Modeling Overlapping and Heterogeneous Perception Variance in Stochastic User Equilibrium Problem with Weibit Route Choice Model

In this study, a new SUE model using the Weibull random error terms is proposed as an alternative to overcome the drawbacks of the multinomial logit (MNL) SUE model. A path-size weibit (PSW) model is developed to relax both independently and identically distributed assumptions, while retaining an analytical closed-form solution. Specifically, this route choice model handles route overlapping through the path-size factor and captures the route-specific perception variance through the Weibull distributed random error terms. Both constrained entropy-type and unconstrained equivalent MP formulations for the PSW-SUE are provided. In addition, model extensions to consider the demand elasticity and combined travel choice of the PSW-SUE model are also provided. Unlike the logit-based model, these model extensions incorporate the logarithmic expected perceived travel cost as the network level of service to determine the demand elasticity and travel choice. Qualitative properties of these minimization programs are given to establish equivalency and uniqueness conditions. Both path-based and link-based algorithms are developed for solving the proposed MP formulations. Numerical examples show that the proposed models can produce a compatible traffic flow pattern compared to the multinomial probit (MNP) SUE model, and these models can be implemented in a real-world transportation network

A demand model with departure time choice for within-day dynamic traffic assignment

A within-clay dynamic demand model is formulated, embodying, in addition to the classic generation, distribution and modal split stages, an actual demand model taking into account departure time choice. The work focuses on this last stage, represented through an extension of the discrete choice framework to a continuous choice set. The dynamic multimodal supply and equilibrium model based on implicit path enumeration, which have been developed in previous work are outlined here, to define within-day dynamic elastic demand stochastic multimodal equilibrium as a fixed point problem on users flows and transit line frequencies. A MSA algorithm capable, in the case of Logit route choice models, of supplying equilibrium flows and frequencies on real dimension networks, is presented, as well as the specific procedures implementing the departure time choice and actual demand models. Finally, the results obtained on a test network are presented and conclusions are drawn. (c) 2005 Elsevier B.V. All rights reserved

Applications of sensitivity analysis for probit stochastic network equilibrium

Network equilibrium models are widely used by traffic practitioners to aid them in making decisions concerning the operation and management of traffic networks. The common practice is to test a prescribed range of hypothetical changes or policy measures through adjustments to the input data, namely the trip demands, the arc performance (travel time) functions, and policy variables such as tolls or signal timings. Relatively little use is, however, made of the full implicit relationship between model inputs and outputs inherent in these models. By exploiting the representation of such models as an equivalent optimisation problem, classical results on the sensitivity analysis of non-linear programs may be applied, to produce linear relationships between input data perturbations and model outputs. We specifically focus on recent results relating to the probit Stochastic User Equilibrium (PSUE) model, which has the advantage of greater behavioural realism and flexibility relative to the conventional Wardrop user equilibrium and logit SUE models. The paper goes on to explore four applications of these sensitivity expressions in gaining insight into the operation of road traffic networks. These applications are namely: identification of sensitive, ‘critical’ parameters; computation of approximate, re-equilibrated solutions following a change (post-optimisation); robustness analysis of model forecasts to input data errors, in the form of confidence interval estimation; and the solution of problems of the bi-level, optimal network design variety. Finally, numerical experiments applying these methods are reported

Route choice, travel time variability, and rational inattention

This paper sets up a rational inattention model for the route choice problem in a stochastic network where travelers face random travel time. Previous research has assumed that travelers incorporate all provided information without effort. This study assumes that information is costly and that travelers rationally choose how much information to acquire prior to choosing route. We begin with a single traveler and then extend the model to heterogeneous travelers where rationally inattentive user equilibrium (RIUE) is achieved. From the perspective of a single traveler, more information always reduces the impact of travel time variability and increases the probability of choosing a less costly route. However, in RIUE, more information may reduce the social welfare in some scenarios

A methodology for solving the network toll design problem

Congestion pricing has been regarded as an efficient method to reduce network-wide travel cost. In this dissertation, a methodology for toll design is developed to provide policy-makers with suggestions on both where to charge tolls and how much the tolls should be. As opposed to the traditional approach of marginal social cost pricing, this methodology is capable of dealing with the more realistic case, in which only a small number of links can be tolled. Furthermore, this methodology is expanded to accommodate multiple user groups. The toll design problem can be formulated using both deterministic and stochastic route choice models. The most natural formulation of this problem in both cases is a bilevel formulation. Such formulations are very difficult to solve because of the nonconvexity and nondifferentiability of the constraint set. In this dissertation, the problem is converted into a single level, standard nonlinear optimization problem by making certain simplifying assumption. This single-level version of the toll design problem can be solved using a variety of well-developed algorithms. Tests show that this approach can be used to generate reasonable results and provide valuable decision support to policy-makers

Route choice, travel time variability, and rational inattention

This paper sets up a rational inattention model for the route choice problem in a stochastic network where travelers face random travel time. Previous research has assumed that travelers incorporate all provided information without effort. This study assumes that information is costly and that travelers rationally choose how much information to acquire prior to choosing route. We begin with a single traveler and then extend the model to heterogeneous travelers where rationally inattentive user equilibrium (RIUE) is achieved. From the perspective of a single traveler, more information always reduces the impact of travel time variability and increases the probability of choosing a less costly route. However, in RIUE, more information may reduce the social welfare in some scenarios

Network Maintenance and Capacity Management with Applications in Transportation

abstract: This research develops heuristics to manage both mandatory and optional network capacity reductions to better serve the network flows. The main application discussed relates to transportation networks, and flow cost relates to travel cost of users of the network. Temporary mandatory capacity reductions are required by maintenance activities. The objective of managing maintenance activities and the attendant temporary network capacity reductions is to schedule the required segment closures so that all maintenance work can be completed on time, and the total flow cost over the maintenance period is minimized for different types of flows. The goal of optional network capacity reduction is to selectively reduce the capacity of some links to improve the overall efficiency of user-optimized flows, where each traveler takes the route that minimizes the traveler’s trip cost. In this dissertation, both managing mandatory and optional network capacity reductions are addressed with the consideration of network-wide flow diversions due to changed link capacities. This research first investigates the maintenance scheduling in transportation networks with service vehicles (e.g., truck fleets and passenger transport fleets), where these vehicles are assumed to take the system-optimized routes that minimize the total travel cost of the fleet. This problem is solved with the randomized fixed-and-optimize heuristic developed. This research also investigates the maintenance scheduling in networks with multi-modal traffic that consists of (1) regular human-driven cars with user-optimized routing and (2) self-driving vehicles with system-optimized routing. An iterative mixed flow assignment algorithm is developed to obtain the multi-modal traffic assignment resulting from a maintenance schedule. The genetic algorithm with multi-point crossover is applied to obtain a good schedule. Based on the Braess’ paradox that removing some links may alleviate the congestion of user-optimized flows, this research generalizes the Braess’ paradox to reduce the capacity of selected links to improve the efficiency of the resultant user-optimized flows. A heuristic is developed to identify links to reduce capacity, and the corresponding capacity reduction amounts, to get more efficient total flows. Experiments on real networks demonstrate the generalized Braess’ paradox exists in reality, and the heuristic developed solves real-world test cases even when commercial solvers fail.Dissertation/ThesisDoctoral Dissertation Industrial Engineering 201

Two new methods for solving the path‐based stochastic user equilibrium problem

In this paper, we present two new methods for the path-based logit stochastic user equilibrium problem, and investigate their convergence properties. First, a two level partial linearization method is proposed. Second, a dual method is developed. Both of these two methods use second order approximation of the objective function. Our novel methods are compared to Damberg's partial linearization method (Damberg, 1996), which is known to be one of the best performing methods. Numerical results on the Sioux Falls and Winnipeg networks show that, if properly scaled, our new methods can significantly improve the performance of Damberg’s method

A continuous model for coordinated pricing of mixed access modes to transit

The land-use pattern for many cities is a central business district surrounded by sprawling suburbs. This pattern can lead to an inefficient and congestion-prone transportation system due to a reliance on automobiles. This is because high-capacity transit is inefficient in low-density areas where insufficient travelers can access transit. This also poses an equity concern as the monetary cost of faster and more expensive travel disproportionately burdens low income travelers, especially when fixed congestion pricing is imposed. This paper presents a deterministic approximation of a discrete choice model for mixed access and mainline transportation modes, meaning that travelers may use different modes to access a mainline system, such as transit. The purpose is to provide a tractable computationally efficient model to address the first/last mile problem using a system-wide pricing policy that can account for heterogeneous values of time; a problem that is difficult to solve efficiently using a stochastic model. The model is structured for a catchment area around a central access point for a mainline mode, approximating choice by comparing modal utility costs. The underlying utility model accommodates both fixed prices (e.g., parking, fixed tolls, and fares) and distance-based unit prices (e.g. taxi fare, bike-share, and distance tolls) that may be set in a coordinated way with respect to value of time. Using numerical analysis to assess accuracy, the deterministic model achieved results within 3% of a stochastic logit-based model, and within 7% of measured values. The optimization of prices using the final model achieved a 22% reduction in generalized travel time and a 30% improvement in the Gini inequity measure from 0.2 to 0.14