Eva Barrena

Exact formulations and algorithm for the train timetabling problem with dynamic demand

In this paper we study the design and optimization of train timetabling adapted to a dynamic demand environment. This problem arises in rapid train services which are common in most important cities. We present three formulations for the problem, with the aim of minimizing passenger average waiting time. The most intuitive model would consider binary variables representing train departure times but it yields to non-linear objective function. Instead, we introduce flow variables, which allow a linear representation of the objective function. We provide incremental improvements on these formulations, which allows us to evaluate and compare the benefits and disadvantages of each modification. We present a branch-and-cut algorithm applicable to all formulations. Through extensive computational experiments on several instances derived from real data provided by the Madrid Metropolitan Railway, we show the advantages of designing a timetable adapted to the demand pattern, as opposed to a regular timetable. We also perform an extensive computational comparison of all linear formulations in terms of size, solution quality and running time.

A short-turning policy for the management of demand disruptions in rapid transit systems

Rapid transit systems timetables are commonly designed to accommodate passenger demand in sections with the highest passenger load. However, disruptions frequently arise due to an increase in the demand, infrastructure incidences or as a consequence of fleet size reductions. All these circumstances give rise to unsupplied demand at certain stations, which generates passenger overloads in the available vehicles. The design of strategies that guarantee reasonable user waiting time with small increases of operation costs is now an important research topic. This paper proposes a tactical approach to determine optimal policies for dealing with such situations. Concretely, a short-turning strategy is analysed, where some vehicles perform short cycles in order to increase the frequency among certain stations of the lines and to equilibrate the train occupancy level. Turn-back points should be located and service offset should be determined with the objective of diminishing the passenger waiting time while preserving certain level of quality of service. Computational results and analysis for a real case study are provided.

Macroscopic attraction-based simulation of pedestrian mobility: A dynamic individual route-choice approach

This paper presents a dynamic distribution and assignment simulation model based on discrete time simulation techniques and dynamic route assignment for planning, engineering design, and operation analysis of big exhibition events from a pedestrian circulation perspective. Both, the distribution and assignment stages are incorporated in an interlaced way with a dynamic behavior along a specific time horizon. In the proposed model, the individual route choice is dynamically determined as consequence of facilities attractiveness and network congestion. Therefore, in contrast with other simulation approaches, it does not require the usual origin–destination trip matrices to describe the transportation demand or the specification of different paths to be followed by visitors. This modeling approach turns out to be very appropriate for the simulation of these big exhibition events where each visitor usually has multiple and a priori unordered destination choices after entering the scenario.

Counting and enumerating feasible rotating schedules by means of Gröbner bases

This paper deals with the problem of designing and analyzing rotating schedules with an algebraic computational approach. Specifically, we determine a set of Boolean polynomials whose zeros can be uniquely identified with the set of rotating schedules related to a given workload matrix subject to standard constraints. These polynomials constitute zero-dimensional radical ideals, whose reduced Grobner bases can be computed to count and even enumerate the set of rotating schedules that satisfy the desired set of constraints. Thereby, it enables to analyze the influence of each constraint in the same.

Line graphs for a multiplex network.

It is well known that line graphs offer a good summary of the graphs properties, which make them easier to analyze and highlight the desired properties. We extend the concept of line graph to multiplex networks in order to analyze multi-plexed and multi-layered networked systems. As these structures are very rich, different approaches to this notion are required to capture a variety of situations. Some relationships between these approaches are established. Finally, by means of some simulations, the potential utility of this concept is illustrated.

Planning Ecotourism Routes in Nature Parks

The main objective of the Nature Parks is to preserve the diversity and integrity of biotic communities for present and future use. Additionally, the Nature Parks can contribute to the invigoration of the sustainable development and culture heritage of its neighboring regions, as well as to the strengthening of the environmental education for visitors by means of direct experiences. From this double point of view, ecotourism is gaining acceptance as a tool for sustainable development since the income of visitors to protected areas can contribute significantly to support the economy of these areas and of the rural communities. This article proposes different methodologies for determining efficient routes of ecotourism where the main objective is the maximization of the cultural transmission experienced by the visitors along the path traveled. The models are formulated by using integer linear programming and its potential applicability is illustrated in the context of the Donana National Park, Spain.

On setting line frequencies and capacities in dense Railway Rapid Transit networks

The tactical determination of line frequencies in railway networks is usually carried out as a by-product of the Line Planning phase within the general Railway Planning Process. The classical approach need to solve a previous network loading model in order to determine the different paths followed by users in their trips. Then, frequencies are determined assuming a fixed capacity both in vehicles and infrastructure. In this work, we present a general optimization model hat simultaneously determines lines frequency and trains capacity without supposing an a priori passenger behaviour with regard to route choice decisions. The aim is to minimize travel time, transfers and operation costs considering both the user and the service provider points of view. In order to deal with infrastructure capacity, the model also allocates lines to tracks in multi-line open tracks. A little example is used in order to illustrate the model capabilities.