Planning rapid transit networks

[EN] Rapid transit construction projects are major endeavours that require long-term planning by several players, including politicians, urban planners, engineers, management consultants, and citizen groups. Traditionally, operations research methods have not played a major role at the planning level but several tools developed in recent years can assist the decision process and help produce tentative network designs that can be submitted to the planners for further evaluation. This article reviews some indices for the quality of a rapid transit network, as well as mathematical models and heuristics that can be used to design networks. © 2011 Elsevier Ltd.This research was partly funded by the Canadian Natural Sciences and Engineering Research Council under grant no. 39682-10, the Spanish Ministry of Science and Innovation under grant no. MTM 2009-14243 and the Junta de Andalucía, Spain, under grant no. P09-TEP-5022. This support is gratefully acknowledged. Fig. 10 was kindly provided by Giuseppe Bruno. Thanks are due to a referee who provided several valuable comments on an earlier version of this paper.Laporte, G.; Mesa, J.; Ortega, F.; Perea Rojas Marcos, F. (2011). Planning rapid transit networks. Socio-Economic Planning Sciences. 45(3):95-104. https://doi.org/10.1016/j.seps.2011.02.001S9510445

Planning Rapid Transit Networks

Rapid transit construction projects are major endeavours that require long-term planning by several players, including politicians, urban planners, engineers, management consultants, and citizen groups. Traditionally, operations research methods have not played a major role at the planning level but several tools developed in recent years can assist the decision process and help produce tentative network designs that can be submitted to the planners for further evaluation. This article reviews some indices for the quality of a rapid transit network, as well as mathematical models and heuristics that can be used to design networks.Canadian Natural Sciences and Engineering Research Council 39682-10Ministerio de Ciencia e Innovación MTM 2009-14243Junta de Andalucía P09-TEP-502

Designing robust rapid transit networks with alternative routes

The aim of this paper is to propose a model for the design of a robust rapid transit network. In this paper, a network is said to be robust when the effect of disruption on total trip coverage is minimized. The proposed model is constrained by three different kinds of flow conditions. These constraints will yield a network that provides several alternative routes for given origin–destination pairs, therefore increasing robustness. The paper includes computational experiments which show how the introduction of robustness influences network design.Unión Europea FP6-021235-2Ministerio de Fomento PT2007-003-08CCPPMinisterio de Educación y Ciencia TRA2005-09068-C03-01 MTM2006-15054Ministerio de Ciencia e Innovación TRA2008-06782-C02-01Natural Sciences and Engineering Research Council of Canada 39682-0

Connectivity Constraints in Network Analysis

This dissertation establishes mathematical foundations of connectivity requirements arising in both abstract and geometric network analysis. Connectivity constraints are ubiquitous in network design and network analysis. Aside from the obvious applications in communication and transportation networks, they have also appeared in forest planning, political distracting, activity detection in video sequences and protein-protein interaction networks. Theoretically, connectivity constraints can be analyzed via polyhedral methods, in which we investigate the structure of (vertex)-connected subgraph polytope (CSP). One focus of this dissertation is on performing an extensive study of facets of CSP. We present the first systematic study of non-trivial facets of CSP. One advantage to study facets is that a facet-defining inequality is always among the tightest valid inequalities, so applying facet-defining inequalities when imposing connectivity constraints can guarantee good performance of the algorithm. We adopt lifting techniques to provide a framework to generate a wide class of facet-defining inequalities of CSP. We also derive the necessary and sufficient conditions when a vertex separator inequality, which plays a critical role in connectivity constraints, induces a facet of CSP. Another advantage to study facets is that CSP is uniquely determined by its facets, so full understanding of CSP's facets indicates full understanding of CSP itself. We are able to derive a full description of CSP for a wide class of graphs, including forest and several types of dense graphs, such as graphs with small independence number, s-plex with small s and s-defective cliques with small s. Furthermore, we investigate the relationship between lifting techniques, maximum weight connected subgraph problem and node-weight Steiner tree problem and study the computational complexity of generation of facet-defining inequalities. Another focus of this dissertation is to study connectivity in geometric network analysis. In geometric applications like wireless networks and communication networks, the concept of connectivity can be defined in various ways. In one case, connectivity is imposed by distance, which can be modeled by unit disk graphs (UDG). We create a polytime algorithm to identify large 2-clique in UDG; in another case when connectivity is based on visibility, we provide a generalization of the two-guard problem

Graduate School of Engineering and Management Catalog 2018-2019

The Graduate Catalog represents the offerings, programs, and requirements in effect at the time of publication

Networks: A study in Analysis and Design

In this dissertation, we will look at two fundamental aspects of Networks: Network Analysis and Network Design. In part A, we look at Network Analysis area of the dissertation which involves finding the densest subgraph in each graph. The densest subgraph extraction problem is fundamentally a non-linear optimization problem. Nevertheless, it can be solved in polynomial time by an exact algorithm based on the iterative solution of a series of max-flow sub-problems. To approach graphs with millions of vertices and edges, one must resort to heuristic algorithms. We provide an efficient implementation of a greedy heuristic from the literature that is extremely fast and has some nice theoretical properties. An extensive computational analysis shows that the proposed heuristic algorithm proved very effective on many test instances, often providing either the optimal solution or near-optimal solution within short computing times. In part-B, we discuss Network design, which is a cornerstone of mathematical optimization, is about defining the main characteristics of a network satisfying requirements on connectivity, capacity, and level-of-service. In multi-commodity network design, one is required to design a network minimizing the installation cost of its arcs and the operational cost to serve a set of point-to-point connections. This prototypical problem was recently enriched by additional constraints imposing that each origin-destination of a connection is served by a single path satisfying one or more level-of-service requirements, thus defining the Network Design with Service Requirements. These constraints are crucial, e.g., in telecommunications and computer networks, in order to ensure reliable and low-latency communication. We provide a new formulation for the problem, where variables are associated with paths satisfying the end-to-end service requirements. A fast algorithm for enumerating all the exponentially-many feasible paths and, when this is not viable, a column generation scheme that is embedded into a branch-and-cut-and-price algorithm is provided

Aspects of proactive traffic engineering in IP networks

To deliver a reliable communication service over the Internet it is essential for the network operator to manage the traffic situation in the network. The traffic situation is controlled by the routing function which determines what path traffic follows from source to destination. Current practices for setting routing parameters in IP networks are designed to be simple to manage. This can lead to congestion in parts of the network while other parts of the network are far from fully utilized. In this thesis we explore issues related to optimization of the routing function to balance load in the network and efficiently deliver a reliable communication service to the users. The optimization takes into account not only the traffic situation under normal operational conditions, but also traffic situations that appear under a wide variety of circumstances deviating from the nominal case. In order to balance load in the network knowledge of the traffic situations is needed. Consequently, in this thesis we investigate methods for efficient derivation of the traffic situation. The derivation is based on estimation of traffic demands from link load measurements. The advantage of using link load measurements is that they are easily obtained and consist of a limited amount of data that need to be processed. We evaluate and demonstrate how estimation based on link counts gives the operator a fast and accurate description of the traffic demands. For the evaluation we have access to a unique data set of complete traffic demands from an operational IP backbone. However, to honor service level agreements at all times the variability of the traffic needs to be accounted for in the load balancing. In addition, optimization techniques are often sensitive to errors and variations in input data. Hence, when an optimized routing setting is subjected to real traffic demands in the network, performance often deviate from what can be anticipated from the optimization. Thus, we identify and model different traffic uncertainties and describe how the routing setting can be optimized, not only for a nominal case, but for a wide range of different traffic situations that might appear in the network. Our results can be applied in MPLS enabled networks as well as in networks using link state routing protocols such as the widely used OSPF and IS-IS protocols. Only minor changes may be needed in current networks to implement our algorithms. The contributions of this thesis is that we: demonstrate that it is possible to estimate the traffic matrix with acceptable precision, and we develop methods and models for common traffic uncertainties to account for these uncertainties in the optimization of the routing configuration. In addition, we identify important properties in the structure of the traffic to successfully balance uncertain and varying traffic demands

College of Engineering

Cornell University Courses of Study Vol. 93 2001/200