A review on transit assignment modelling approaches to congested networks: a new perspective

This paper reviews a number of studies on both frequency-and schedule-based transit assignment models that have been proposed by far, wherein various behavioural assumptions on a wide range of aspects are embedded. With a reinvestigation on the relationships and homogeneity between different modelling approaches, it explores the representative veins of the models, and thereby extends a new perspective to the existing reviews under a historical context. Meanwhile, both advantages and disadvantages of these methods are presented. On the strength of the analyses and discussions of the state-of-the-art transit assignment models, further research directions are suggested

A model for setting services on auxiliary bus lines under congestion

In this paper, a mathematical programming model and a heuristically derived solution is described to assist with the efficient planning of services for a set of auxiliary bus lines (a bus-bridging system) during disruptions of metro and rapid transit lines. The model can be considered static and takes into account the average flows of passengers over a given period of time (i.e., the peak morning traffic hour) Auxiliary bus services must accommodate very high demand levels, and the model presented is able to take into account the operation of a bus-bridging system under congested conditions. A general analysis of the congestion in public transportation lines is presented, and the results are applied to the design of a bus-bridging system. A nonlinear integer mathematical programming model and a suitable approximation of this model are then formulated. This approximated model can be solved by a heuristic procedure that has been shown to be computationally viable. The output of the model is as follows: (a) the number of bus units to assign to each of the candidate lines of the bus-bridging system; (b) the routes to be followed by users passengers of each of the origin–destination pairs; (c) the operational conditions of the components of the bus-bridging system, including the passenger load of each of the line segments, the degree of saturation of the bus stops relative to their bus input flows, the bus service times at bus stops and the passenger waiting times at bus stops. The model is able to take into account bounds with regard to the maximum number of passengers waiting at bus stops and the space available at bus stops for the queueing of bus units. This paper demonstrates the applicability of the model with two realistic test cases: a railway corridor in Madrid and a metro line in Barcelona Planificación de los servicios de lineas auxiliares de autobuses durante las incidencias de las redes de metro y cercanías. El modelo estudia el problema bajo condiciones de alta demanda y condiciones de congestión. El modelo no lineal resultante es resuelto mediante heurísticas que demuestran su utilidad. Se demuestran los resultados en dos corredores de las ciudades de Barcelona y Madrid

Limited Stop Services Design Considering Variable Dwell Time and Operating Capacity Constraints

This article proposes an optimization model to set frequencies, vehicle capacities, required fleet and the stops serving each route along a transit corridor which minimize the total user and operating costs. The optimization problem is solved by applying the ?Black Hole? algorithm, which imitates the movement of stars (solutions), towards a black hole (Best solution). The main contributions of the model are based on incorporating variable dwell times depending on bus stop demand not only to the passenger perceived journey times but also to the bus cycle times and on considering capacity constraints in both vehicles and bus tops. This led to a more accurate and realistic operating times and user perceived journey times. The application of the model to two case studies and the sensitivity analysis carried out demonstrate that for low levels of demand, constant dwell times can be assumed but being these times different between the different stops of the corridor, considering their demand. However, with high level of demand the difference found in operating costs and travel times strongly recommend incorporating variable dwell times in the model in order to achieve a more realistic design of transit corridor strategies

Strategy-based dynamic assignment in transit networks with passenger queues

This thesis develops a mathematical framework to solve the problem of dynamic assignment in densely connected public transport (or transit – the two words are interchangeably used) networks where users do not time their arrival at a stop with the lines’ timetable (if any is published). In the literature there is a fairly broad agreement that, in such transport systems, passengers would not select the single best itinerary available, but would choose a travel strategy, namely a bundle of partially overlapping itineraries diverging at stops along different lines. Then, they would follow a specific path depending on what line arrives first at the stop. From a graph-theory point of view, this route-choice behaviour is modelled as the search for the shortest hyperpath (namely an acyclic sub-graph which includes partially overlapping single paths) to the destination in the hypergraph that describes the transit network. In this thesis, the hyperpath paradigm is extended to model route choice in a dynamic context, where users might be prevented from boarding the lines of their choice because of capacity constraints. More specifically, if the supplied capacity is insufficient to accommodate the travel demand, it is assumed that passenger congestion leads to the formation of passenger First In, First Out (FIFO) queues at stops and that, in the context of commuting trips, passengers have a good estimate of the expected number of vehicle passages of the same line that they must let go before being able to board. By embedding the proposed demand model in a fully dynamic assignment model for transit networks, this thesis also fills in the gap currently existing in the realm of strategy-based transit assignment, where – so far – models that employ the FIFO queuing mechanism have proved to be very complex, and a theoretical framework for reproducing the dynamic build-up and dissipation of queues is still missing.Open Acces

Optimizing integrated service for a transit route with heterogeneous demand

The methodology developed in this dissertation attempts to optimize integrated service that minimizes the total cost, including user and supplier costs, of a transit route with heterogeneous demand. While minimizing total cost, a set of practical constraints, such as capacity, operable fleet size and frequency conservation, are considered. The research problem is presented in three scenarios, consisting of various service patterns (e.g., all-stop, short-turn and express) under heterogeneous demand. A logit-based model was used to estimate passenger transfer demand. An exhaustive search method was developed to find the optimal solutions for a simplified transit route with six stops, and a Genetic Algorithm (GA) was developed to find the optimal solution for a real-world, large scale transit route. The optimized variables include the combination of service patterns, the associated service frequencies, and stops skipped by the express service. A six-stop transit route was designed and analyzed via a proof-of-concept demonstration to ensure that the developed models are capable of finding the optimal solutions. A sensitivity analysis was conducted, which enables transit planners to quantify the impact of various model parameters (e.g., user value of time, vehicle capacity, operating cost, etc.) to the decision variables and the objective function. Finally, the developed models and solution algorithm were applied to optimize integrated service for a real world bus route in New Jersey

Capacity assessment of railway infrastructure: Tools, methodologies and policy relevance in the EU context

The transport sector is increasingly faced with several issues related to the rising of traffic demand such as congestion, energy consumption, noise, pollution, safety, etc.. Due to its low external and environmental costs, railway can be considered (together with inland waterways and short-sea-shipping) as a key factor for the sustainable development of a more competitive and resource-efficient transport system (European Commission, White Paper 2011). In order to reinforce the role of rail in European transport , there is a strong need of addressing the efficiency of the system and customers' satisfaction through targeted actions, i.e. rising reliability and quality of service. This becomes particularly pressing as many parts of the existing railway infrastructures are reaching their maximum capacity thus shrinking their capability to provide users and customers a higher or even adequate level of service. Taking also into account that transport demand forecasts for 2030 clearly show a marked increase of rail activity across the whole Europe, we aim to address the issue of rail congestion in the context of relevant policy questions: Is the actual rail Infrastructure really able to absorb forecasted traffic, without significant impacts on punctuality of the system? Would the already planned interventions on the European railway infrastructure guarantee an adequate available capacity and consequently adequate reliability and level of service? To which extent would the coveted competition in an open railway market be influenced by capacity scarcity, mainly during peak hours or along more profitable corridors? An accurate estimation of capacity of the rail network can help answer these questions, leading policy makers to better decisions and helping to minimize costs for users. In this context this report explores the issue of capacity scarcity and sets this issue in the context of other relevant policy issues (track access charges, cost/benefit and accessibility measures, maintenance programmes, freight services’ reliability, external, marginal congestion or scarcity cost for rail, impacts of climate changes, etc.), providing a methodological review of capacity and punctuality assessment procedures. To better explore the real applicability and the time and/or data constraints of each methodology, the study reports some practical applications to the European railway network. Finally in the last section the report discusses the topic from a modelling perspective, as the quantitative estimation of railway capacity constraints is a key issue in order to provide better support to transport policies at EU level.JRC.J.1-Economics of Climate Change, Energy and Transpor

Framework for integrated planning of bus and paratransit services in Indian cities

Public transport services in India and many other developing countries are provided by a combination of formal-Government led public transport systems and informal paratransit or Intermediate Public Transport (IPT) systems, which offer shuttle services along high demand corridors with passengers boarding and alighting at multiple points. Despite limited Government support, paratransit systems continue to thrive in many cities serving a crucial shared mobility need of users, without which cities would have more private vehicle usage. Due to their informal nature and the perceived competition to formal public transport systems, they have traditionally been either excluded from the public transport planning processes or designed as a feeder service to the formal transit system. The current thesis recognises paratransit’s role in serving end to end travel demand needs, particularly in developing economies with limited public transport supply and not just being a feeder to the formal public transport system. Hence, we develop an integrated planning framework that enables formal and informal public transport systems to operate as complementary systems towards meeting the mobility needs of the city. We proved an integrated planning framework based on comprehensive understanding of the demand and supply characteristics of both formal and informal systems which currently operate independently to realign services and complement each other. The tactical planning stage of public transport planning i.e. frequency setting was identified as the ideal stage of planning for integration of the two types of services. This will ensure continuity of their existing route networks and at the same time allow for paratransit services’ flexibility to switch operations between routes. Visakhapatnam, a representative medium sized Indian city with a significant presence of formal public transport in the form of city bus services and paratransit services provided by three-wheeler auto-rickshaws with a seating capacity of three to six passengers, was selected as the case city to demonstrate the methodology. A household survey based data collection and analysis methodology was adopted to analyse the socio-economic and travel demand characteristics of city bus and paratransit users. The variables impacting users’ choice between these two systems were derived through binary logistic regression. The high frequency and low occupancy paratransit systems were more popular among shorter trips, while longer trips preferred the fixed table bus systems. The operational characteristics of bus and paratransit systems were derived through a combination of primary surveys with paratransit operators and secondary data on the city bus operations. Data regarding their network of operation, services offered, passenger demand and revenue generated were collected for analysis. Buses perform a service function in the city by operating throughout the day and on a wider network, while paratransit operates with a profit motive only on high demand corridors and during peak hours. A Data Envelopment Analysis (DEA) based methodology was adopted to compare the performance efficiency of the two systems using a set of input and output indicators that define the performance of the two systems. Paratransit operations were identified to be more efficient compared to buses, due to their demand responsive operations. The lower efficiency of buses was also due to their service obligation to the city to provide affordable services throughout the day, even in areas with low demand. A bi-level transit assignment and frequency optimisation framework is developed to integrate formal bus and paratransit services. The lower-level of the model solves for the multi- modal transit assignment problem while the upper level solves for the integrated frequency optimisation problem. The transit assignment problem was solved from the users perspective i.e. to minimise their travel time through the user-equilibrium method. The frequency optimisation problem was solved using an integer programming formulation with the objective of minimising operational cost of bus and paratransit systems while meeting constraints like the travel demand on any link. The outputs from the optimisation exercise were used to quantify the impact of the public transport system at various levels i.e. users total travel time spent in the system, operators cost of providing the services and the overall impact on the society by estimating its road space requirement and emissions. Alternative user demand and transit supply scenarios were tested to assess their impacts on the society. The results show significant operational cost benefits of an integrated transit assignment and frequency planning approach where paratransit provides demand responsive services for short distance trips while formal public transport provides fixed schedule services on with broader network coverage. The analysis established the complimentary role played by bus and paratransit systems in meeting users travel demands. Therefore, it is recommended that cities harness both the systems towards meeting increasing travel needs of developing economies. Formal transit will continue to be the core of the public transport system, providing fixed route services, while paratransit can augment its capacity on high demand corridors and during peak hours. The planning and frequency optimisation framework developed in this thesis can help cities in identifying the modal-mix of fixed route public transport and on-demand services

Optimization of Number of Operators and Allocation of New Lines in an Oligopolistic Transit Market

This paper proposes a novel model for determining the optimal number of transit operators and the allocation of new lines in an oligopolistic transit market. The proposed model consists of three interrelated sub-models that are associated with three types of players; namely, transit authority, transit operators, and transit passengers. In practice, the operating cost per unit of transit line of each operator is decreasing in the number of lines that it operates. These effects which are referred to as the scale economies of transit operations are explicitly incorporated in the proposed model. On the basis of a logit-type transit passenger travel choice sub-model with elastic demand, the fares and frequencies of transit services are determined by an oligopolistic competitive equilibrium model (i. e. transit operator sub-model). The transit authority sub-model for optimization of the number of operators and the allocation of new lines is expressed as a 0-1 integer programming problem. It can be solved by an implicit enumeration heuristic solution algorithm. Numerical results show that both the scale economies and the market demand level have significant impacts on the optimal number of operators and the allocation schemes of new lines. Ignoring the effects of scale economies on transit operations may lead transit authorities to make biased decisions. © 2010 Springer Science+Business Media, LLC.postprin

Online Predictive Optimization Framework for Stochastic Demand-Responsive Transit Services

This study develops an online predictive optimization framework for dynamically operating a transit service in an area of crowd movements. The proposed framework integrates demand prediction and supply optimization to periodically redesign the service routes based on recently observed demand. To predict demand for the service, we use Quantile Regression to estimate the marginal distribution of movement counts between each pair of serviced locations. The framework then combines these marginals into a joint demand distribution by constructing a Gaussian copula, which captures the structure of correlation between the marginals. For supply optimization, we devise a linear programming model, which simultaneously determines the route structure and the service frequency according to the predicted demand. Importantly, our framework both preserves the uncertainty structure of future demand and leverages this for robust route optimization, while keeping both components decoupled. We evaluate our framework using a real-world case study of autonomous mobility in a university campus in Denmark. The results show that our framework often obtains the ground truth optimal solution, and can outperform conventional methods for route optimization, which do not leverage full predictive distributions.Comment: 34 pages, 12 figures, 5 table

Models and Solution Algorithms for Asymmetric Traffic and Transit Assignment Problems

Modeling the transportation system is important because it provides a “common ground” for discussing policy and examining the future transportation plan required in practices. Generally, modeling is a simplified representation of the real world; however, this research added value to the modeling practice by investigating the asymmetric interactions observed in the real world in order to explore potential improvements of the transportation modeling. The Asymmetric Transportation Equilibrium Problem (ATEP) is designed to precisely model actual transportation systems by considering asymmetric interactions of flows. The enhanced representation of the transportation system by the ATEP is promising because there are various asymmetric interactions in real transportation such as intersections, highway ramps, and toll roads and in the structure of the transit fares. This dissertation characterizes the ATEP with an appropriate solution algorithm and its applications. First, the research investigates the factors affecting the convergence of the ATEP. The double projection method is applied to various asymmetric types and complexities in the different sizes of networks in order to identify the influential factors including demand intensities, network configuration, route composition between modes, and sensitivity of the cost function. Secondly, the research develops an enhancement strategy for improvement in computational speed for the double projection method. The structural characteristics of the ATEP are used to develop the convergence enhancement strategy that significantly reduces the computational burdens. For the application side, instances of asymmetric interactions observed in in-vehicle crowding and the transit fare structure are modeled to provide a suggestion on policy approach for a transit agency. The direct application of the crowding model into the real network indicates that crowd modeling with multi user classes could influence the public transportation system planning and the revenue achievement of transit agencies. Moreover, addition of the disutility factor, crowding, not always causes the increase of disutility from the transit uses. The application of the non-additive fare structure in the Utah Transit Authority (UTA) network addresses the potential of the distance-based fare structure should the UTA make a transition to this fare structure from their current fare model. The analysis finds that the zero base fare has the highest potential for increasing the transit demand. However, collecting less than $0.50 with a certain buffer distance for the first boarding has potential for attracting the users to UTA\u27s transit market upon the fare structure change