Modeling and analysis of stochastic networks with shared resources.

Traditional network models have played an important role over the last four decades in providing insight in the dynamics of telecommunication, computer and manufacturing systems. At the core of database management systems, high speed packet switching architectures, online computing, web server architectures, etc., one can find the fundamental features of Parallel and Distributed Processing (PDP) systems. The goal of the research presented here is to study the dynamics of PDP systems with shared resources and the various optimization issues arising with their dynamical behavior. This would allow one to construct efficient real-time operational schemes which can optimize the systems with respect to various performance metrics, such as throughput, job delays and backlogs, load balancing, reliability, etc. The main result of this thesis is divided into two parts. In the first part, two general models that capture the basic features of many real life systems are introduced. In addition, a class of dynamic control policies are introduced and shown to maximize the throughput capacity of the proposed models under weak stochastic assumptions. In the second part, the delay performance of several control policies are examined and compared via a simulation study. It is noted that simulations of large systems are expensive both in terms of CPU time and of time required to write the usually custom-made computer code. In order to adequately capture the underlying response surface of interest using the smallest possible number of simulation runs, a general methodological framework is introduced, with a demonstration of a few examples. It is noted that the proposed flexible methodology borrows the ideas from the field of experimental design, and, it outperforms the multivariate adaptive regression splines (MARS) approach in prediction.PhDApplied SciencesOperations researchPure SciencesStatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/123328/2/3075405.pd