A variational inequality model for dynamic route choice and algorithm

The nonlinear equation system approach to solving dynamic user optimal simultaneous route and departure time choice problems

19 - Variational Inequality Model of Ideal Dynamic User-Optimal Route Choice

Modeling passenger route choices is crucial for analyzing and predicting public transportation demand. One of the most popular methods is to use probabilistic route choice (PRC) models (also known as discrete choice models in general), which have broad applications in transportation, economics, politics, and other fields. However, its performance varies depending on the characteristics of the origin–destination (OD) trip data and should be examined carefully. This paper proposes a framework for validating the PRC model on its application to urban rail transit (URT) networks containing small‐scale OD trip data. The concept of small‐scale data is defined at first for each OD pair considering the desired confidence level and the variance of route choices. Then, a travel time range (TTR)‐based method is put forward to deduce passengers’ actual route choices as a benchmark for verifying PRC models. The difference and regularity analysis between the actual route choices and the model predictions are also performed with a twofold comparison. A case study on the Nanchang metro in China shows that the actual daily passenger volumes on routes of small‐scale OD pairs diverge remarkably from the estimations of the PRC model. The PRC model’s performance is further discussed when the small‐scale OD trip data accumulate to a larger scale over multiple days (e.g., several months). This study reveals the inherent limitation of PRC models in estimating the travel behaviors of passengers in a small‐scale population. Several practical implications are discussed to improve the route choice model and passenger flow analysis.

We use data from the Swiss national household travel survey to 1. analyze the socioeconomic determinants for intermodal travel in Switzerland and 2. estimate a first large-scale multimodal recursive logit route choice model for urban trip making. We show that intermodal travel is mostly associated with ownership of transit subscriptions, which allow free at the point-of-use public transportation. We also present a framework using open-source data to generate the multimodal network for the recursive logit model estimation. The fact that the model only needs a multimodal network to model the transport supply makes it independent of path sampling algorithms for the choice-set construction and it thus provides an alternative to classic mode and route choice models, since it can estimate mode and route choice parameters with directly observed routes, removing the sampling bias. By eliminating the need to sample alternative paths for estimation, it also simplifies the estimation process, making it a viable choice as an integral solution for joint route and mode choice modelling.

Modelling intermodal travel in Switzerland: A recursive logit approach

In order to simulate the transportation system of a large region dynamically, three things have to be known and modelled: who wants to go where at what departure time (destination choice), which route to the destination is selected (route choice), and finally how the locomotion along this route is performed in time (travelling). This article deals with the second and third question. Firstly, it is shown how the dynamic route choice problem could be solved by a simulation—based approach. Surprisingly, when comparing this approach to the classic static one, it turns out to be simpler and applicable to larger networks than its classical counterpart. Secondly, by using a simplified model of car—following, most of the phenomena observed in real traffic can be reproduced by the simulation. The realism achieved with this model allows a reliable estimation of the emissions caused by traffic (car traffic amounts to roughly 80% of the total travel volume). The model is numerically very efficient, enabling the simulation of large road networks with more than 1 million individual cars in real time Finally, preliminary results are mentioned concerning the possibility of expanding this simplified microscopic approach to the destination choice modelling. Following this route of thinking further finally leads to an integrated, microscopic, and dynamic approach to transportation planning and control. The first steps toward this aim has been done within the FVU.

This study introduces a novel simulation-based approach for addressing the stochastic Dynamic Traffic Assignment (DTA) problem, specifically targeting large, congested networks under dynamic conditions which is a characteristic of urban mobility environment. The proposed methodology leverages an underlying random walk model for route selection, drawing inspiration from the concept of equivalent impedance in electrical networks. This alternative route choice model iteratively condenses non-overlapping subnetworks into virtual links, allowing for the dynamic estimation of equivalent time-dependent virtual travel costs. Consequently, the downstream link choice probabilities for all destinations are computed, and by employing a random walk model, the route choice decision-making process is shifted to nodes. This approach closely aligns with travelers' real-life behavior, supporting a finer temporal segmentation of evolving traffic conditions and improving the precision of performance assessments. Furthermore, the route choice model addresses the limitations of other Markovian route choice models in handling overlapping routes and scaling issues.

This study introduces the novel concept of local detouredness, i.e. detours on subsections of a route, as a new phenomenon for understanding and modelling route choice. Traditionally, Stochastic User Equilibrium (SUE) traffic assignment models have been concerned with judging the attractiveness of a route by its total route cost. However, through empirical analysis we show that considering solely the global properties of a route is insufficient. We find that it is important to consider local detouredness both when determining realistic and tractable route choice sets and when determining route choice probabilities. For example, analysis of observed route choice data shows that route usage tends to decay with local detouredness, and that there is an apparent limit on the amount of local detouredness seen as acceptable. No existing models can account for this systematically and consistently, which is the motivation for the new route choice model proposed in this paper: the Bounded Choice Model with Local Detour Threshold (BCM-LDT). The BCM-LDT model incorporates the effect of local detouredness on route choice probability, and has an in-built mechanism that assigns zero probabilities to routes violating a bound on total route costs and/or a threshold on local detouredness. Thereby, the model consistently predicts which routes are used and unused. Moreover, the probability expression is closed-form and continuous. SUE conditions for the BCM-LDT are given, and solution existence is proven. Exploiting the special structure of the problem, a novel solution algorithm is proposed where flow averaging is integrated with a modified branch-and-bound method that iteratively column-generates all routes satisfying local and global bounds. Numerical experiments are conducted on small-scale and large-scale networks, establishing that equilibrated solutions can be found and demonstrating the influence of the BCM-LDT parameters on choice set size and flow allocation.

The unprecedented growth of passenger throughput in large airport terminals highlights the importance of analyzing passengers’ movement to achieve airport terminal’s elaborate management. Based on the theory of original social force model, video data from a departure hall of a large airport terminal in China were analyzed to summarize passengers’ path planning characteristics. Then, a double‐level model was established to describe passengers’ path planning behaviors. At the decision level of the proposed model, the avoiding force model including common avoiding force and additional horizontal avoiding force was established on the basis of setting time and space limitations for taking avoiding action and was used to describe passengers’ path planning in close‐range space. At the tactical level of the proposed model, the route and node choice models were established to describe passengers’ path planning in long‐range space. In the route choice model, a distribution of intermediate destination areas was proposed, with detouring distance, pedestrian density, speed difference, and pedestrian distribution considered in choosing an intermediate destination area. In the node choice model, the walking distance, the quantity of people waiting, and luggage were considered in choosing a check‐in counter or security check channel. The main parameters of the proposed model were confirmed according to video data. Simulation results show that the proposed model can simulate departure passengers’ path planning behaviors at an acceptable accuracy level.

The route choice problem is complicated in typical transportation networks because of the size of the choice set and because of the overlapping problem since many routes share links. Well-known models like the probit and the logit were further developed in an attempt to overcome these problems. The logit model has the appeal of being relatively close to the probit model while keeping a convenient analytical closed form. However, the simple multinomial logit model cannot correctly represent route choice, especially with respect to the overlapping problem. Other hierarchical logit models can potentially overcome the overlapping problem. The recently developed generalized nested logit (GNL) model is found to be very suitable for route choice, as is the cross-nested logit (CNL) model. The inclusion of the congestion effect in the route choice problem is accounted for in stochastic user equilibrium (SUE) problems. The development of a SUE formulation for the GNL model is presented. In addition, how to adapt the GNL model to route choice in a way similar to that of the CNL model is shown. An equivalent SUE formulation for the GNL model is developed. In this way, a unified framework is presented to relate GNL-type models, which are derived from discrete choice theory, with aggregate entropy formulations. A preliminary algorithm is developed to illustrate the potential application of the GNL formulation for real networks.

Handling uncertainty in route choice models: From probabilistic to possibilistic approaches

Adaptive route choice models are studied that explicitly capture travelers’ route choice adjustments according to information on realized network conditions in stochastic time-dependent networks. Two types of adaptive route choice models are explored: an adaptive path model in which a sequence of path choice models are applied at intermediate decision nodes and a routing policy choice model in which the alternatives correspond to routing policies rather than paths at the origin. A routing policy in this study is a decision rule that maps from all possible pairs (e.g., node, time) to the next links out of the node. Existing route choice models that can be estimated on disaggregate revealed preferences assume a deterministic network setting from the traveler's perspective and cannot capture the traveler's proactive adaptive behavior under uncertain traffic conditions. The literature includes a number of algorithmic studies of optimal routing policy problems, but the estimation of a routing policy choice model is a new research area. The specifications of estimating the two adaptive route choice models are established and the feasibility of estimation from path observations is demonstrated on an illustrative network. Prediction results from three models–nonadaptive path model, adaptive path model, and routing policy model–are compared. The routing policy model is shown to better capture the option value of diversion than the adaptive path model. The difference between the two adaptive models and the nonadaptive model is larger in terms of expected travel time if the network is more stochastic, indicating that the benefit of adaptivity is more significant in a more unpredictable network.

We formulate a joint dynamical traffic system that encompasses both route choice and traffic control in which the signal controller interacts with and adapts to the route choices of travelers, and vice versa. Travelers’ route choice dynamics are captured by a recurrence function, which governs the system evolution from day to day. Traffic control also adjusts its plan from day to day in response to the route choices of travelers. We show that this joint dynamical system has a set of fixed points in which both the user equilibrium is achieved and the traffic signal converges to a fixed-time plan. We address equilibrium stability and convergence of this joint dynamical system through analyzing the Jacobian matrix associated with each fixed point. We demonstrate the attraction domains of this joint problem and illustrate their importance and relevance for designing adaptive traffic control through some numerical examples.

Determinants of route choice behavior: A comparison of shop versus work trips using the Potential Path Area - Gateway (PPAG) algorithm and Path-Size Logit

This research focuses on improving cycle path design by analyzing the determinants of route choice for bicycle users. The study uses a large GPS dataset to develop a route choice model for the inner-city of Amsterdam. The main research question is to identify the factors that influence route choice decisions, which is broken down into sub-questions related to the contribution of the GPS dataset to route choice models, the relevant variables for bicycle users' route choices, and the effect of these variables on route choice. The study finds that route attributes, such as distance and cycle path quality, and contextual variables, such as trip type and time of day, have a significant effect on bicycle users' route choices. The results provide insights for designing more desirable bicycle infrastructure in urban areas.