A Fire Fighter's Problem

Suppose that a circular fire spreads in the plane at unit speed. A single fire fighter can build a barrier at speed $v>1$. How large must $v$ be to ensure that the fire can be contained, and how should the fire fighter proceed? We contribute two results. First, we analyze the natural curve \mbox{FF}_v that develops when the fighter keeps building, at speed $v$, a barrier along the boundary of the expanding fire. We prove that the behavior of this spiralling curve is governed by a complex function $(e^{w Z} - s \, Z)^{-1}$, where $w$ and $s$ are real functions of $v$. For $v>v_c=2.6144 \ldots$ all zeroes are complex conjugate pairs. If $\phi$ denotes the complex argument of the conjugate pair nearest to the origin then, by residue calculus, the fire fighter needs $\Theta( 1/\phi)$ rounds before the fire is contained. As $v$ decreases towards $v_c$ these two zeroes merge into a real one, so that argument $\phi$ goes to~0. Thus, curve \mbox{FF}_v does not contain the fire if the fighter moves at speed $v=v_c$. (That speed $v>v_c$ is sufficient for containing the fire has been proposed before by Bressan et al. [7], who constructed a sequence of logarithmic spiral segments that stay strictly away from the fire.) Second, we show that any curve that visits the four coordinate half-axes in cyclic order, and in inreasing distances from the origin, needs speed $v>1.618\ldots$, the golden ratio, in order to contain the fire. Keywords: Motion Planning, Dynamic Environments, Spiralling strategies, Lower and upper boundsComment: A preliminary version of the paper was presented at SoCG 201

DISPATCHING AND RELOCATION OF EMERGENCY VEHICLES ON FREEWAYS: THEORIES AND APPLICATIONS

Resource allocation decisions are made to serve the current emergency without knowing which future emergency will be occurring. Different ordered combinations of emergencies result in different performance outcomes. Even though future decisions can be anticipated with scenarios, previous models follow an assumption that events over a time interval are independent. This dissertation follows an assumption that events are interdependent, because speed reduction and rubbernecking due to an initial incident provoke secondary incidents. The misconception that secondary incidents are not common has resulted in overlooking a look-ahead concept. This dissertation is a pioneer in relaxing the structural assumptions of independency during the assignment of emergency vehicles. When an emergency is detected and a request arrives, an appropriate emergency vehicle is immediately dispatched. We provide tools for quantifying impacts based on fundamentals of incident occurrences through identification, prediction, and interpretation of secondary incidents. A proposed online dispatching model minimizes the cost of moving the next emergency unit, while making the response as close to optimal as possible. Using the look-ahead concept, the online model flexibly re-computes the solution, basing future decisions on present requests. We introduce various online dispatching strategies with visualization of the algorithms, and provide insights on their differences in behavior and solution quality. The experimental evidence indicates that the algorithm works well in practice. After having served a designated request, the available and/or remaining vehicles are relocated to a new base for the next emergency. System costs will be excessive if delay regarding dispatching decisions is ignored when relocating response units. This dissertation presents an integrated method with a principle of beginning with a location phase to manage initial incidents and progressing through a dispatching phase to manage the stochastic occurrence of next incidents. Previous studies used the frequency of independent incidents and ignored scenarios in which two incidents occurred within proximal regions and intervals. The proposed analytical model relaxes the structural assumptions of Poisson process (independent increments) and incorporates evolution of primary and secondary incident probabilities over time. The mathematical model overcomes several limiting assumptions of the previous models, such as no waiting-time, returning rule to original depot, and fixed depot. The temporal locations flexible with look-ahead are compared with current practice that locates units in depots based on Poisson theory. A linearization of the formulation is presented and an efficient heuristic algorithm is implemented to deal with a large-scale problem in real-time

Exploration of smart infrastructure for drivers of autonomous vehicles

The connection between vehicles and infrastructure is an integral part of providing autonomous vehicles information about the environment. Autonomous vehicles need to be safe and users need to trust their driving decision. When smart infrastructure information is integrated into the vehicle, the driver needs to be informed in an understandable manner what the smart infrastructure detected. Nevertheless, interactions that benefit from smart infrastructure have not been the focus of research, leading to knowledge gaps in the integration of smart infrastructure information in the vehicle. For example, it is unclear, how the information from two complex systems can be presented, and if decisions are made, how these can be explained. Enriching the data of vehicles with information from the infrastructure opens unexplored opportunities. Smart infrastructure provides vehicles with information to predict traffic flow and traffic events. Additionally, it has information about traffic events in several kilometers distance and thus enables a look ahead on a traffic situation, which is not in the immediate view of drivers. We argue that this smart infrastructure information can be used to enhance the driving experience. To achieve this, we explore designing novel interactions, providing warnings and visualizations about information that is out of the view of the driver, and offering explanations for the cause of changed driving behavior of the vehicle. This thesis focuses on exploring the possibilities of smart infrastructure information with a focus on the highway. The first part establishes a design space for 3D in-car augmented reality applications that profit from smart infrastructure information. Through the input of two focus groups and a literature review, use cases are investigated that can be introduced in the vehicle's interaction interface which, among others, rely on environment information. From those, a design space that can be used to design novel in-car applications is derived. The second part explores out-of-view visualizations before and during take over requests to increase situation awareness. With three studies, different visualizations for out-of-view information are implemented in 2D, stereoscopic 3D, and augmented reality. Our results show that visualizations improve the situation awareness about critical events in larger distances during take over request situations. In the third part, explanations are designed for situations in which the vehicle drives unexpectedly due to unknown reasons. Since smart infrastructure could provide connected vehicles with out-of-view or cloud information, the driving maneuver of the vehicle might remain unclear to the driver. Therefore, we explore the needs of drivers in those situations and derive design recommendations for an interface which displays the cause for the unexpected driving behavior. This thesis answers questions about the integration of environment information in vehicles'. Three important aspects are explored, which are essential to consider when implementing use cases with smart infrastructure in mind. It enables to design novel interactions, provides insights on how out-of-view visualizations can improve the drivers' situation awareness and explores unexpected driving situations and the design of explanations for them. Overall, we have shown how infrastructure and connected vehicle information can be introduced in vehicles' user interface and how new technology such as augmented reality glasses can be used to improve the driver's perception of the environment.Autonome Fahrzeuge werden immer mehr in den alltäglichen Verkehr integriert. Die Verbindung von Fahrzeugen mit der Infrastruktur ist ein wesentlicher Bestandteil der Bereitstellung von Umgebungsinformationen in autonome Fahrzeugen. Die Erweiterung der Fahrzeugdaten mit Informationen der Infrastruktur eröffnet ungeahnte Möglichkeiten. Intelligente Infrastruktur übermittelt verbundenen Fahrzeugen Informationen über den prädizierten Verkehrsfluss und Verkehrsereignisse. Zusätzlich können Verkehrsgeschehen in mehreren Kilometern Entfernung übermittelt werden, wodurch ein Vorausblick auf einen Bereich ermöglicht wird, der für den Fahrer nicht unmittelbar sichtbar ist. Mit dieser Dissertation wird gezeigt, dass Informationen der intelligenten Infrastruktur benutzt werden können, um das Fahrerlebnis zu verbessern. Dies kann erreicht werden, indem innovative Interaktionen gestaltet werden, Warnungen und Visualisierungen über Geschehnisse außerhalb des Sichtfelds des Fahrers vermittelt werden und indem Erklärungen über den Grund eines veränderten Fahrzeugverhaltens untersucht werden. Interaktionen, welche von intelligenter Infrastruktur profitieren, waren jedoch bisher nicht im Fokus der Forschung. Dies führt zu Wissenslücken bezüglich der Integration von intelligenter Infrastruktur in das Fahrzeug. Diese Dissertation exploriert die Möglichkeiten intelligenter Infrastruktur, mit einem Fokus auf die Autobahn. Der erste Teil erstellt einen Design Space für Anwendungen von augmentierter Realität (AR) in 3D innerhalb des Autos, die unter anderem von Informationen intelligenter Infrastruktur profitieren. Durch das Ergebnis mehrerer Studien werden Anwendungsfälle in einem Katalog gesammelt, welche in die Interaktionsschnittstelle des Autos einfließen können. Diese Anwendungsfälle bauen unter anderem auf Umgebungsinformationen. Aufgrund dieser Anwendungen wird der Design Space entwickelt, mit Hilfe dessen neuartige Anwendungen für den Fahrzeuginnenraum entwickelt werden können. Der zweite Teil exploriert Visualisierungen für Verkehrssituationen, die außerhalb des Sichtfelds des Fahrers sind. Es wird untersucht, ob durch diese Visualisierungen der Fahrer besser auf ein potentielles Übernahmeszenario vorbereitet wird. Durch mehrere Studien wurden verschiedene Visualisierungen in 2D, stereoskopisches 3D und augmentierter Realität implementiert, die Szenen außerhalb des Sichtfelds des Fahrers darstellen. Diese Visualisierungen verbessern das Situationsbewusstsein über kritische Szenarien in einiger Entfernung während eines Übernahmeszenarios. Im dritten Teil werden Erklärungen für Situationen gestaltet, in welchen das Fahrzeug ein unerwartetes Fahrmanöver ausführt. Der Grund des Fahrmanövers ist dem Fahrer dabei unbekannt. Mit intelligenter Infrastruktur verbundene Fahrzeuge erhalten Informationen, die außerhalb des Sichtfelds des Fahrers liegen oder von der Cloud bereit gestellt werden. Dadurch könnte der Grund für das unerwartete Fahrverhalten unklar für den Fahrer sein. Daher werden die Bedürfnisse des Fahrers in diesen Situationen erforscht und Empfehlungen für die Gestaltung einer Schnittstelle, die Erklärungen für das unerwartete Fahrverhalten zur Verfügung stellt, abgeleitet. Zusammenfassend wird gezeigt wie Daten der Infrastruktur und Informationen von verbundenen Fahrzeugen in die Nutzerschnittstelle des Fahrzeugs implementiert werden können. Zudem wird aufgezeigt, wie innovative Technologien wie AR Brillen, die Wahrnehmung der Umgebung des Fahrers verbessern können. Durch diese Dissertation werden Fragen über Anwendungsfälle für die Integration von Umgebungsinformationen in Fahrzeugen beantwortet. Drei wichtige Themengebiete wurden untersucht, welche bei der Betrachtung von Anwendungsfällen der intelligenten Infrastruktur essentiell sind. Durch diese Arbeit wird die Gestaltung innovativer Interaktionen ermöglicht, Einblicke in Visualisierungen von Informationen außerhalb des Sichtfelds des Fahrers gegeben und es wird untersucht, wie Erklärungen für unerwartete Fahrsituationen gestaltet werden können

Aeronautical engineering: A continuing bibliography with indexes (supplement 291)

This bibliography lists 757 reports, articles, and other documents introduced into the NASA scientific and technical information system in May. 1993. Subject coverage includes: design, construction and testing of aircraft and aircraft engines; aircraft components, equipment, and systems; ground support systems; and theoretical and applied aspects of aerodynamics and general fluid dynamics

Approximation Algorithms for the Geometric Firefighter and Budget Fence Problems

Let R denote a connected region inside a simple polygon, P. By building 1-dimensional barriers in P ∖ R, we want to separate from Rpart(s) of P of maximum area. In this paper we introduce two versions of this problem. In the budget fence version the region R is static, and there is an upper bound on the total length of barriers we may build. In the basic geometric firefighter version we assume that R represents a fire that is spreading over P at constant speed (varying speed can also be handled). Building a barrier takes time proportional to its length, and each barrier must be completed before the fire arrives. In this paper we are assuming that barriers are chosen from a given set Bthat satisfies a certain linearity condition. For example, this condition is satisfied for barrier curves in general position, if any two barriers cross at most once. Even for simple cases (e. g., P a convex polygon and B the set of all diagonals), both problems are shown to be NP-hard. Our main result is an efficient ≈ 11.65 approximation algorithm for the firefighter problem. Since this algorithm solves a much more general problem—a hybrid of scheduling and maximum coverage—it may find wider application. We also provide a polynomial-time approximation scheme for the budget fence problem, for the case where barriers chosen from B must not cross

Approximation Algorithms for the Geometric Firefighter and Budget Fence Problems

Let R denote a connected region inside a simple polygon, P. By building barriers (typically straight-line segments) in P∖R, we want to separate from R part(s) of P of maximum area. All edges of the boundary of P are assumed to be already constructed or natural barriers. In this paper we introduce two versions of this problem. In the budget fence version the region R is static, and there is an upper bound on the total length of barriers we may build. In the basic geometric firefighter version we assume that R represents a fire that is spreading over P at constant speed (varying speed can also be handled). Building a barrier takes time proportional to its length, and each barrier must be completed before the fire arrives. In this paper we are assuming that barriers are chosen from a given set B that satisfies certain conditions. Even for simple cases (e.g., P is a convex polygon and B the set of all diagonals), both problems are shown to be NP-hard. Our main result is an efficient ≈11.65 approximation algorithm for the firefighter problem, where the set B of allowed barriers is any set of straight-line segments with all endpoints on the boundary of P and pairwise disjoint interiors. Since this algorithm solves a much more general problem—a hybrid of scheduling and maximum coverage—it may find wider applications. We also provide a polynomial-time approximation scheme for the budget fence problem, for the case where barriers chosen from a set of straight-line cuts of the polygon must not cross