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Queueing networks with blocking have proved useful in modeling stochastic service systems, such as computer and communication networks, manufacturing, traffic control, transportation, facility planning and many others. In this dissertation, we begin with studying the properties of a GI/G/1/N queue. We not only examine the characteristics of the queue length, busy periods, blocking probabilities, and transition probabilities between states, but also analyze properties of the general distributions. Based on the mathematical structures of the parameter space and solution space, a stochastic comparison method is utilized to classify the group of general distributions, and a diffusion process is utilized to approximate the blocking probability for a GI/G/1/N queue. The remainder of this dissertation is concerned with a generalized design methodology for open finite queueing networks. A hierarchical methodology is presented, in which large scale systems are divided into different subsystems, and dynamic programming is used to determine the decision variables, such as buffer size, for the systems with respect to the following two conflicting objectives: (1) Maximize average throughput; (2) Minimize processing cost. All theoretical results are tested by means of digital simulation and the different experiments are presented as an illustration of the proposed design methodology. Finally, open questions and directions for future research concludes the dissertation.

Master of Science / Department of Industrial & Manufacturing Systems Engineering / Todd W. Easton / Westside High School (WHS) of Omaha, Nebraska utilizes a novel scheduling system called Modular scheduling. This system offers numerous advantages over the standard school day in terms of student learning and faculty development. Modular Scheduling allows teachers to design the structure of their own classes by adjusting the frequency, duration and location of each of their daily lessons. Additionally, teachers are able combine their classes with those of other teachers and team-teach. Modular scheduling also allows for open periods in both students’ and teachers’ schedules. During this time, students are able to complete school work or seek supplemental instruction with a teacher who is also free. Teachers are able to use their open mods to plan, meet in teams and help students who have fallen behind. Currently, a semester’s class schedules are constructed over the course of a seven week period by a full-time employee using a computer program developed in FORTRAN®. The process is extremely tedious and labor intensive which has led to considerable wasted time, cost and frustration. This thesis presents a novel scheduling program called the SMART Scheduler that is able to do in seconds what previously took weeks to accomplish. Once parameters have been input, The SMART Scheduler is able to create cohesive class schedules within a modular environment in less than 6 seconds. The research presented describes the steps that were taken in developing the SMART Scheduler as well as computational results of its implementation using actual data provided by WHS. The goal of this research is to enable WHS and other schools to efficiently and effectively utilize modular scheduling to positively affect student learning.