Estuaries are some of the most productive yet threatened ecosystems in the world. Despite their importance they face significant threats through changes to river flow, eutrophication, rapid population growth long the caost and harvesting of natural resources. A number of international studies have been conducted investigating the structure and functioning of an array of ecosystems using ecological network analysis. Energy flow networks have been contsructed for coastal, lagoonal, intertidial and, most notably, permantently open estuaries. Despite the valualble insights contributed by these and other studies, a lack of information on the majority of estuarine ecosystems exists.

This dissertation focuses on the performance analysis of multiclass open queueing networks using semi-martingale reflecting Brownian motion (SRBM) approximation. It consists of four parts. In the first part, we derive a strong approximation for a multiclass feedforward queueing network, where jobs after service completion can only move to a downstream service station. Job classes are partitioned into groups. Within a group, jobs are served in the order of arrival; that is, a first-in-first-out (FIFO) discipline is in force, and among groups, jobs are served under a pre-assigned preemptive priority discipline. We obtain an SRBM as the result of strong approximation for the network, through an inductive approach. Based on the strong approximation, some procedures are proposed to approximate the stationary distribution of various performance measures of the queueing network. Our work extends and complements the previous work done on the feedforward queueing network. The numeric examples show that the strong approximation provides a better approximation than that suggested by a straightforward interpretation of the heavy traffic limit theorem. In the second part, we develop a Brownian approximation for a general multiclass queueing network with a set of single-server stations that operate under a combination of FIFO (first-in-first-out) and priority service disciplines and are subject to random breakdowns. Our intention here is to illustrate how to approximate a queueing network by an SRBM, not to justify such approximation. We illustrate through numerical examples in comparison against simulation that the SRBM model, while not always supported by a heavy traffic limit theorem, possesses good accuracy in most cases, even when the systems are moderately loaded. Through analyzing special networks, we also discuss the existence of the SRBM approximation in relation to the stability and the heavy traffic limits of the networks. In most queueing network applications, the stationary distributions of queueing networks are of great interest. It becomes natural to approximate these stationary distributions by the stationary distributions of the approximating SRBMs. Although we are able to characterize the stationary distribution of an SRBM, except in few limited cases, it is extremely difficult to obtain the stationary distribution analytically. In the third part of the dissertation, we propose a numerical algorithm, referred to as BNA/FM (Brownian network analyzer with finite element method), for computing the stationary distribution of an SRBM in a hypercube. SRBM in a hypercube serves as an approximate model of queueing networks with finite buffers. Our BNA/FM algorithm is based on finite element method and an extension of a generic algorithm developed in the previous work. It uses piecewise polynomials to form an approximate subspace of an infinite dimensional functional space. The BNA/FM algorithm is shown to produce good estimates for stationary probabilities, in addition to stationary moments. This is in contrast to the BNA/SM (Brownian network analyzer with spectral method) developed in the previous work, where global polynomials are used to form the approximate subspace and they sometime fail to produce meaningful estimates of these stationary probabilities. We also report extensive computational experiences from our implementation that will be useful for future numerical research on SRBMs. A three-station tandem network with finite buffers is presented to illustrate the effectiveness of the Brownian approximation model and our BNA/FM algorithm. In the last part of the dissertation, we extend the BNA/FM algorithm to calculate the stationary distribution of an SRBM in an orthant. This type of SRBM arises as a Brownian approximation model for queueing networks with infinite buffers. We prove the convergence theorems which justify the extension. A three-machine job shop example is presented to illustrate the accuracy of our extended BNA/FM algorithm. In fact, this extended algorithm is also used in the first two parts of this dissertation to analyze the performance of several queueing network examples and it gives fairly good performance estimates in most cases. / Business, Sauder School of / Graduate

No description available.

The maintenance and supply system of the Atlantic Missile Range Communications Network (AMRCN) is modeled to determine the optimum level of men and parts which must be available at Cape Kennedy, the source of supply, in order to minimize the level of failed equipment at the four remote sites. The system is simulated utilizing a DYNAMO model. DYNAMO is a compiler for translating and running continuous models (models described by a set of differential equations). Flow diagrams of the breakdowns, men, and parts and the information flow between these segments of the model are presented. The results obtained are discussed and the optimal solution noted.

In this paper we study properties of a queue with instantaneous Bernoulli feedback where the service discipline is one of two symmetric disciplines. For the processor sharing queue with exponentially distributed service requirements we analyze the departure process, imbedded queue lengths, and the input and output processes. We determine the semi-Markov kernel of the internal flow processes and compute their stationary interval distributions and forward recurrence time distributions. For generally distributed service times, we analyze the output process using a continuous state Markov process. We compare the case where service times are exponentially distributed to the case where they are generally distributed. For the infinite server queue with feedback, we show that the output process is never renewal when the feedback probability is non-zero. We compute the time until the next output in three special cases. / Ph. D.

Thesis (PhD)--University of Stellenbosch, 2004. / ENGLISH ABSTRACT: Please refer to full text for abstract.

published_or_final_version / Civil Engineering / Doctoral / Doctor of Philosophy

Understanding of a global biological network structure by studying its simple local properties through the well-developed field of graph theory is of interest. In particular, in this research an observed biological network was explored through a simulation study. However, one difficulty in such exploration lies on the fitting of graphical models on biological network data. An Exponential Random Graph Model (ERGM) was considered to determine estimations of the several network attributes of complex biological network data. We also compared the estimates of observed network to our random simulated network for both Markov Chain Monte Carlo Maximum Likelihood Estimation (MCMCMLE) and Maximum Pseudo Likelihood Estimation (MPLE) methods under ERGM. The motivation behind this was to determine how different the observed network could be from a randomly simulated network if the physical numbers of attributes were approximately same. Cut-off points of some common attributes of interest for different order of nodes were determined through simulations. We implemented our method to a known regulatory network database of E. coli. / Department of Mathematical Sciences

Doctorat en Sciences / info:eu-repo/semantics/nonPublished

Thesis. 1975. Ph.D.--Massachusetts Institute of Technology. Dept. of Civil Engineering. / Bibliography: leaves 221-224. / Ph.D.