Mark Hickman

An Analytic Stochastic Model for the Transit Vehicle Holding Problem

This paper describes an analytic model that determines the optimal vehicle holding time at a control stop along a transit route. This model is based on a stochastic transit service model presented by Andersson and Scalia-Tomba (1981) and enhanced by Marguier (1985). The use of a stochastic service model allows greater realism in the analytic modeling. Making use of these results, the paper presents an analytic model that may be used to determine the optimal holding time for a vehicle at a control stop. As it is formulated, the single vehicle holding problem is a convex quadratic program in a single variable, and is easily solved using gradient or line search techniques. The analytic holding model overcomes two noted problems in the literature: it includes stochastic service attributes of vehicle running times and passenger boarding and alighting processes, and the model may be used for real-time control purposes. The use and potential benefits of the model are illustrated in a simple example. This model may be useful in developing a computerized decision support system to enhance the effectiveness of transit operational decision-making.

PASSENGER TRAVEL TIME AND PATH CHOICE IMPLICATIONS OF REAL-TIME TRANSIT INFORMATION

Abstract This paper considers information systems in public transit in which the passenger receives information in real time regarding projected vehicle travel times. Such information systems may have value to passengers in situations where they may choose among different origin-to-destination paths. To provide a preliminary assessment of these systems, an analytic framework is presented to evaluate path choices and travel time benefits resulting from real-time information. A behavioral model of transit path choice is presented that frames the choice in terms of a decision whether to board a departing vehicle. Furthermore, this path choice model accommodates network travel times that are both stochastic and time-dependent, two elements that have been neglected in previous studies but are critical to evaluating real-time information systems. The path choice model is extended to demonstrate how real-time information may be incorporated by the passenger in making a path choice decision. This analytic framework is applied to a case study corridor at the Massachusetts Bay Transportation Authority (MBTA), using a computer simulation to model vehicle movements and passenger path choices in the corridor. The results suggest that real-time information yields only very modest improvements in passenger service measures such as the origin-to-destination travel times and the variability of trip times. Based on this analysis, the quantitative benefits of real-time information for transit passenger path choices appear to be questionable.

The Real-Time Stop-Skipping Problem

As a departure from previous studies on the stop–skipping control problem, this study investigates the possibility of implementing a stop–skipping policy for operations control in a real–time manner. Stop–skipping is investigated for a service disruption of varying length, occurring in the middle of a route, as a means of responding to the disruption more rapidly. Based on a preliminary analysis that shows that a basic stop–skipping policy may not be appropriate for real–time application, a policy alternative is constructed such that the control vehicle can still drop off passengers at stops in the skipping segment. The stop–skipping strategy is formulated separately for both policies as a nonlinear integer programming problem. The problem formulation includes assumptions of random distributions of passenger boardings and alightings, specifically with the binomial distribution and Poisson distribution representing the passenger alighting and boarding processes, respectively. The problem solution uses an exhaustive search method by taking advantage of the relatively small scale of the problem. A simulation study is conducted to examine how the performance of the two stop–skipping policies changes with the passenger distribution pattern, the service disruption location, the disruption length, as well as the vehicle travel time variability on the route. These simulation results suggest that both policies are not very sensitive to the travel time variability individually, when compared to other major factors. However, the travel time variability could contribute significantly to the difference in performance of the two policies because it affects the performance of the two policies in opposite ways. For both normal and downtown–oriented passenger distribution patterns, both policies perform similarly in term of total passenger waiting time reduction for a majority of cases. However, a significant difference in the performance of the two policies can still be seen for a large percentage of cases under varying circumstances. These results suggest that the downtown–oriented passenger distribution pattern may present the most desirable condition for the policy alternative. For the reverse–direction passenger distribution pattern, the policy alternative rarely outperforms the basic policy due to the inherent dynamics of the policy itself.

Methods of analyzing traffic imagery collected from aerial platforms

A limitation of most traditional methods of traffic data collection is that they rely on techniques that are strictly local in nature. Aerial imagery sensors can provide sufficient resolution to sense vehicle locations and movements across broader spatial and temporal scales. Digital imagery, global positioning systems, and automated image processing can be used to improve the spatial coverage, accuracy and cost-effectiveness of the data collection and reduction. In this paper, an approach for collecting and analyzing aerial imagery is given. To illustrate the value of the imagery, the paper outlines methods to generate estimates of speeds, travel times, densities, and queueing delays.

Chapter 2 Public Transit

Publisher Summary This chapter reviews a survey on the operations research literature applied to the domain of public transit, with a focus on recent contributions. It highlights a fruitful cooperation between the public transit agencies and the operations research community. Indeed, public transit has provided interesting and challenging problems to operations research, while operations research has been successful at solving efficiently several important public transit problems—for example, network design, timetabling, vehicle scheduling, and crew scheduling. New problems—the integration of vehicle and crew scheduling, bus parking and dispatching, as well as a wide variety of real-time control problems—that presents new challenges to the operations research community have also been studied recently. Research on these problems has already suggested innovative models and solution methodologies, which might be applicable in practice in a near future. The main goal of most transit agencies is to offer to the population a service of good quality that allows passengers to travel easily at a low fare. The agencies, thus, have a social mission that aims at reducing pollution and traffic congestion as well as increasing the mobility of the population.

Transit Service and Path Choice Models in Stochastic and Time-Dependent Networks

This paper develops a new path choice model that incorporates both time-dependent and stochastic transit service characteristics, and allows passengers to update path choice decisions while waiting. To develop this model, a new transit service model is proposed that represents route segments using a shuttle model. Such a model balances requirements for stochastic and time-dependent service modeling with the ability to aggregate to a larger transit corridor or network. This service model leads to a dynamic model of transit path choice, in which the passenger may wait until a vehicle is about to depart before making a boarding decision. A formal definition of this dynamic path choice model is given, and its differences with previous path choice models are noted. Based on this definition, two mathematical formulations of the dynamic model are developed. The first formulation assumes that the passenger will use the dynamic model for all possible vehicle departure times in the future, and is formulated as an optimal control problem. It is shown mathematically that this problem formulation is a less-constrained version of previous path choice models. However, because of some analytic and behavioral difficulties with this first model, a more well-behaved constrained formulation is also presented. A small corridor example demonstrates the significant differences in path choices and travel times between the constrained dynamic model and more traditional path choice models. Limitations of these dynamic path choice models are also discussed.

Computer-aided Systems in Public Transport

The scope of this volume centers on advancements in the state of art and the state of the practice in computer-aided systems in public transport. Yet, this volume illustrates a greater breadth of subjects in this area. The common theme remains the use of computer-aided methods and operations research techniques to improve: (1) information management; (2) network and route planning; (3) vehicle and crew scheduling and rostering; (4) vehicle monitoring and management; and, (5) practical experience with scheduling and public transport planning methods. This volume consists of selected papers presented at the Ninth International Conference on Computer-Aided Scheduling of Public Transport.

The Holding Problem at Multiple Holding Stations

Inherent stochasticity within the transit operating environment suggests there may be benefits of holding vehicles at more than one holding station on a route. In this paper, the holding problem at multiple holding stations considers holding vehicles at a given subset of stations on the route. By approximating the vehicle dwell time as the passenger boarding time, the holding problem at multiple holding stations can be modeled as a convex quadratic programming problem, with the objective function as a convex quadratic function subject to many linear constraints. This particular problem can be solved by a heuristic that decomposes the overall problem into sub-problems which can be solved to optimality. Also, a hypothetical numerical example is presented to illustrate the effectiveness of the problem formulation and heuristic.

Integrated Land Use-Transport Model System with Dynamic Time-Dependent Activity-Travel Microsimulation

The development of integrated land use–transport model systems has long been of interest because of the complex interrelationships between land use, transport demand, and network supply. This paper describes the design and prototype implementation of an integrated model system that involves the microsimulation of location choices in the land use domain, activity–travel choices in the travel demand domain, and individual vehicles on networks in the network supply modeling domain. Although many previous applications of integrated transport demand–supply models have relied on a sequential coupling of the models, the system presented in this paper involves a dynamic integration of the activity–travel demand model and the dynamic traffic assignment and simulation model with appropriate feedback to the land use model system. The system has been fully implemented, and initial results of model system runs in a case study test application suggest that the proposed model design provides a robust behavioral framework for simulation of human activity–travel behavior in space, time, and networks. The paper provides a detailed description of the design, together with results from initial test runs.

Trip purpose inference using automated fare collection data

In this paper, we exploit the extensive smart card transaction data for deriving useful information about transit passenger behavior, namely trip purpose or activity. We show how the automated fare collection data (e.g., smart card) can be used to infer trip purpose and to reveal travel patterns in an urban area. A case study demonstrates the process of trip purpose inference based on smart card data from Metro Transit in the Minneapolis/St. Paul metropolitan area.