Seungkyu Ryu

Transport Network Design Problem under Uncertainty: A Review and New Developments

This paper aims to provide a state-of-the-art review of the transport network design problem (NDP) under uncertainty and to present some new developments on a bi-objective-reliable NDP (BORNDP) model that explicitly optimizes the capacity reliability and travel time reliability under demand uncertainty. Both are useful performance measures that can describe the supply-side reliability and demand-side reliability of a road network. A simulation-based multi-objective genetic algorithm solution procedure, which consists of a traffic assignment algorithm, a genetic algorithm, a Pareto filter, and a Monte-Carlo simulation, is developed to solve the proposed BORNDP model. A numerical example based on the capacity enhancement problem is presented to demonstrate the tradeoff between capacity reliability and travel time reliability in the NDP.

L∞-Norm Path Flow Estimator for Handling Traffic Count Inconsistencies: Formulation and Solution Algorithm

Path flow estimator PFE is a single-level network observer proposed to estimate path flows and origin-destination flows from traffic counts in a transportation network. The PFE model handles the traffic count inconsistency problem by allowing user to specify appropriate error bounds or confidence interval on the traffic counts. This approach, although flexible, introduces a systematic bias in underestimating the total demand when improper error bounds are specified. This paper presents an L-norm PFE model that minimizes the systematic bias of the total demand estimate encountered in the PFE model by determining the least maximum absolute error needed to accommodate measurement errors and traffic count inconsistencies within the estimation process. A solution algorithm based on the dual formulation combined with a column generation procedure is developed for solving the proposed L-norm PFE model. Numerical results are presented to illustrate the features and applicability of the proposed L-norm PFE model and solution algorithm.

Modeling Physical and Environmental Side Constraints in Traffic Equilibrium Problem

ABSTRACT The traffic equilibrium problem plays an important role in urban transportation planning and management. It predicts vehicular flows on the transportation network by assigning travel demands given in terms of an origin-destination trip table to routes in a network according to some behavioral route choice rules. In this paper, we enhance the realism of the traffic equilibrium problem by explicit modeling various physical and environment restrictions as side constraints. These side constraints are a useful means for describing queuing and congestion effects, restraining traffic flows to limit the amount of emissions, and modeling different traffic control policies. A generalized side-constrained traffic equilibrium (GSCTE) model is presented and some characterizations of the equilibrium solutions are discussed. The model is formulated as a variational inequality problem and solved by a predictor-corrector decomposition algorithm. Two numerical experiments are conducted to demonstrate some properties of the GSCTE model and the convergence properties of the decomposition algorithm.

Computation and application of the paired combinatorial logit stochastic user equilibrium problem

The paired combinatorial logit (PCL) model is one of the recent extended logit models adapted to resolve the overlapping problem in the route choice problem, while keeping the analytical tractability of the logit choice probability function. However, the development of efficient algorithms for solving the PCL model under congested and realistic networks is quite challenging, since it has large-dimensional solution variables as well as a complex objective function. In this paper, we examine the computation and application of the PCL stochastic user equilibrium (SUE) problem under congested and realistic networks. Specifically, we develop an improved path-based partial linearization algorithm for solving the PCL SUE problem by incorporating recent advances in line search strategies to enhance the computational efficiency required to determine a suitable stepsize that guarantees convergence. A real network in the city of Winnipeg is applied to examine the computational efficiency of the proposed algorithm and the robustness of various line search strategies. In addition, in order to acquire the practical implications of the PCL SUE model, we investigate the effectiveness of how the PCL model handles the effects of congestion, stochasticity, and similarity in comparison with the multinomial logit stochastic traffic equilibrium problem and the deterministic traffic equilibrium problem.

A self-adaptive Armijo stepsize strategy with application to traffic assignment models and algorithms

Stepsize determination is an important component of algorithms for solving several mathematical formulations. In this article, a self-adaptive Armijo strategy is proposed to determine an acceptable stepsize in a more efficient manner. Instead of using a fixed initial stepsize in the original Armijo strategy, the proposed strategy allows the starting stepsize per iteration to be self-adaptive. Both the starting stepsize and the acceptable stepsize are thus allowed to decrease as well as increase by making use of the information derived from previous iterations. This strategy is then applied to three well-known algorithms for solving three traffic equilibrium assignment problems with different complexity. Specifically, we implement this self-adaptive strategy in the link-based Frank–Wolfe algorithm, the route-based disaggregate simplicial decomposition algorithm and the route-based gradient projection algorithm for solving the classical user equilibrium problem, the multinomial logit-based stochastic user equilibrium (MNL SUE) and the congestion-based C-logit SUE problem, respectively. Some numerical results are also provided to demonstrate the efficiency and applicability of the proposed self-adaptive Armijo stepsize strategy implemented in traffic assignment algorithms.

A modified gradient projection algorithm for solving the elastic demand traffic assignment problem

This paper develops a path-based traffic assignment algorithm for solving the elastic demand traffic assignment problem (EDTAP). A modified path-based gradient projection (GP) method combined with a column generation is suggested for solving the equivalent excess-demand reformulation of the problem in which the elastic demand problem is reformulated as a fixed demand problem through an appropriate modification of network representation. Numerical results using a set of real transportation networks are provided to demonstrate the efficiency of the modified GP algorithm for solving the excess-demand formulation of the EDTAP. In addition, a sensitivity analysis is conducted to examine the effects of the scaling parameter used in the elastic demand function on the estimated total demand, number of generated paths, number of used paths, and computational efforts of the modified GP algorithm.

Modeling Demand Elasticity and Route Overlapping in Stochastic User Equilibrium Through Paired Combinatorial Logit Model

In this paper an equivalent mathematical programming formulation is provided for modeling demand elasticity and route overlapping in the stochastic user equilibrium (SUE) problem. The elastic demand establishes the equilibrium between supply function and demand function on the basis of microeconomics. Because the elasticity of demand is an important factor in predicting the future demand pattern and avoiding the potential biased assessment in transportation planning, the elasticity of travel demand must be modeled endogenously. The route overlapping problem is handled by the paired combinatorial logit (PCL) model while retaining the analytical tractability of the logit choice probability function. The PCL SUE model with elastic demand (PCL-SUE-ED) explicitly models the elasticity of travel demand and the effect of route overlapping on travel choice and route choice simultaneously. A path-based partial linearization algorithm is also developed for solving the PCL-SUE-ED model. In addition, a self-regulated averaging line search strategy is incorporated into the algorithm to minimize the computational efforts required to determine a suitable step size that guarantees convergence. Numerical results are provided to examine the features of the PCL-SUE-ED model as well as the efficiency of the path-based partial linearization algorithm.

Solving the combined modal split and traffic assignment problem with two types of transit impedance function

The gradient projection (GP) algorithm has been shown as a successful path-based algorithm for solving various traffic assignment problems. In this paper, the GP algorithm is adapted for solving the combined modal split and traffic assignment (CMSTA) problem, which can be viewed as an elastic demand traffic equilibrium problem (EDTEP) with two modes. Using the excess-demand formulation of EDTEP, the CMSTA problem is reformulated and solved by a modified GP algorithm. Numerical results based on a real bi-modal network in the city of Winnipeg, Canada are provided to demonstrate the efficiency and robustness of the modified path-based GP algorithm for solving the CMSTA problem. In addition, the CMSTA problem is investigated with two types of impedance function for the transit mode and with different degrees of dispersion for the modal split function. The computational results show the modified GP algorithm outperforms the classical Evans algorithm for both types of transit impedance function, and it can be as efficient as the original GP algorithm for solving the traffic assignment problem with fixed demand.

Alternative Planning Tool for Small Metropolitan Planning Organization in Utah

Current practice in modeling network traffic for planning applications is a four-step travel demand forecasting model (trip generation, trip distribution, mode choice, and traffic assignment) that requires travel surveys and specialized technical staff to operate. Although such a modeling approach has been used in practice in major metropolitan planning organizations (MPOs), many small MPOs usually do not have sufficient resources to conduct travel surveys or to house technical staff for model development and maintenance. The purpose of this paper is to develop a simplified planning tool specifically targeted at small MPOs. A case study of a small MPO in Utah demonstrates how the tool can be implemented in practice.

Two-Stage Bicycle Traffic Assignment Model

AbstractCycling has been considered as a healthy, environmentally friendly, and economical alternative mode of travel to motorized vehicles (especially private motorized vehicles). However, bicycle...