Computing the reliability of a network is a #P-complete problem, therefore estimation by means of simulation often becomes a favourable choice. In modern communication networks, link failure probabilities are usually small and hence network failures become rare events. This poses a challenge to estimate the network reliability. In this thesis we present different techniques for network reliability estimation. There are two main sampling techniques in reliability estimation: combinatorial and permutational sampling. Combinatorial sampling has the advantage of speed but has poor performance in rare event simulations. Permutational sampling gives good simulation performance but at a higher computational cost. We combine the two techniques and propose a hybrid sampling scheme called Tree Cut and Merge. By employing simple bounding together with clever conditional sampling, the TCM scheme achieves over 10(superscript 7) times speed up in certain classes of heterogeneous networks. The Crude Monte Carlo (combinatorial) component in the Tree Cut and Merge scheme may cause problems in some situations. In bad cases, the slow convergence problem re-appears. To address the problem, we modifed the scheme by introducing the Importance Sampling technique. The new Tree Cut and Merge with Importance Sampling scheme maintained the speed advantage of the Tree Cut and Merge and minimizes, at the same time, the potential problems caused by the Crude Monte Carlo component. Associated with the Importance Sampling technique, a new technique called the Cross-Entropy method has been developed in the late 90's to find the optimal Importance Sampling parameters. By employing the Cross-Entropy technique, we propose a new scheme called the Merge Process with Cross-Entropy. The new scheme improves the Merge Process in nearly all classes of network; in contrast, Tree Cut and Merge with Importance Sampling scheme sees the greatest improvement in heterogeneous networks. Besides estimating the reliability of a single network, this thesis also investigates a closely related problem: estimating the difference in reliability of two very similar networks. The problem is closely linked to the applications in the areas of network optimization, network evolution, reconfiguration and recovery, for example. The fact that the probabilities of rare events are hard to estimate makes estimating their difference even more difficult. Coupled and differential sampling techniques are proposed and applied to various schemes in this thesis. They prove to be superior to the conventional independent "estimate and subtract" method. Interestingly, these concepts also lead to new ideas regarding the estimation of the reliability of networks that are similar to networks with polynomially computable reliability. / Thesis (Ph.D.)--School of Mathematical Sciences, 2005.

This thesis presents a new forecasting technique that estimates energy demand by applying a Bayesian approach to forecasting. We introduce our Bayesian Heating Oil Forecaster (BHOF), which forecasts daily heating oil demand for individual customers who are enrolled in an automatic delivery service provided by a heating oil sales and distribution company. The existing forecasting method is based on linear regression, and its performance diminishes for new customers who lack historical delivery data. Bayesian methods, on the other hand, respond effectively in the start-up situation where no prior data history is available. / Our Bayesian Heating Oil Forecaster uses forecasters' past performances for existing customers to adjust the current forecast for target customers. We adapted a Bayesian approach to forecasting combined with domain knowledge and original ideas to develop our Bayesian Heating Oil Forecaster, which forecasts demand for target customers without relying on their historical deliveries. / Performance evaluation demonstrates that our Bayesian Heating Oil Forecaster shows increased performance over the existing forecasting method when the two techniques are combined. We used Root Mean Squared Error (RMSE) and Mean Absolute Percent Error (MAPE) to compare the performance of the two algorithms. Compared to the existing forecasting method alone, our Simple Average model, which combines the forecasts from the existing forecasting method and our Bayesian Heating Oil Forecaster, recorded an overall improvement of 2.4% in RMSE, 5.0% in MAPE Actual, and 2.8% in MAPE Capacity for company A and 0.3%, 7.1%, and 2.8% for company B.

The current Record of Study presents the qualitative and quantitative analysis of a company's network of distribution centers with the purpose of determining the convenience and the feasibility to reconfigure such a network. The study was performed with a multidisciplinary team of people within and outside of the organization. The distribution network was modeled in various forms and different solutions were obtained as new information was gathered from questionnaires, from observation and from the company's databases. Finally a recommendation was formulated to modify the current configuration of the distribution network and the feasibility to implement the suggested solution in practice was evaluated.

<p>The connection between elliptic stochastic diffusion processes and partial differential equations is rich and well understood. This connection is not very well understood when the stochastic differential equation takes values in an infinite dimensional space such as a function space. In this case, the diffusion is a stochastic partial differential equation (SPDE) and the notion of ellipticity is ambiguous. We establish a sufficient condition on the diffusion coefficient of a class of nonlinear SPDEs, which is analogous to the nondegeneracy condition in finite dimensions, that allows for the existence of a Markov transition density that is absolutely continuous with respect to an infinite dimensional Gaussian measure.</p><p>In the second part of this work, we consider a two-station queueing network that processes <italic>K</italic> job types. The first station in this network is a polling station, and we assume that the second station is operating under any nonidling service discipline. We consider diffusion-scaled versions of many of the processes governing this system, and we show that the scaled two-dimensional <italic>total</italic> workload process converges to Brownian motion in a wedge. We also show that the scaled immediate workload process for station 2 does not converge, but admits an averaging principle.</p> / Dissertation

The current Record of Study presents the qualitative and quantitative analysis of a company's network of distribution centers with the purpose of determining the convenience and the feasibility to reconfigure such a network. The study was performed with a multidisciplinary team of people within and outside of the organization. The distribution network was modeled in various forms and different solutions were obtained as new information was gathered from questionnaires, from observation and from the company's databases. Finally a recommendation was formulated to modify the current configuration of the distribution network and the feasibility to implement the suggested solution in practice was evaluated.

Thesis (M.S. in Operations Research)--Naval Postgraduate School, September 1990. / Thesis Advisor(s): Lawphongpanich, Siriphong. Second Reader: Block, Paul. "September 1990." Description based on title screen as viewed on December 22, 2009. DTIC Descriptor(s): Maintenance, Stations, Deployment, United States, Optimization, Environments, Peacetime, Models, Training, Naval Personnel, Integer Programming, Algebra, Efficiency, Cycles, Supply Depots, Aircraft Carriers, Naval Operations, Mixing, Microcomputers, Budgets, Mathematical Models. DTIC Identifier(s): Aircraft Carriers, Deployment, Theses, Military Forces(United States), Computer programs, Computerized Simulation, Maintenance, Naval Personnel. Author(s) subject terms:Carrier, Optimization, Deployment Model. Includes bibliographical references (p. 63). Also available in print.

Thesis (Ph. D.)--Rutgers University, 2008. / "Graduate Program in Operations Research." Includes bibliographical references (p. 419-435).

Thesis (M.S.)--Naval Postgraduate School, 2002. / Thesis advisor(s): David Olwell, Samuel E. Buttrey. Includes bibliographical references (p. 79). Also available online.

Thesis (Ph.D.) -- University of Texas at Arlington, 2008.

Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2009. / Source: Dissertation Abstracts International, Volume: 70-06, Section: B, page: 3718. Adviser: Srinivasa M. Salapaka. Includes bibliographical references (leaves 144-148) Available on microfilm from Pro Quest Information and Learning.