allocation decisions are important for the performance of a data streaming system. The processing graph of a data streaming system forms a fork and join network. The underlying data processing tasks consists of a rich set of semantics that include synchronous and asynchronous data fork and data join. The different types of semantics and processing requirements introduce complex interdependence between various data streams within the network. We study the distributed resource allocation problem in such systems with the goal of achieving the maximum total utility of output streams. For networks with only synchronous fork and join semantics, we present several decentralized iterative algorithms using primal and dual based optimization techniques. For general networks with both synchronous and asynchronous fork and join semantics, we present a novel modeling framework to formulate the resource allocation problem, and present a shadow-queue based decentralized iterative algorithm to solve the resource allocation problem. We show that all the algorithms guarantee optimality and demonstrate through simulation that they can adapt quickly to dynamically changing environments.