Route Planning in Transportation Networks

We survey recent advances in algorithms for route planning in transportation networks. For road networks, we show that one can compute driving directions in milliseconds or less even at continental scale. A variety of techniques provide different trade-offs between preprocessing effort, space requirements, and query time. Some algorithms can answer queries in a fraction of a microsecond, while others can deal efficiently with real-time traffic. Journey planning on public transportation systems, although conceptually similar, is a significantly harder problem due to its inherent time-dependent and multicriteria nature. Although exact algorithms are fast enough for interactive queries on metropolitan transit systems, dealing with continent-sized instances requires simplifications or heavy preprocessing. The multimodal route planning problem, which seeks journeys combining schedule-based transportation (buses, trains) with unrestricted modes (walking, driving), is even harder, relying on approximate solutions even for metropolitan inputs.Comment: This is an updated version of the technical report MSR-TR-2014-4, previously published by Microsoft Research. This work was mostly done while the authors Daniel Delling, Andrew Goldberg, and Renato F. Werneck were at Microsoft Research Silicon Valle

Design and evaluation of improvement method on the web information navigation - A stochastic search approach

With the advent of fast growing Internet and World Wide Web (the Web), more and more companies enhance the business competitiveness by conducting electronic commerce. At the same time, more and more people gather or process information by surfing on the Web. However, due to unbalanced Web traffic and poorly organized information, users suffer from slow communication and disordered information. To improve the situation, information providers can analyze the traffic and Uniform Resource Locator (URL) counters to adjust the information layering and organization; nevertheless, heterogeneous navigation patterns and dynamic fluctuating Web traffic complicate the improvement process. Alternatively, improvement can be made by giving direct guidance to the surfers in navigating the Web sites. In this paper, information retrieval on a Web site is modeled as a Markov chain associated with the corresponding dynamic Web traffic and designated information pages. We consider four models of information retrieval based on combination of the level of skill or experience of the surfers as well as the degree of navigation support by the sites. Simulation is conducted to evaluate the performance of the different types of navigation guidance. In addition, we evaluate the four models of information retrieval in terms of complexity and applicability. The paper concludes with a research summary and a direction for future research efforts. © 2009 Elsevier B.V. All rights reserved.postprin

Design and evaluation of improvement method on the Web information navigation - a stochastic search approach

With the advent of fast growing Internet and World Wide Web (WWW), more and more companies start the electronic commerce to enhance the business competitiveness. On the other hand, more and more people surf on the Web for information gathering/processing. Due to unbalanced traffic and poorly organized information, users suffer the slow communication and disordered information organization. The information provider can analyze the traffic and uniform resource locator (URL) counters to adjust the organization; however, heterogeneous navigation patterns and dynamic fluctuating Web traffic make the tuning process very complicated. Alternatively the user may be provided with guidance to navigate through the Web pages efficiently. In this paper, a Web site was modeled as a Markov chain associated with the corresponding dynamic traffic and designated information pages. We consider four models: inexperienced surfers on guidance-less sites, experienced surfers on guidance-less sites, sites with the mean-length guidance, and sites with the known-first-arc guidance (generalized as sites with dynamic stochastic shortest path guidance). Simulation is conducted to evaluate the performance of the different types of navigation guidance. We also propose a reformulation policy to highlight the hyperlinks as steering guidance. The evolution on complexity and applicability is also discussed for the design guideline of general improvement methods. The paper concludes with the summary and future directions.published_or_final_versio

The Multiobjective Average Network Flow Problem: Formulations, Algorithms, Heuristics, and Complexity

Integrating value focused thinking with the shortest path problem results in a unique formulation called the multiobjective average shortest path problem. We prove this is NP-complete for general graphs. For directed acyclic graphs, an efficient algorithm and even faster heuristic are proposed. While the worst case error of the heuristic is proven unbounded, its average performance on random graphs is within 3% of the optimal solution. Additionally, a special case of the more general biobjective average shortest path problem is given, allowing tradeoffs between decreases in arc set cardinality and increases in multiobjective value; the algorithm to solve the average shortest path problem provides all the information needed to solve this more difficult biobjective problem. These concepts are then extended to the minimum cost flow problem creating a new formulation we name the multiobjective average minimum cost flow. This problem is proven NP-complete as well. For directed acyclic graphs, two efficient heuristics are developed, and although we prove the error of any successive average shortest path heuristic is in theory unbounded, they both perform very well on random graphs. Furthermore, we define a general biobjective average minimum cost flow problem. The information from the heuristics can be used to estimate the efficient frontier in a special case of this problem trading off total flow and multiobjective value. Finally, several variants of these two problems are discussed. Proofs are conjectured showing the conditions under which the problems are solvable in polynomial time and when they remain NP-complete

MODELS AND SOLUTION ALGORITHMS FOR EQUITABLE RESOURCE ALLOCATION IN AIR TRAFFIC FLOW MANAGEMENT

Population growth and economic development lead to increasing demand for travel and pose mobility challenges on capacity-limited air traffic networks. The U.S. National Airspace System (NAS) has been operated near the capacity, and air traffic congestion is expected to remain as a top concern for the related system operators, passengers and airlines. This dissertation develops a number of model reformulations and efficient solution algorithms to address resource allocation problems in air traffic flow management, while explicitly accounting for equitable objectives in order to encourage further collaborations by different stakeholders. This dissertation first develops a bi-criteria optimization model to offload excess demand from different competing airlines in the congested airspace when the predicted traffic demand is higher than available capacity. Computationally efficient network flow models with side constraints are developed and extensively tested using datasets obtained from the Enhanced Traffic Management System (ETMS) database (now known as the Traffic Flow Management System). Representative Pareto-optimal tradeoff frontiers are consequently generated to allow decision-makers to identify best-compromising solutions based on relative weights and systematical considerations of both efficiency and equity. This dissertation further models and solves an integrated flight re-routing problem on an airspace network. Given a network of airspace sectors with a set of waypoint entries and a set of flights belonging to different air carriers, the optimization model aims to minimize the total flight travel time subject to a set of flight routing equity, operational and safety requirements. A time-dependent network flow programming formulation is proposed with stochastic sector capacities and rerouting equity for each air carrier as side constraints. A Lagrangian relaxation based method is used to dualize these constraints and decompose the original complex problem into a sequence of single flight rerouting/scheduling problems. Finally, within a multi-objective utility maximization framework, the dissertation proposes several practically useful heuristic algorithms for the long-term airport slot assignment problem. Alternative models are constructed to decompose the complex model into a series of hourly assignment sub-problems. A new paired assignment heuristic algorithm is developed to adapt the round robin scheduling principle for improving fairness measures across different airlines. Computational results are presented to show the strength of each proposed modeling approach

Modeling and Algorithmic Development for Selected Real-World Optimization Problems with Hard-to-Model Features

Mathematical optimization is a common tool for numerous real-world optimization problems. However, in some application domains there is a scope for improvement of currently used optimization techniques. For example, this is typically the case for applications that contain features which are difficult to model, and applications of interdisciplinary nature where no strong optimization knowledge is available. The goal of this thesis is to demonstrate how to overcome these challenges by considering five problems from two application domains. The first domain that we address is scheduling in Cloud computing systems, in which we investigate three selected problems. First, we study scheduling problems where jobs are required to start immediately when they are submitted to the system. This requirement is ubiquitous in Cloud computing but has not yet been addressed in mathematical scheduling. Our main contributions are (a) providing the formal model, (b) the development of exact and efficient solution algorithms, and (c) proofs of correctness of the algorithms. Second, we investigate the problem of energy-aware scheduling in Cloud data centers. The objective is to assign computing tasks to machines such that the energy required to operate the data center, i.e., the energy required to operate computing devices plus the energy required to cool computing devices, is minimized. Our main contributions are (a) the mathematical model, and (b) the development of efficient heuristics. Third, we address the problem of evaluating scheduling algorithms in a realistic environment. To this end we develop an approach that supports mathematicians to evaluate scheduling algorithms through simulation with realistic instances. Our main contributions are the development of (a) a formal model, and (b) efficient heuristics. The second application domain considered is powerline routing. We are given two points on a geographic area and respective terrain characteristics. The objective is to find a ``good'' route (which depends on the terrain), connecting both points along which a powerline should be built. Within this application domain, we study two selected problems. First, we study a geometric shortest path problem, an abstract and simplified version of the powerline routing problem. We introduce the concept of the k-neighborhood and contribute various analytical results. Second, we investigate the actual powerline routing problem. To this end, we develop algorithms that are built upon the theoretical insights obtained in the previous study. Our main contributions are (a) the development of exact algorithms and efficient heuristics, and (b) a comprehensive evaluation through two real-world case studies. Some parts of the research presented in this thesis have been published in refereed publications [119], [110], [109]

The effects of redundancy and information manipulation on traffic networks

Traffic congestion is one of the most frequently encountered problems in real life. It is not only a scientific concern of scholars, but also an inevitable issue for most of the individuals living in urban areas. Since every driver in traffic networks tries to minimize own journey length, and volume of the traffic prevents coordination between individuals, a cooperative behavior will not be provided spontaneously in order to decrease the total cost of the network and the time spent on traffic jams. In order to perceive the effects of cooperative behavior, we develop an agent based traffic application, in which adaptive agents are able to receive traffic information and have different path selection strategies, in order to decrease own journey lengths. We lead them to a cooperative behavior by manipulating the traffic information they receive. Also, by constructing a redundant road to the network, we conceive the importance of the adaptivity to varying information. Moreover, we analyze network topologies of Scale Free, Random, and Small World networks to evaluate the compatibility as traffic networks. Then we try to create fair traffic networks from the network topologies above, in which the selfish behaviors of non adaptive drivers causes less congestion and total journey lengths, by road closures. By doing these experiments an analyses, we obtain a deeper perception about the importance of adaptivity, information retrieval, topology, and redundancy for traffic networks

Modelling adaptive routing in Wide Area Networks

Bibliography: leaves 132-138.This study investigates the modelling of adative routing algorithms with specific reference to the algorithm of an existing Wide Area Network (WAN). Packets in the network are routed at each node on the basis of routing tables which contain internal and external delays for each route from the node. The internal delay on a route represents the time that packets queued for transmission will have to wait before being transmitted, while the external delay on a route represents the delay to other nodes via that route. Several modelling methods are investigated and compared for the purpose of identifying the most appropriate and applicable technique. A model of routing in the WAN using an analytic technique is described. The hypothesis of this study is that dynamic routing can be modelled as a sequence of models exhibiting fixed routing. The modelling rationale is that a series of analytic models is run and solved. The routing algorithm of the WAN studied is such that, if viewed at any time instant, the network is one with static routing and no buffer overflow. This characteristic, together with a real time modelling requirement, influences the modelling technique which is applied. Each model represents a routing update interval and a multiclass open queueing network is used to solve the model during a particular interval. Descriptions of the design and implementation of X wan, an X Window based modelling system, are provided. A feature of the modelling system is that it provides a Graphical User Interface (GUI), allowing interactive network specification and the direct observation of network routing through the medium of this interface. Various applications of the modelling system are presented, and overall network behaviour is examined. Experimentation with the routing algorithm is conducted, and (tentative) recommendations are made on ways in which network performance could be improved. A different routing algorithm is also implemented, for the purpose of comparison and to demonstrate the ease with which this can be affected