We study the large deviation behaviour of simple random walks in dimension three or more in this thesis. The first part of the thesis concerns the number of lattice sites visited by the random walk. We call this the range of the random walk. We derive a large deviation principle for the probability that the range of simple random walk deviates from its mean. Our result describes the behaviour for deviation below the typical value. This is a result analogous to that obtained by van den Berg, Bolthausen, and den Hollander for the volume of the Wiener sausage. In the second part of the thesis, we are interested in the number of lattice sites visited by two independent simple random walks starting at the origin. We call this the intersection of ranges. We derive a large deviation principle for the probability that the intersection of ranges by time n exceeds a multiple of n. This is also an analogous result of the intersection volume of two independent Wiener sausages.

Master of Science / Department of Civil Engineering / Sunanda Dissanayake / Kansas experienced about 60,000 crashes annually from 2013 to 2016, 25% of which occurred at urban intersections. Hence, urban intersections in Kansas are one of the most critical locations in terms of frequency of crashes. Therefore, an accurate prediction of crashes at these locations would help identify critical intersections with a higher probability of an occurrence of crash, which would help in selecting appropriate countermeasures to reduce those crashes. The crash prediction models provided in the Highway Safety Manual (HSM) predict crashes using traffic and geometric data for various roadway facilities, which are incorporated through Safety Performance Functions (SPFs) and Crash Modification Factors. The primary objective of this study was to estimate calibration factors for different types of urban intersection in Kansas. This study followed the crash prediction method and calibration procedure provided in the HSM to estimate calibration factors for four different urban intersection types in Kansas: 3-leg unsignalized intersections with stop control on the minor approach (3ST), 3-leg signalized intersections (3SG), 4-leg unsignalized intersections with stop control on the minor approach (4ST), and 4-leg signalized intersections (4SG). Following the HSM methodology, the required data elements were collected from various sources. The Annual Average Daily Traffic (AADT) data were extracted from Kansas Crash Analysis & Reporting System (KCARS) database and GIS Shapefiles downloaded from Federal Highway Administration website. For some of 3ST and 3SG intersections, minor-street AADT was not available. Hence, multiple linear regression models were developed for the estimation of minor-street AADT. Crash data were extracted from the Kansas Crash Analysis and Reporting System database, and other geometric data were extracted using Google Earth. The HSM requirement for sample size is 30 to 50 sites, with at least 100 crashes per year for the study period for the combined set of sites. In this study, the study period for 3ST, 3SG, and 4SG intersections were taken as 2013 to 2015, and 2014 to 2016 for 4ST, based on the availability of recent crash data at the beginning of the calibration procedure for each facility type. The sample size considered for calibration was 234 for 3ST, 89 for 3SG, 167 for 4ST, and 198 for 4SG intersections. Out of the 234 3ST intersections, minor-street AADT was estimated using multiple linear regression models for 106 intersections. For 3SG intersections, minor-street AADT was estimated for 21 out of the 89 intersections. The calibration factors for these facility types were estimated to be 0.64 for 3SG, 0.51 for 3ST, 1.17 for 4SG, and 0.61 for 4ST when considering crashes of all severities. Considering only the fatal and injury crashes, the calibration factors were estimated as 0.52 for 3SG, 0.40 for 3ST, 2.00 for 4SG, and 0.73 for 4ST. The calibration factors show that the HSM methodology underpredicted crashes for 4SG, and overpredicted crashes for other three intersection types. The reliability of the calibration factors was assessed with the help of Cumulative Residual plots and coefficient of variation. The results from the goodness-of-fit tests showed that the calibration factors were not reliable and showed bias in the prediction of crashes. Hence, calibration functions were developed, and their reliability were examined. The results showed that calibration functions had better reliability as compared to calibration factors, with more accuracy in crash prediction. The findings from this study can be used to identify intersections with a higher probability of having crashes in the future. Suitable countermeasures can be applied at critical locations which would help reduce the number of crashes at urban intersections in Kansas; thus increasing the safety.

Este trabalho avalia a influência de veículos de grande porte na capacidade de interseções rodoviárias em nível não semaforizadas, verificando as variações no comportamento de caminhões e ônibus durante manobras de cruzamento, em função de seu comprimento e de sua relação potência/peso. Foram realizadas análises das distribuições dos tempos de cruzamento e da aceitação de \"gaps\" por diferentes tipos de veículos, sendo utilizados modelos Logit para representar o comportamento desses veículos nos cruzamentos. Estes modelos serviram como base na elaboração de um simulador, para determinar a capacidade potencial das interseções e para calcular os fatores de conversão de veículos de grande porte em veículos de passageiro. / This study assesses the influence of heavy vehicles on the capacity of unsignalized rural intersections. This is done through the study of vehicle behavior during crossing maneuvers that can be attributed to length and power-to-weight ratio. Crossing time distributions and gap acceptance of diferent types of vehicles were analysed, and Logit models were used to represent their behavior. These models and a simulation model were used to determine the potencial capacity of intersections and to calculate factors to convert heavy vehicles into passenger vehicles.

Communication networks are vulnerable to natural as well as man-made disasters. The geographical layout of the network influences the impact of these disasters. It is therefore, necessary to identify areas that could be most affected by a disaster and redesign those parts of the network so that the impact of a disaster has least effect on them. In this work, we assume that disasters which have a circular impact on the network. The work presents two new algorithms, namely the WHF-PG algorithm and the WHF-NPG algorithm, designed to solve the problem of finding the locations of disasters that would have the maximum disruptive effect on the communication infrastructure in terms of capacity.

The problem of dilemma zone protection and red-light-running is especially important in certain rural intersections due to the higher speeds at these intersections and their isolated nature. In addition, the presence of a larger percentage of trucks mean that adequate warning and help need to be given to these truck drivers in order to enable them to stop safely, or proceed through the intersection before the onset of red. To curb any potential danger at such intersections, a Texas Department of Transportation (TxDOT) research project on Advanced Warning for End of Green Phase (AWEGS) at high speed intersections deployed AWEGS at two rural intersection sites ?? Tx 6 @ FM 185 near Waco and US 290 @ FM 577 in Brenham. The deployment of AWEGS involved a Level 1 and a later upgrade to a more efficient Level 2 in Waco. Initial results on red-light-running, even though promising, were expressed as observed red-light-running events per day. These resulting rates did not reflect exposure, and the results also raised some concerns with regards to some increase in red-light-running from Level 1 to Level 2. A more detailed analysis of the red-light-running issue at these two sites is provided in this thesis. The main areas of red-light-running analyses presented here are with respect to the reductions in red-light-running rates for the exposure factors of number of cycles and vehicular volumes, the comparison of day and night RLR rates and the nature of speeds of vehicles running the red light at the intersection in Waco. AWEGS was found to reduce the total red-light-running per exposure factor after its deployment. Both Level 1 and Level 2 AWEGS operations were found to reduce red-light-running by up to 60%. Generally, total red-light-running per exposure factor between Level 1 and Level 2 was found to be about the same. Level 2 had lower daytime red-light-running rates and higher nighttime rates than Level 1. Generally, day rates were found to be higher than night rates for all levels of AWEGS deployment. It is recommended that, to better understand the operational aspects of AWEGS and to improve its operations, more implementation of AWEGS and further tests be done. An automated method to collect and analyze data needs to be developed as well as a means of automatically recording video data for calibration and verification It is also recommended that Level 1 technology be implemented in areas where the Level 2 technology may be either too complex or too expensive.

There is increased interest in building modern roundabouts in Georgia and in the United States because of the safety and operational benefits that can be realized from this type of intersection. With this interest comes the increasing need to be able to estimate the capacity that a roundabout can provide after it is built. In the early 2000s, a National Cooperative Highway Research Program (NCHRP) study was conducted that, among other tasks, developed single-lane and multi-lane roundabout capacity estimation equations. These equations, presented in the Highway Capacity Manual 2010 (HCM 2010), can be calibrated using locally determined values of follow-up headway and critical headway. This study was designed to calibrate the HCM 2010 roundabout capacity equation for single-lane roundabouts to driving conditions in Georgia. In order to develop estimates of the calibration parameters, video imagery was recorded for 13 approaches at six roundabouts in Georgia for approximately two hours during the peak period. A total of 29.5 hours of video was recorded. Data from three of these roundabouts forms the basis of this thesis. The videos were processed by a Java program to collect time stamps that were subsequently used in Microsoft Excel to calculate the follow-up and critical headway values required for calibration. The values of critical headway and follow-up headway that were found from the video data are presented in the results as well as the single-lane capacity equations calibrated from the data. Two types of analysis were done, one that includes exiting vehicles and one that does not include exiting vehicles. When exiting vehicles were excluded, the weighted average of follow-up and critical headway were found to be 3.46 and 4.17 seconds respectively and when exiting vehicles were included in the analysis the weighted averages of the follow-up and critical headway were found to be 2.80 seconds and 3.34 seconds respectively. It was found that exiting vehicles do have an impact on the operations at the roundabout in most cases, and including exiting vehicles in the analysis tends to increase the capacity predicted by the calibrated equations.

This ethno-historical undertaking captures the story of the implementation of one major US city's first and only single-sex public school and the consequent shaping of the school culture according to its unique context. A comprehensive literature review demonstrates race, socioeconomic status, gender, sexuality, and other contextual factors are important considerations when probing educational access and achievement and the development of school cultures. Moreover, principals -- their individual attributes and the cultures they create -- are key to understanding and interrogating equitable practices in schools. Findings substantiate the complex interface between historical, political, and socio-cultural contexts, stakeholder decision making in the ethnographic present, and the enactment and negotiation school culture vis-à-vis the intersectionalities of student identities. Findings suggest the conditions that facilitated the high achievement of the students in this study might be transferred under the right conditions including: a balance of strong leadership and principal and teacher autonomy; the enduring belief that any student can and will learn; a rigorous, non-segregated, college prep program, and; an informal curriculum that prepares students for academic and professional cultures. Findings also bring to the fore important considerations that must be addressed by practitioners and policymakers alike; specifically, students' difficulties concerning the "burden of acting white" and the "burden of acting straight." Finally, findings from this study suggest single-sex public options can be done legitimately and effectively but additional safeguards must be implemented by the US Department of Education to ensure both male and female students' civil rights are protected. Additionally, while some magnet schools such as the one studied are local sites of resistance that play a liberatory role for those distinctively involved, one cannot surmise that such local efforts -- which may be viewed by some as a site of relative privilege -- can alone overcome the serious striations that exist in the greater society. / text

The purpose of this research is to develop an intersection safety evaluation tool that is capable of assisting designers and planners in the assessment of alternative intersection designs. A conflict exposure model utilizing design hour volumes, intersection configuration and traffic control measures is proposed to achieve this goal. This approach makes use of data typically available for preliminary intersection design. The research goes beyond existing safety performance models which only examine non-directional average daily traffic (ADT) or practices which only account for the geometric and lane configuration of an intersection, such as conflict point analysis. Conflict prediction models are developed for left-turn angle, right-turn, rear end and sideswipe crashes. These models were developed through the analysis of over 1000 simulation scenarios evaluating a full range of approach and turning volumes, lane configurations and traffic control strategies. The quantifiable metrics provided can be used to inform and improve alternative intersection selection processes by differentiating between alternatives based on a surrogate safety performance. This research may be used in screening of intersection alternatives to select the most beneficial design based on objective safety performance metrics.

We design an Ordinary Delay Differential Equation model for car to car interaction with switching between four distinct force terms including "free acceleration'', "follow acceleration'', "follow braking'', and aggressive driving''. We calibrate this model by recreating a real experiment on spontaneous formation of traffic jams. Once simulations of our model match those of the experiment we develop a model of both intersections using traffic lights, and intersections using roundabouts. Using our calibrated car interaction model we compare traffic light versus roundabout efficiencies in both flux and fuel consumption. We also use simulation results to extract information relevant to macroscopic traffic models. A relationship between flux and density known as The Fundamental Diagram is derived, and we discuss a technique for comparing microscopic to macroscopic models. / Graduate / 0405 / gmcgrego@uvic.ca

Intersection crashes accounted for 47 percent of the total number of crashes in the State of Georgia from 2000-2005, and as a location where crashes occur, represent the largest number of crash locations in the state. Federal legislation requires states to implement statewide safety plans to reduce fatalities, crashes, and improve safety. Intersections vary in different ways and there are individual factors that can cause an intersection to be safer or more dangerous than another. Acquiring better, uniform, and more updated information with regard to intersection crashes will enable transportation officials to prescribe policies for improving safety in an easier and more expedited manner. This thesis recommends a five-part program for intersection safety that will enable Georgia transportation officials to better analyze, identify, and implement countermeasures at intersections that are determined to be the most hazardous. The plan consists of: 1. Standardized Hazardous Intersection Identification Method 2. Statewide Public Involvement task force 3. Automated Police Crash Reporting Through Improved Technologies 4. Strategic Highway Safety Plan (SHSP) Intersection Safety Strategies (8 State Comparison) 5. Statewide Minimal Intersection Safety Equipment The five parts of this plan lead to a statewide standard method of analyzing intersections based on uniform collection methods and uniform equipment statewide.