Maintenance optimization for transportation systems with demand responsiveness

We present a quadratic programming framework to address the problem of finding optimal maintenance policies for multifacility transportation systems. The proposed model provides a computationally-appealing framework to support decision making, while accounting for functional interdependencies that link the facilities that comprise these systems. In particular, the formulation explicitly captures the bidirectional relationship between demand and deterioration. That is, the state of a facility, i.e., its condition or capacity, impacts the demand/traffic; while simultaneously, demand determines a facility’s deterioration rate. The elements that comprise transportation systems are linked because the state of a facility can impact demand at other facilities. We provide a series of numerical examples to illustrate the advantages of the proposed framework. Specifically, we analyze simple network topologies and traffic patterns where it is optimal to coordinate (synchronize or alternate) interventions for clusters of facilities in transportation systems.     

Economic resilience to transportation failure: a computable general equilibrium analysis

This study develops and applies a multimodal computable general equilibrium (CGE) framework to investigate the role of resilience in the economic consequences of transportation system failures. Vulnerability and economic resilience of different modes of transportation infrastructure, including air, road, rail, water and local transit, are assessed using a CGE model that incorporates various resilience tactics including modal substitution, trip conservation, excess capacity, relocation/rerouting, and service recapture. The linkages between accessibility, vulnerability, and resilience are analyzed. The model is applied to the transportation system failures in the aftermath of Hurricane Katrina to illustrate its capabilities. The analytical framework, however, has broader applications and can provide insights for resource allocations to enhance emergent responses to unexpected events and to improve resilient design of transportation infrastructure systems.     

Dynamic activity-travel assignment in multi-state supernetworks

The integration of activity-based modeling and dynamic traffic assignment for travel demand analysis has recently attracted ever-increasing attention. However, related studies have limitations either on the integration structure or the number of choice facets being captured. This paper proposes a formulation of dynamic activity-travel assignment (DATA) in the framework of multi-state supernetworks, in which any path through a personalized supernetwork represents a particular activity-travel pattern (ATP) at a high level of spatial and temporal detail. DATA is formulated as a discrete-time dynamic user equilibrium (DUE) problem, which is reformulated as an equivalent variational inequality (VI) problem. A generalized dynamic link disutility function is established with the accommodation of different characteristics of the links in the supernetworks. Flow constraints and non-uniqueness of equilibria are also investigated. In the proposed formulation, the choices of departure time, route, mode, activity sequence, activity and parking location are all unified into one time-dependent ATP choice. As a result, the interdependences among all these choice facets can be readily captured. A solution algorithm based on the route-swapping mechanism is adopted to find the user equilibrium. A numerical example with simulated scenarios is provided to demonstrate the advantages of the proposed approach.     

Complementarity formulations for the cell transmission model based dynamic user equilibrium with departure time choice, elastic demand and user heterogeneity

In this paper we formulate the dynamic user equilibrium problem with an embedded cell transmission model on a network with a single OD pair, multiple parallel paths, multiple user classes with elastic demand. The formulation is based on ideas from complementarity theory. The travel time is estimated based on two methods which have different transportation applications: (1) maximum travel time and (2) average travel time. These travel time functions result in linear and non-linear complementarity formulations respectively. Solution existence and the properties of the formulations are rigorously analyzed. Extensive computational experiments are conducted to demonstrate the benefits of the proposed formulations on various test networks.     

Dynamic user equilibrium with side constraints for a traffic network: Theoretical development and numerical solution algorithm

This paper investigates a traffic volume control scheme for a dynamic traffic network model which aims to ensure that traffic volumes on specified links do not exceed preferred levels. The problem is formulated as a dynamic user equilibrium problem with side constraints (DUE-SC) in which the side constraints represent the restrictions on the traffic volumes. Travelers choose their departure times and routes to minimize their generalized travel costs, which include early/late arrival penalties. An infinite-dimensional variational inequality (VI) is formulated to model the DUE-SC. Based on this VI formulation, we establish an existence result for the DUE-SC by showing that the VI admits at least one solution. To analyze the necessary condition for the DUE-SC, we restate the VI as an equivalent optimal control problem. The Lagrange multipliers associated with the side constraints as derived from the optimality condition of the DUE-SC provide the traffic volume control scheme. The control scheme can be interpreted as additional travel delays (either tolls or access delays) imposed upon drivers for using the controlled links. This additional delay term derived from the Lagrange multiplier is compared with its counterpart in a static user equilibrium assignment model. If the side constraint is chosen as the storage capacity of a link, the additional delay can be viewed as the effort needed to prevent the link from spillback. Under this circumstance, it is found that the flow is incompressible when the link traffic volume is equal to its storage capacity. An algorithm based on Euler’s discretization scheme and nonlinear programming is proposed to solve the DUE-SC. Numerical examples are presented to illustrate the mechanism of the proposed traffic volume control scheme.     

Infrastructure deployment under uncertainties and competition: The biofuel industry case

Technological paradigm shifts often come with a newly emerging industry that seeks a viable infrastructure deployment plan to compete against established competitors. Such phenomenon has been repeatedly seen in the field of transportation systems, such as those related to the booming bioenergy production, among others. We develop a game-theoretic modeling framework using a continuum approximation scheme to address the impacts of competition on the optimal infrastructure deployment. Furthermore, we extend the model to incorporate uncertainties in supply/demand and the risk of facility disruptions. Analytical properties of the optimal infrastructure system are obtained, based on which fast numerical solution algorithms are developed. Several hypothetical problem instances are used to illustrate the effectiveness of the proposed algorithms and to quantify the impacts of various system parameters. A large-scale biofuel industry case study for the U.S. Midwest is conducted to obtain additional managerial insights.     

Integrated planning of static and dynamic charging infrastructure for electric vehicles

This paper investigates the optimal deployment of static and dynamic charging infrastructure considering the interdependency between transportation and power networks. Static infrastructure means plug-in charging stations, while the dynamic counterpart refers to electrified roads or charging lanes enabled by charging-while-driving technology. A network equilibrium model is first developed to capture the interactions among battery electric vehicles’ (BEVs) route choices, charging plans, and the prices of electricity. A mixed-integer bi-level program is then formulated to determine the deployment plan of charging infrastructure to minimize the total social cost of the coupled networks. Numerical examples are provided to demonstrate travel and charging plans of BEV drivers and the competitiveness of static and dynamic charging infrastructure. The numerical results on three networks suggest that (1) for individual BEV drivers, the choice between using charging lanes and charging stations is more sensitive to parameters including value of travel time, service fee markup, and battery size, but less sensitive to the charging rates and travel demand; (2) deploying more charging lanes is favorable for transportation networks with sparser topology while more charging stations can be more preferable for those denser networks.     

On the flexibility of using marginal distribution choice models in traffic equilibrium

Traffic equilibrium models are fundamental to the analysis of transportation systems. The stochastic user equilibrium (SUE) model which relaxes the perfect information assumption of the deterministic user equilibrium is one such model. The aim of this paper is to develop a new user equilibrium model, namely the MDM-SUE model, that uses the marginal distribution model (MDM) as the underlying route choice model. In this choice model, the marginal distributions of the path utilities are specified but the joint distribution is not. By focusing on the joint distribution that maximizes expected utility, we show that MDM-SUE exists and is unique under mild assumptions on the marginal distributions. We develop a convex optimization formulation for the MDM-SUE. For specific choices of marginal distributions, the MDM-SUE model recreates the optimization formulation of logit SUE and weibit SUE. Moreover, the model is flexible since it can capture perception variance scaling at the route level and allows for modeling different user preferences by allowing for skewed distributions and heavy tailed distributions. The model can also be generalized to incorporate bounded support distributions and discrete distributions which allows to distinguish between used and unused routes within the SUE framework. We adapt the method of successive averages to develop an efficient approach to compute MDM-SUE traffic flows. In our numerical experiments, we test the ability of MDM-SUE to relax the assumption that the error terms are independently and identically distributed random variables as in the logit models and study the additional modeling flexibility that MDM-SUE provides on small-sized networks as well as on the large network of the city of Winnipeg. The results indicate that the model provides both modeling flexibility and computational tractability in traffic equilibrium.     

Modeling the choice continuum: an integrated model of residential location,auto ownership,bicycle ownership,and commute tour mode choice decisions

The integrated modeling of land use and transportation choices involves analyzing a continuum of choices that characterize people’s lifestyles across temporal scales. This includes long-term choices such as residential and work location choices that affect land-use, medium-term choices such as vehicle ownership, and short-term choices such as travel mode choice that affect travel demand. Prior research in this area has been limited by the complexities associated with the development of integrated model systems that combine the long-, medium- and short-term choices into a unified analytical framework. This paper presents an integrated simultaneous multi-dimensional choice model of residential location, auto ownership, bicycle ownership, and commute tour mode choices using a mixed multidimensional choice modeling methodology. Model estimation results using the San Francisco Bay Area highlight a series of interdependencies among the multi-dimensional choice processes. The interdependencies include: (1) self-selection effects due to observed and unobserved factors, where households locate based on lifestyle and mobility preferences, (2) endogeneity effects, where any one choice dimension is not exogenous to another, but is endogenous to the system as a whole, (3) correlated error structures, where common unobserved factors significantly and simultaneously impact multiple choice dimensions, and (4) unobserved heterogeneity, where decision-makers show significant variation in sensitivity to explanatory variables due to unobserved factors. From a policy standpoint, to be able to forecast the “true” causal influence of activity-travel environment changes on residential location, auto/bicycle ownership, and commute mode choices, it is necessary to capture the above-identified interdependencies by jointly modeling the multiple choice dimensions in an integrated framework.     

Optimal deployment of public charging stations for plug-in hybrid electric vehicles

This paper develops an equilibrium modeling framework that captures the interactions among availability of public charging opportunities, prices of electricity, and destination and route choices of plug-in hybrid electric vehicles (PHEVs) at regional transportation and power transmission networks coupled by PHEVs. The modeling framework is then applied to determine an optimal allocation of a given number of public charging stations among metropolitan areas in the region to maximize social welfare associated with the coupled networks. The allocation model is formulated as a mathematical program with complementarity constraints, and is solved by an active-set algorithm. Numerical examples are presented to demonstrate the models and offer insights on the equilibrium of the coupled transportation and power networks, and optimally allocating resource for public charging infrastructure.     

Optimal competitive freight network design as hierarchical variational inequalities programming problems

Freight networks are a case of systems that multiple participants are composing interrelations along the complete supply chain. Their interrelations correspond to alternative behavior, namely, cooperation, non-cooperation and competition, while they are large-scale spatially distributed systems combining multiple means of transportation and the infrastructure and equipment typically utilized for servicing demand, results to a complex system integration. In this paper, the case of the optimal design of freight networks is investigated, aiming to highlight the particularities emerging in this case of transportation facilities strategic and/or operational planning and the multiple game-theoretic and equilibrium problems that are structured in cascade and in hierarchies. The application that is investigated here focuses in the design of a significant ‘player’ of the freight supply chain, namely container terminals, while the proposed framework will aim on analyzing investment strategies built on integrated demand–supply models and the optimal network design format. The approach will build on the multilevel Mathematical Programming with Equilibrium Constraints (MPECs) formulation, but is further extended to cope with the properties introduced by the ‘designers’ (infrastructure authorities), shippers and carriers competition in all levels of MPECs. Since container terminals are typically competing each other, the nomenclature used here for formulating appropriate MPECs problems are based on hierarchies of Variational Inequalities (VI) problems, able to capture the alternative relationships emerging in realistic freight supply chains. The proposed formulations of the competitive network design case is addressed by a novel approach of co-evolutionary agents, which can be regarded as new in equilibrium estimation. Finally, the results are compared with alternative network design cases, namely the centralized cooperative and exchanging design. Under this analysis it is able to highlight the differences among alternative design cases, but moreover an estimation of the ‘price of anarchy’ in transportation systems design is offered, an element of both theoretical as well as practical relevance.     

A network enhancement model with integrated lane reorganization and traffic control strategies

Lane reorganization strategies such as lane reversal, one‐way street, turning restriction, and cross elimination have demonstrated their effectiveness in enhancing transportation network capacity. However, how to select the most appropriate combination of those strategies in a network remains challenging to transportation professionals considering the complex interactions among those strategies and their impacts on conventional traffic control components. This article contributes to developing a mathematical model for a traffic equilibrium network, in which optimization of lane reorganization and traffic control strategies are integrated in a unified framework. The model features a bi‐level structure with the upper‐level model describing the decision of the transportation authorities for maximizing the network capacity. A variational inequality (VI) formulation of the user equilibrium (UE) behavior in choosing routes in response to various strategies is developed in the lower level. A genetic algorithm (GA) based heuristic is used to yield meta‐optimal solutions to the model. Results from extensive numerical analyses reveal the promising property of the proposed model in enhancing network capacity and reducing congestion. Copyright © 2016 John Wiley & Sons, Ltd.     

Approximate network loading and dual-time-scale dynamic user equilibrium

In this paper we present a dual-time-scale formulation of dynamic user equilibrium (DUE) with demand evolution. Our formulation belongs to the problem class that Pang and Stewart (2008) refer to as differential variational inequalities. It combines the within-day time scale for which route and departure time choices fluctuate in continuous time with the day-to-day time scale for which demand evolves in discrete time steps. Our formulation is consistent with the often told story that drivers adjust their travel demands at the end of every day based on their congestion experience during one or more previous days. We show that analysis of the within-day assignment model is tremendously simplified by expressing dynamic user equilibrium as a differential variational inequality. We also show there is a class of day-to-day demand growth models that allow the dual-time-scale formulation to be decomposed by time-stepping to yield a sequence of continuous time, single-day, dynamic user equilibrium problems. To solve the single-day DUE problems arising during time-stepping, it is necessary to repeatedly solve a dynamic network loading problem. We observe that the network loading phase of DUE computation generally constitutes a differential algebraic equation (DAE) system, and we show that the DAE system for network loading based on the link delay model (LDM) of Friesz et al. (1993) may be approximated by a system of ordinary differential equations (ODEs). That system of ODEs, as we demonstrate, may be efficiently solved using traditional numerical methods for such problems. To compute an actual dynamic user equilibrium, we introduce a continuous time fixed-point algorithm and prove its convergence for effective path delay operators that allow a limited type of nonmonotone path delay. We show that our DUE algorithm is compatible with network loading based on the LDM and the cell transmission model (CTM) due to Daganzo (1995). We provide a numerical example based on the much studied Sioux Falls network.     

Dynamic user optimal traffic assignment on congested multidestination networks

An equivalent continuous time optimal control problem is formulated to predict the temporal evolution of traffic flow pattern on a congested multiple origin-destination network, corresponding to a dynamic generalization of Wardropian user equilibrium. Optimality conditions are derived using the Pontryagin minimum principle and given economic interpretations, which are generalizations of similar results previously reported for single-destination networks. Analyses of sufficient conditions for optimality and of singular controls are also given. Under the steady-state assumptions, the model is shown to be a proper dynamic extension of Beckmann's mathematical programming problem for a static user equilibrium traffic assignment.     

An integrated modelling approach for the bicriterion vehicle routing and scheduling problem with environmental considerations

The consideration of pollution in routing decisions gives rise to a new routing framework where measures of the environmental implications are traded off with business performance measures. To address this type of routing decisions, we formulate and solve a bi-objective time, load and path-dependent vehicle routing problem with time windows (BTL-VRPTW). The proposed formulation incorporates a travel time model representing realistically time varying traffic conditions. A key feature of the problem under consideration is the need to address simultaneously routing and path finding decisions. To cope with the computational burden arising from this property of the problem we propose a network reduction approach. Computational tests on the effect of the network reduction approach on determining non-dominated solutions are reported. A generic solution framework is proposed to address the BTL-VRPTW. The proposed framework combines any technique that creates capacity-feasible routes with a routing and scheduling method that aims to convert the identified routes to problem solutions. We show that transforming a set of routes to BTL-VRPTW solutions is equivalent to solving a bi-objective time dependent shortest path problem on a specially structured graph. We propose a backward label setting technique to solve the emerging problem that takes advantage of the special structure of the graph. The proposed generic solution framework is implemented by integrating the routing and scheduling method into an Ant Colony System algorithm. The accuracy of the proposed algorithm was assessed on the basis of its capability to determine minimum travel time and fuel consumption solutions. Although the computational results are encouraging, there is ample room for future research in algorithmic advances on addressing the proposed problem.     

Modeling user adoption of advanced traveler information systems: a control theoretic approach for optimal endogenous growth

This study is a subsequent development of the dynamic evolution model of the market penetration of advanced traveler information systems (ATIS) proposed by Yang and Meng [Transport. Res. A 35 (2001) 895]. In previous study we have shown that a benefit-driven, user-optimal ATIS market does not necessarily lead to a socially optimal growth and optimal stationary equilibrium level of market penetration of ATIS products or services. The current study proposes an optimal time-dependent service pricing strategy so as to minimize total system cost throughout the time horizon of growth or optimally reach a socially desirable target level of ATIS market penetration in a final stationary equilibrium. We formulate the problem of interest as an optimal control problem and propose an efficient solution algorithm together with a numerical demonstration of the characteristics of the study problem.     

A cell transmission model for dynamic lane reversal with autonomous vehicles

Autonomous vehicles admit consideration of novel traffic behaviors such as reservation-based intersection controls and dynamic lane reversal. We present a cell transmission model formulation for dynamic lane reversal. For deterministic demand, we formulate the dynamic lane reversal control problem for a single link as an integer program and derive theoretical results. In reality, demand is not known perfectly at arbitrary times in the future. To address stochastic demand, we present a Markov decision process formulation. Due to the large state size, the Markov decision process is intractable. However, based on theoretical results from the integer program, we derive an effective heuristic. We demonstrate significant improvements over a fixed lane configuration both on a single bottleneck link with varying demands, and on the downtown Austin network.     

Projecting adoption of truck powertrain technologies and CO2 emissions in line-haul networks

In this paper we present a mixed-integer linear program to represent the decision-making process for heterogeneous fleets selecting vehicles and allocating them on freight delivery routes to minimize total cost of ownership. This formulation is implemented to project alternative powertrain technology adoption and utilization trends for a set of line-haul fleets operating on a regional network. Alternative powertrain technologies include compressed (CNG) and liquefied natural gas (LNG) engines, hybrid electric diesel, battery electric (BE), and hydrogen fuel cell (HFC). Future policies, economic factors, and availability of fueling and charging infrastructure are input assumptions to the proposed modeling framework. Powertrain technology adoption, vehicle utilization, and resulting CO₂ emissions predictions for a hypothetical, representative regional highway network are illustrated. A design of experiments (DOE) is used to quantify sensitivity of adoption outcomes to variation in vehicle performance parameters, fuel costs, economic incentives, and fueling and charging infrastructure considerations. Three mixed-adoption scenarios, including BE, HFC, and CNG vehicle market penetration, are identified by the DOE study that demonstrate the potential to reduce cumulative CO₂ emissions by more than 25% throughout the period of study.     

Integrating mesoscopic dynamic traffic assignment with agent-based travel behavior models for cumulative land development impact analysis

A number of approaches have been developed to evaluate the impact of land development on transportation infrastructure. While traditional approaches are either limited to static modeling of traffic performance or lack a strong travel behavior foundation, today’s advanced computational technology makes it feasible to model an individual traveler’s response to land development. This study integrates dynamic traffic assignment (DTA) with a positive agent-based microsimulation travel behavior model for cumulative land development impact studies. The integrated model not only enhances the behavioral implementation of DTA, but also captures traffic dynamics. It provides an advanced yet practical approach to understanding the impact of a single or series of land development projects on an individual driver’s behavior, as well as the aggregated impacts on the demand pattern and time-dependent traffic conditions. A simulation-based optimization (SBO) approach is proposed for the calibration of the modeling system. The SBO calibration approach enhances the transferability of this integrated model to other study areas. Using a case study that focuses on the cumulative land development impact along a congested corridor in Maryland, various regional and local travel behavior changes are discussed to show the capability of this tool for behavior side estimations and the corresponding traffic impacts.