Algorithmic contributions to bilevel location problems with queueing and user equilibrium : exact and semi-exact approaches

Bien que la littérature sur le problème d'emplacement soit vaste, la plupart des publications considèrent des modèles simples, dans lesquels une autorité centrale assigne les utilisateurs aux installations les plus proches. Des caractéristiques plus réalistes, telles que le comportement des usagers, la compétition et la congestion, sont souvent négligées, peut-être en raison de leur nature hautement non-linéaire «compliquée». Quelques articles ont incorporé ces traits, mais uniquement de facon séparée, et seulement des approches heuristiques ont été proposées comme méthodes de résolution. Le problème d'emplacement d'installations consiste à localiser un ensemble d'installations de manière optimale afin de répondre à une demande donnée. Dans un environnement congestioné où les usagers ont le choix, les installations sont généralement modélisées sous la forme de files d'attente. Les utilisateurs sélectionnent les installations à fréquenter en fonction de leur utilité perçue, qui est généralement écrite comme une combinaison linéaire de la distance de déplacement, du temps d'attente dans les installations, etc. En résulte un modèle dit "à deux niveaux" appartenant à la classe des programmes mathématiques à contraintes d'équilibre (MPEC en anglais), où l'équilibre peut être exprimé sous la forme d'une inéquation variationnelle. Notre travail est axé sur le problème d'emplacement d'installations où les usagers ont le choix (CC-FLP en anglais) et nous fournissons un certain nombre de contributions importantes. Du point de vue de la modélisation, nous proposons différents modèles qui capturent les principales caractéristiques du CC-FLP. Pour ces programmes non-linéaires, discrets, et NP-difficiles, nous avons conçu des algorithmes exactes et d'approximation, ainsi que des heuristiques sur-mesure. Notre travail couvre trois articles. Dans le premier article, nous considérons différents modèles qui intègrent l'abandon aux centres de services, en raison des places limitées dans la file d'attente, tandis que le comportement des utilisateurs peut être déterministe ou stochastique. Dans ce dernier cas, le comportement des usagers correspond au principe d'équilibre de Wardrop, tandis que dans le premier cas, les clients se distribuent entre les établissements selon un modèle de choix d'utilité aléatoire Logit. Au-delà de l'analyse des propriétés théoriques du modèle, nous concevons une heuristique menée par les usagers et un algorithme d'approximation linéaire pour lequel nous prouvons une borne d'erreur de l'approximation, dans le cas d'une file d'attente M/M/1. Le second article est consacré à la conception d'un nouvel algorithme de `Branch and Bound' (B&B) pour résoudre une sous-classe plus générale des MPEC. L'algorithme est implémenté et évalué sur un CC-FLP. L'idée est de traiter virtuellement chaque nœud de l'arbre B& B comme un problème d'optimisation distinct, afin de tirer parti de la puissance des solveurs MILP et de leur prétraitement fort au niveau de la racine. Notre approche algorithmique est basée sur une combinaison de programmation linéaire à nombres entiers et mixtes (MILP en anglais), de techniques de linéarisation et de la résolution itérative de sous-problèmes convexes, et nécessite une gestion d’arbre sophistiquée. Dans le troisième article, nous incorporons les prix dans le CC-FLP. Le prix est une variable de décision continue, tout comme la localisation et le niveaux et de service, et les utilisateurs l'intègrent dans leur utilité. Les concepts de tarification du réseaux et de CC-FLP étant fusionnés en un seul modèle, le problème devient extrêmement difficile, également en raison de la présence de variables de localisation et de niveau de service, ainsi que de délais d'attente bidimensionnels. Pour ce programme à deux niveaux non-convexe, nous avons conçu un algorithme basé sur des approximations linéaires emprunté à la fois à la littérature sur la localisation et à la tarification du réseau.While the location literature is vast, most papers consider simpler models, in which a central authority assigns users to the closest facilities. More realistic traits, such as user behaviour, competition, and congestion are often overlooked, perhaps due to their `complicating' highly non-linear nature. A few papers did incorporate them, but separately, and only heuristic approaches have been proposed as solution methods. The facility location problem consists in optimally locating a set of facilities in order to satisfy a given demand. In a congested user-choice environment, facilities are typically modeled as queues, and users select the facilities to patronize based on their perceived utility, which is, in general, written as linear combination of travel distance, waiting time at facilities, etc. The resulting bilevel model belongs to the class of mathematical programs with equilibrium constraints (MPECs), where the equilibrium can be expressed as a variational inequality. Our work is focused on the \emph{competitive congested user-choice facility location problem} (CC-FLP), and we provide a number of strong contributions. From the modeling point of view, we propose various models that capture the key features of CC-FLP. For these NP-hard discrete nonlinear programs we designed exact and approximated algorithms, as well as tailored heuristics. Our work spans three papers. In the first article we consider different models that incorporate balking at facilities, due to limited places in the queue, while user behaviour can be either deterministic or stochastic. In the latter case, user behaviour fits Wardrop's equilibrium principle, while in the former case, customers distribute among facilities according to a Logit random utility choice model. Beyond the analysis of the model's theoretical properties, we design a user-driven heuristic and a linear approximation algorithm, for which we prove a bound on the approximation error, for the M/M/1 queue. The second paper is dedicated to the design of a novel exact branch-and-bound (B&B) algorithm for solving a more general subclass of MPECs, which is implemented and evaluated on a CC-FLP. The idea is to virtually treat each node of the B&B tree as a separate optimization problem, in oder to leverage the strength of the MILP solvers and their strong preprocessing at the root node. Our algorithmic approach is based on a combination of Mixed-Integer Linear Programming (MILP), linearization techniques and the iterative solution of convex subproblems, and requires a sophisticated tree management. In the third paper we incorporate mill pricing into the CC-FLP. Price is a continuous decision variable, along with the location and service levels, and user incorporate it into their utility. Since concepts from network pricing and CC-FLP are merged into a single model, the problem becomes extremely challenging, also due to the presence of facility location and service level decision variables, as well as bivariate queueing delays. For this non-convex bilevel program we devise an algorithm based on linear approximations, that borrows from both location and network pricing literature

A Comprehensive Survey of Potential Game Approaches to Wireless Networks

Potential games form a class of non-cooperative games where unilateral improvement dynamics are guaranteed to converge in many practical cases. The potential game approach has been applied to a wide range of wireless network problems, particularly to a variety of channel assignment problems. In this paper, the properties of potential games are introduced, and games in wireless networks that have been proven to be potential games are comprehensively discussed.Comment: 44 pages, 6 figures, to appear in IEICE Transactions on Communications, vol. E98-B, no. 9, Sept. 201

Bridging the user equilibrium and the system optimum in static traffic assignment: a review

Solving the road congestion problem is one of the most pressing issues in modern cities since it causes time wasting, pollution, higher industrial costs and huge road maintenance costs. Advances in ITS technologies and the advent of autonomous vehicles are changing mobility dramatically. They enable the implementation of a coordination mechanism, called coordinated traffic assignment, among the sat-nav devices aiming at assigning paths to drivers to eliminate congestion and to reduce the total travel time in traffic networks. Among possible congestion avoidance methods, coordinated traffic assignment is a valuable choice since it does not involve huge investments to expand the road network. Traffic assignments are traditionally devoted to two main perspectives on which the well-known Wardropian principles are inspired: the user equilibrium and the system optimum. User equilibrium is a user-driven traffic assignment in which each user chooses the most convenient path selfishly. It guarantees that fairness among users is respected since, when the equilibrium is reached, all users sharing the same origin and destination will experience the same travel time. The main drawback in a user equilibrium is that the system total travel time is not minimized and, hence, the so-called Price of Anarchy is paid. On the other hand, the system optimum is an efficient system-wide traffic assignment in which drivers are routed on the network in such a way the total travel time is minimized, but users might experience travel times that are higher than the other users travelling from the same origin to the same destination, affecting the compliance. Thus, drawbacks in implementing one of the two assignments can be overcome by hybridizing the two approaches, aiming at bridging users’ fairness to system-wide efficiency. In the last decades, a significant number of attempts have been done to bridge fairness among users and system efficiency in traffic assignments. The survey reviews the state-of-the-art of these trade-off approaches

Overview of the Global Sanitation Problem

human development, water, sanitation

Load shedding in network monitoring applications

Monitoring and mining real-time network data streams are crucial operations for managing and operating data networks. The information that network operators desire to extract from the network traffic is of different size, granularity and accuracy depending on the measurement task (e.g., relevant data for capacity planning and intrusion detection are very different). To satisfy these different demands, a new class of monitoring systems is emerging to handle multiple and arbitrary monitoring applications. Such systems must inevitably cope with the effects of continuous overload situations due to the large volumes, high data rates and bursty nature of the network traffic. These overload situations can severely compromise the accuracy and effectiveness of monitoring systems, when their results are most valuable to network operators. In this thesis, we propose a technique called load shedding as an effective and low-cost alternative to over-provisioning in network monitoring systems. It allows these systems to handle efficiently overload situations in the presence of multiple, arbitrary and competing monitoring applications. We present the design and evaluation of a predictive load shedding scheme that can shed excess load in front of extreme traffic conditions and maintain the accuracy of the monitoring applications within bounds defined by end users, while assuring a fair allocation of computing resources to non-cooperative applications. The main novelty of our scheme is that it considers monitoring applications as black boxes, with arbitrary (and highly variable) input traffic and processing cost. Without any explicit knowledge of the application internals, the proposed scheme extracts a set of features from the traffic streams to build an on-line prediction model of the resource requirements of each monitoring application, which is used to anticipate overload situations and control the overall resource usage by sampling the input packet streams. This way, the monitoring system preserves a high degree of flexibility, increasing the range of applications and network scenarios where it can be used. Since not all monitoring applications are robust against sampling, we then extend our load shedding scheme to support custom load shedding methods defined by end users, in order to provide a generic solution for arbitrary monitoring applications. Our scheme allows the monitoring system to safely delegate the task of shedding excess load to the applications and still guarantee fairness of service with non-cooperative users. We implemented our load shedding scheme in an existing network monitoring system and deployed it in a research ISP network. We present experimental evidence of the performance and robustness of our system with several concurrent monitoring applications during long-lived executions and using real-world traffic traces.Postprint (published version

The economics of managing congestion: with special reference to backcountry recreation

The management of congestible recreation resources has been based largely on the concept of satisfaction. This concept is poorly defined and often does not reflect objectives for management of recreation resources. One way of addressing these problems is to define and use measurable objectives for management of recreation resources. One such objective is economic efficiency. The concept of efficiency is defined and economic theory developed to identify efficient allocations of congestible resources, the efficient capacities of resources under different allocation mechanisms, and the efficiency costs of use of lottery-based allocation mechanisms. The usefulness of this body of economic theory in allocation of backcountry recreational resources is addressed through investigation of ability to measure demand for congestible resources, and the problems associated with use of surrogate measures of demand. Theoretical models of efficient management of congestible resources cannot be applied with the current state of knowledge because existing non-market valuation methods are not able to identify Hicksian-compensated demand functions for congestible backcountry recreation. Use of Marshallian demand measures introduces the possibility of resource misallocations of unknown direction and magnitude

Evolutionary Solutions and Internet Applications for Algorithmic Game Theory

The growing pervasiveness of the internet has created a new class of algorithmic problems: those in which the strategic interaction of autonomous, self-interested entities must be accounted for. So motivated, we seek to (1) use game theoretic models and techniques to study practical problems in load balancing, data streams and internet traffic congestion, and (2) demonstrate the usefulness of evolutionary game theory's adaptive learning model as an analytical and evaluative tool.First we consider the evolutionary game theory concept of stochastic stability, and propose the price of stochastic anarchy as an alternative to the price of anarchy for quantifying the cost of having no central authority. Unlike Nash equilibria, stochastically stable states are the result of natural dynamics of large populations of computationally bounded agents, and are resilient to small perturbations from ideal play. To illustrate the utility of stochastic stability, we study the load balancing game on related machines, which has an unbounded price of anarchy, even in the case of two jobs and two machines. We show that in contrast, even in the general case, the price of stochastic anarchy is bounded.Next, we propose auction-based mechanisms for admission control of continuous queries to a Data Stream Management System. When submitting a query, each user also submits a bid: how much she is willing to pay for her query to run. Our mechanisms must admit queries and set payments in a way that maximizes system revenue while incentivizing customers to use the system honestly. We propose several manipulation-resistant payment mechanisms and prove that one guarantees a profit close to a standard profit benchmark, and the others perform well experimentally.Finally, we study the long standing problem of congestion control at bottleneck routers on the internet. We examine the effectiveness of commonly-used queuing policies when each network endpoint is self-interested and has no information about the other endpoints' actions or preferences. By employing evolutionary game theory, we find that while bottleneck routers face heavy congestion at stochastically stable states under policies being currently deployed, a practical policy that was recently proposed yields fair and efficient conditions with no congestion

Trustworthy Knowledge Planes For Federated Distributed Systems

In federated distributed systems, such as the Internet and the public cloud, the constituent systems can differ in their configuration and provisioning, resulting in significant impacts on the performance, robustness, and security of applications. Yet these systems lack support for distinguishing such characteristics, resulting in uninformed service selection and poor inter-operator coordination. This thesis presents the design and implementation of a trustworthy knowledge plane that can determine such characteristics about autonomous networks on the Internet. A knowledge plane collects the state of network devices and participants. Using this state, applications infer whether a network possesses some characteristic of interest. The knowledge plane uses attestation to attribute state descriptions to the principals that generated them, thereby making the results of inference more trustworthy. Trustworthy knowledge planes enable applications to establish stronger assumptions about their network operating environment, resulting in improved robustness and reduced deployment barriers. We have prototyped the knowledge plane and associated devices. Experience with deploying analyses over production networks demonstrate that knowledge planes impose low cost and can scale to support Internet-scale networks