Braess' paradox is a counter-intuitive phenomenon which can occur in congesting networks. It refers to those cases where the introduction of a new link in the network results in the total travel time on the network increasing. The dissertation starts by introducing the traffic assignment problem and the concept of equilibrium in traffic assignment. The concept of equilibrium is based on Wardrop's first principle that all travellers will attempt to minimize their own travel time regardless of the effect on others. A literature review includes details of a number of papers that have been published investigating theoretical aspects of the paradox. There is also a brief description of Game Theory and the Nash Equilibrium. It has been shown that the equilibrium assignment is an example of Nash Equilibrium. The majority of work that has been published deals with networks where the delay functions that are used to compute the travel times on the links of the network do not include explicit representation of the capacity of the links. In this dissertation a network that is similar in form to the one first presented by Braess was constructed with the difference being that the well-known BPR function was used in the delay functions. This network was used to show that a number of findings that had been presented previously using simpler functions also applied to this network. It was shown that when it occurs, Braess' paradox only occurs over a range of values at relatively low levels of congestion. Real-world networks were then investigated and it was found that similar results occurred to those found in the simpler test networks that are often used in discussions of the paradox. Two methodologies of eliminating the paradox were investigated and the results are presented. / Decision Sciences / M.Sc.

Braess' paradox is a counter-intuitive phenomenon which can occur in congesting networks. It refers to those cases where the introduction of a new link in the network results in the total travel time on the network increasing. The dissertation starts by introducing the traffic assignment problem and the concept of equilibrium in traffic assignment. The concept of equilibrium is based on Wardrop's first principle that all travellers will attempt to minimize their own travel time regardless of the effect on others. A literature review includes details of a number of papers that have been published investigating theoretical aspects of the paradox. There is also a brief description of Game Theory and the Nash Equilibrium. It has been shown that the equilibrium assignment is an example of Nash Equilibrium. The majority of work that has been published deals with networks where the delay functions that are used to compute the travel times on the links of the network do not include explicit representation of the capacity of the links. In this dissertation a network that is similar in form to the one first presented by Braess was constructed with the difference being that the well-known BPR function was used in the delay functions. This network was used to show that a number of findings that had been presented previously using simpler functions also applied to this network. It was shown that when it occurs, Braess' paradox only occurs over a range of values at relatively low levels of congestion. Real-world networks were then investigated and it was found that similar results occurred to those found in the simpler test networks that are often used in discussions of the paradox. Two methodologies of eliminating the paradox were investigated and the results are presented. / Decision Sciences / M.Sc.

abstract: This research develops heuristics to manage both mandatory and optional network capacity reductions to better serve the network flows. The main application discussed relates to transportation networks, and flow cost relates to travel cost of users of the network. Temporary mandatory capacity reductions are required by maintenance activities. The objective of managing maintenance activities and the attendant temporary network capacity reductions is to schedule the required segment closures so that all maintenance work can be completed on time, and the total flow cost over the maintenance period is minimized for different types of flows. The goal of optional network capacity reduction is to selectively reduce the capacity of some links to improve the overall efficiency of user-optimized flows, where each traveler takes the route that minimizes the traveler’s trip cost. In this dissertation, both managing mandatory and optional network capacity reductions are addressed with the consideration of network-wide flow diversions due to changed link capacities. This research first investigates the maintenance scheduling in transportation networks with service vehicles (e.g., truck fleets and passenger transport fleets), where these vehicles are assumed to take the system-optimized routes that minimize the total travel cost of the fleet. This problem is solved with the randomized fixed-and-optimize heuristic developed. This research also investigates the maintenance scheduling in networks with multi-modal traffic that consists of (1) regular human-driven cars with user-optimized routing and (2) self-driving vehicles with system-optimized routing. An iterative mixed flow assignment algorithm is developed to obtain the multi-modal traffic assignment resulting from a maintenance schedule. The genetic algorithm with multi-point crossover is applied to obtain a good schedule. Based on the Braess’ paradox that removing some links may alleviate the congestion of user-optimized flows, this research generalizes the Braess’ paradox to reduce the capacity of selected links to improve the efficiency of the resultant user-optimized flows. A heuristic is developed to identify links to reduce capacity, and the corresponding capacity reduction amounts, to get more efficient total flows. Experiments on real networks demonstrate the generalized Braess’ paradox exists in reality, and the heuristic developed solves real-world test cases even when commercial solvers fail. / Dissertation/Thesis / Doctoral Dissertation Industrial Engineering 2017

The Braess Paradox is a rare phenomenon that only occurs under specific scenarios. This project aims to study the probability of the Braess Paradox occurring in a Directed Weighted Graph while the number of edges increases. The graphs in the experiment are focused on studying the occurrence of the Braess Paradox in a directed weighted scale-free network while transforming it into a directed weighted complete graph. A simulation model is used to simulate the bots traveling through a network to detect the occurrence of the Braess Paradox, considering the increase of directed weighted edges. A Graph Neural Network (GNN) is later used to train on the data produced by the simulation model.

La microscopie de grille à balayage (SGM pour Scanning GateMicroscopy), développée à la fin des années 1990, est devenue un outilpuissant pour étudier les propriétés électroniques locales dans lesnano-dispositifs semi-conducteurs. La SGM est basée sur la techniqueAFM, mais la pointe métallique est utilisée comme une grille mobilecouplée capacitivement au dispositif, et les propriétés de transportélectronique sont étudiées sous l'influence de cette grille,fournissant des informations spatiales à haute résolution. Cette thèsedécrit d'abord le remplacement de la détection optique de notresystème AFM par une détection piézo-électrique utilisant un diapason àquartz, puis les résultats de mesures SGM sur divers nano-dispositifs,qui sont tous fabriqués à partir d'hétérostructures InGaAs / InAlAscontenant un gaz d'électrons bi-dimensionnel (2DEG) de grande mobilitésitué à quelques dizaines de nanomètres sous la surface. Sur unesimple constriction, nous étudions l'interaction pointe-échantillonavec deux approches: la force électrostatique et l'effet capacitif.Sur une boite quantique, nous étudions les phénomènes de blocage deCoulomb lorsque la pointe est utilisée comme une grille pour modulerla charge à l'intérieur de la boite. Dans un travail sur le paradoxede Braess, avec l'aide de simulations numériques, nous découvrons uneffet paradoxal en modulant la largeur du canal central dans undispositif mésoscopique en forme de double anneau, en analogie avec leparadoxe qui se produit dans un réseau classique. Par une étudedétaillée de l'évolution de la conductance, nous découvrons enfinplusieurs pièges de charge dans les images SGM, et proposons un modèlepour interpréter le changement de conductance en présence de pièges decharge. Nous développons alors une méthode pour imager directement lespièges de charge par des mesures de transconductance avec unemodulation de la tension sur la pointe. / Scanning gate microscopy (SGM), developed in the late 1990's, has become a powerful tool to investigate the local electronic properties in semiconductor nano devices. SGM is based on the AFM technique but the metallic tip is used as a movable gate capacitively coupled to the device, and the electron transport property is studied on influence of this gate, providing spatial information with high resolution. This thesis presents the update of the force detection mode of our AFM system from optical method to force sensing by a quartz tuning fork, and the SGM measurement results on various nano devices, all of which are fabricated from InGaAs/InAlAs heterostructures containing a high mobility 2DEG located a few tens of nanometers below the surface. On a 2DEG constriction, we investigate the tip-sample interaction with two approaches: the capacitive force and the gate effect. On a quantum dot, we study the Coulomb blockade phenomena where the tip is used as a gate to modulate the charging/discharging inside the dot. In a work on Braess paradox, with the help of numerical simulations, we discover a Braess paradox effect by modulating a channel width in a ‘double-ring' shaped mesoscopic device in analogy with the one that occurs in a classical network. By a detailed study of the conductance changes, we discover several charge traps from the SGM map, and propose a model to interpret the conductance change with the presence of charge traps. We develop a method to directly image the charge traps by transconductance measurements with a voltage modulation on the tip.

La microscopie de grille à balayage (SGM pour Scanning GateMicroscopy), développée à la fin des années 1990, est devenue un outilpuissant pour étudier les propriétés électroniques locales dans lesnano-dispositifs semi-conducteurs. La SGM est basée sur la techniqueAFM, mais la pointe métallique est utilisée comme une grille mobilecouplée capacitivement au dispositif, et les propriétés de transportélectronique sont étudiées sous l'influence de cette grille,fournissant des informations spatiales à haute résolution. Cette thèsedécrit d'abord le remplacement de la détection optique de notresystème AFM par une détection piézo-électrique utilisant un diapason àquartz, puis les résultats de mesures SGM sur divers nano-dispositifs,qui sont tous fabriqués à partir d'hétérostructures InGaAs / InAlAscontenant un gaz d'électrons bi-dimensionnel (2DEG) de grande mobilitésitué à quelques dizaines de nanomètres sous la surface. Sur unesimple constriction, nous étudions l'interaction pointe-échantillonavec deux approches: la force électrostatique et l'effet capacitif.Sur une boite quantique, nous étudions les phénomènes de blocage deCoulomb lorsque la pointe est utilisée comme une grille pour modulerla charge à l'intérieur de la boite. Dans un travail sur le paradoxede Braess, avec l'aide de simulations numériques, nous découvrons uneffet paradoxal en modulant la largeur du canal central dans undispositif mésoscopique en forme de double anneau, en analogie avec leparadoxe qui se produit dans un réseau classique. Par une étudedétaillée de l'évolution de la conductance, nous découvrons enfinplusieurs pièges de charge dans les images SGM, et proposons un modèlepour interpréter le changement de conductance en présence de pièges decharge. Nous développons alors une méthode pour imager directement lespièges de charge par des mesures de transconductance avec unemodulation de la tension sur la pointe.