I. Ömer Verbas

Time-Dependent Origin–Destination Demand Estimation: Challenges and Methods for Large-Scale Networks with Multiple Vehicle Classes

This paper proposes a modified bi-level optimization algorithm to estimate the time-dependent origin–destination trip matrices for large-scale networks with multiple vehicle classes. Methodologies are presented to overcome the challenges caused by the scale of the problem. The upper-level problem, a bound-constrained quadratic problem, had many variables and parameters for a network with around 68,000 links, 28,000 nodes, and 3,700 zones. Techniques to reduce the number of variables and parameters are described in this study, along with an approach to reduce the time and memory requirement of the lower-level problem. Furthermore, the basic approach, which had been applied only to a single vehicle class, was extended and adapted in this study to estimate matrices for single-occupancy and high-occupancy vehicles jointly. Two solution packages, MINOS and KNITRO, were tested for the upper-level problem. The solution package KNITRO was run with an option to use an interior point–conjugate gradient algorithm, which was well suited to large-scale nonlinear problems. The modified bi-level algorithm was applied to estimate the time-dependent demand patterns for the New York City regional network.

Stretching resources: sensitivity of optimal bus frequency allocation to stop-level demand elasticities

Bus transit route frequencies in practice are often set reactively, without consideration of ridership elasticity to the service frequency provided. Where elasticities are used in frequency allocation, a single across the board value or two respective values for peak and off-peak are used for the entire set of routes and stops throughout the day. With growing availability of ridership data, estimation of spatially and temporally disaggregated elasticities is possible. But do these make a difference in the resulting solution to the frequency allocation problem? This study is intended to examine this question by comparing the quality of solutions obtained using an optimal frequency allocation model with different sets of elasticities corresponding to varying levels of disaggregation. Three main methodologies for estimating ridership elasticity with respect to headway are compared in the context of a transit network frequency setting framework: (1) temporal elasticities based on time of day, (2) spatial elasticities via grouping stops into demand, supply and land use classes and (3) spatio-temporal elasticities using a linear regression model. Elasticities based only on temporal aggregation result in an underestimation of the potential improvements as compared to elasticities which account for some spatial characteristics, such as land use and the opportunity to transfer. It is also important to capture longer-term effects—over a year or more—because seasonal activity patterns may bias elasticity estimates over shorter time horizons.

Finding Least Cost Hyperpaths in Multimodal Transit Networks: Methodology, Algorithm, and Large-Scale Application

This paper presents a least cost hyperpath algorithm that captures the complexities that arise in a transit network because of the number of transfers, the standing and overcrowding penalties, the availability of walking and biking in addition to the transit modes, and the mode-specific limitations such as availability of bike parking. The problem was formulated as a mathematical program, and then a hybrid label setting–correcting algorithm was proposed as a solution. The multi-modal time- and approach-dependent algorithm does not require spatial or temporal expansion of the network; this feature results in good computational performance for large-scale applications. Scenario runs performed on the large-scale Chicago Transit Authority network, in Illinois, validate the accuracy and performance of the algorithm.

Dynamic Assignment-Simulation Methodology for Multimodal Urban Transit Networks

This paper presents an integrated transit assignment-simulation tool. Finding least cost hyperpaths in a large-scale network and assigning travelers onto these paths are computationally challenging problems. Moreover, modeling the spatial and temporal complexities in a transit network that result from the discontinuities in transit events, such as missing a connection and not receiving a seat, exacerbates the issue of capturing realism. These challenges are overcome by (a) using a least cost hyperpath algorithm that captures the multimodal, multipattern, time-, and approach-dependent features of a transit network to provide realistic optimal strategies; (b) using a gap-based assignment approach to reach fast convergence; and (c) developing a multiagent particle simulation platform that is able to capture the heterogeneities and the discontinuities in travel. The platform was tested on the Chicago Transit Authority network of 14,000 nodes and 64,000 links; 1.25 million travelers were assigned and simulated, along with 21,000 transit vehicles. The assignment-simulation framework can be used as a network evaluation tool to assist decision making at the strategic and operational levels.

Integrated Mode Choice and Dynamic Traveler Assignment in Multimodal Transit Networks: Mathematical Formulation, Solution Procedure, and Large-Scale Application

This paper introduces an integrated mode choice–multimodal transit assignment model and solution procedure intended for large-scale urban applications. The cross-nested logit mode choice model assigns travelers to car, transit, or park-and-ride. The dynamic multimodal transit assignment–simulation model determines minimum hyperpaths and assigns and simulates transit and park-and-ride travelers iteratively until the network approaches a state of equilibrium. After a given number of iterations, the updated transit network travel times are fed into the mode choice model and the model reassigns travelers to transit, car, or park-and-ride. The outer feedback loop between the mode choice model and the transit assignment model continues until the mode probabilities for each traveler do not change between iterations. A unique contribution of the method presented in this paper is that it reaches mode choice convergence with the use of disaggregate agents (travelers) instead of aggregate modal flows at the origin–destination level. The integrated model is successfully implemented on the Chicago Transit Agency’s bus and train network in Illinois. Different procedures for reaching convergence are tested; the results suggest that a gap-based formulation is more efficient than the method of successive averages.