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

The reliability-based stochastic transit assignment problem with elastic demand

This paper examines the reliability-based stochastic transit assignment problem with elastic demand. A Variational Inequality (VI) model for this problem is developed. The VI model considers capacity, waiting time and in-vehicle travel time as stochastic variables, and includes Spiess and Florian’s (1989) and de Cea and Fernández’s (1993) models as special cases. A reliability-based stochastic user equilibrium condition is defined to capture the route choice behavior of passengers. To illustrate the properties of the VI model, numerical studies were conducted on de Cea and Fernández’s (1993) network. The studies also show that Spiess and Florian’s and de Cea and Fernández’s models can overestimate the system performance substantially.postprin

Stochastic on-time arrival problem in transit networks

This article considers the stochastic on-time arrival problem in transit networks where both the travel time and the waiting time for transit services are stochastic. A specific challenge of this problem is the combinatorial solution space due to the unknown ordering of transit line arrivals. We propose a network structure appropriate to the online decision-making of a passenger, including boarding, waiting and transferring. In this framework, we design a dynamic programming algorithm that is pseudo-polynomial in the number of transit stations and travel time budget, and exponential in the number of transit lines at a station, which is a small number in practice. To reduce the search space, we propose a definition of transit line dominance, and techniques to identify dominance, which decrease the computation time by up to 90% in numerical experiments. Extensive numerical experiments are conducted on both a synthetic network and the Chicago transit network.Comment: 29 pages; 12 figures. This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0

Optimal route design of electric transit networks considering travel reliability

Travel reliability is the most essential determinant for operating the transit system and improving its service level. In this study, an optimization model for the electric transit route network design problem is proposed, under the precondition that the locations of charging depots are predetermined. Objectives are to pursue maximum travel reliability and meanwhile control the total cost within a certain range. Constraints about the bus route and operation are also considered. A Reinforcement Learning Genetic Algorithm is developed to solve the proposed model. Two case studies including the classic Mandl\u27s road network and a large road network in the context of Zhengzhou city are conducted to demonstrate the effectiveness of the proposed model and the solution algorithm. Results suggest that the proposed methodology is helpful for improving the travel reliability of the transit network with minimal cost increase

Dynamic traffic assignment: model classifications and recent advances in travel choice principles

Dynamic Traffic Assignment (DTA) has been studied for more than four decades and numerous reviews of this research area have been conducted. This review focuses on the travel choice principle and the classification of DTA models, and is supplementary to the existing reviews. The implications of the travel choice principle for the existence and uniqueness of DTA solutions are discussed, and the interrelation between the travel choice principle and the traffic flow component is explained using the nonlinear complementarity problem, the variational inequality problem, the mathematical programming problem, and the fixed point problem formulations. This paper also points out that all of the reviewed travel choice principles are extended from those used in static traffic assignment. There are also many classifications of DTA models, in which each classification addresses one aspect of DTA modeling. Finally, some future research directions are identified.postprin

The line planning routing game

In this paper, we propose a novel algorithmic approach to solve line planning problems. To this end, we model the line planning problem as a game where the passengers are players which aim at minimizing individual objective functions composed of travel time, transfer penalties, and a share of the overall cost of the solution. To find equilibria of this routing game, we use a best-response algorithm. We investigate, under which conditions on the line planning model a passenger’s best-response can be calculated efficiently and which properties are needed to guarantee convergence of the best-response algorithm. Furthermore, we determine the price of anarchy which bounds the objective value of an equilibrium with respect to a system- optimal solution of the line planning problem. For problems where best-responses cannot be found efficiently, we propose heuristic methods. We demonstrate our findings on some small computational examples

Price of anarchy for reliability-based traffic assignment and network design

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Least Expected Time Paths in Stochastic Schedule-Based Transit Networks

We consider the problem of determining a least expected time (LET) path that minimizes the number of transfers and the expected total travel time in a stochastic schedule-based transit network. A time-dependent model is proposed to represent the stochastic transit network where vehicle arrival times are fully stochastically correlated. An exact label-correcting algorithm is developed, based on a proposed dominance condition by which Bellman’s principle of optimality is valid. Experimental results, which are conducted on the Ho Chi Minh City bus network, show that the running time of the proposed algorithm is suitable for real-time operation, and the resulting LET paths are robust against uncertainty, such as unknown traffic scenarios

A new schedule-based transit assignment model with travel strategies and supply uncertainties

This paper proposes a new scheduled-based transit assignment model. Unlike other schedule-based models in the literature, we consider supply uncertainties and assume that users adopt strategies to travel from their origins to their destinations. We present an analytical formulation to ensure that on-board passengers continuing to the next stop have priority and waiting passengers are loaded on a first-come-first-serve basis. We propose an analytical model that captures the stochastic nature of the transit schedules and in-vehicle travel times due to road conditions, incidents, or adverse weather. We adopt a mean variance approach that can consider the covariance of travel time between links in a space–time graph but still lead to a robust transit network loading procedure when optimal strategies are adopted. The proposed model is formulated as a user equilibrium problem and solved by an MSA-type algorithm. Numerical results are reported to show the effects of supply uncertainties on the travel strategies and departure times of passengers.postprin