Hierarchical network-based equilibrium model and algorithm for a mixed-traffic urban transport system

Abstract

Many equilibrium models and algorithms based on homogeneous motorized traffic have been devised to model urban transport systems in developed countries, but they are inadequate when it comes to represent mixed-traffic urban transport systems, including automobiles, transit, bicycles, and pedestrians, in developing countries such as China or India. In these cases, traffic flow on a road segment is an aggregated result of travellers' combined mode/route choices and corresponding interactions. Therefore, a special assignment model and algorithm are needed for modeling these distinct behaviors. In this article, the structure of a mixed-traffic urban transport system is analyzed and then expanded and represented using a hierarchical network model based on graph theory. Based on the analysis of travelers' combined mode/route choices, generalized travel cost functions and link impedance functions for different modes are formulated, where the interferences between different modes on the same road segments are taken into account. Due to the ‘asymmetric’ nature of these functions, a variational inequality model is proposed to represent the equilibrium assignment problem in a mixed-traffic urban transport system. The corresponding solution algorithm is also presented. Finally, a numerical example is provided to illustrate the practicality of the proposed model and algorithm.     

Electric vehicle park-charge-ride programs: A planning framework and case study in Chicago

In suburban areas, combining the use of electric vehicles (EV) and transit systems in an EV Park-Charge-Ride (PCR) approach can potentially help improve transit accessibility, facilitate EV charging and adoption, and reduce the need for long-distance driving and ensuing impacts. Despite the anticipated growth of EV adoption and charging demand, PCR programs are limited. With a focus on multi-modal trips, this study proposes a generic planning process that integrates EV infrastructure development with transit systems, develops a systematic assessment approach to fostering the PCR adoption, and illustrates a case implementation in Chicago. Specifically, this study develops a Suitability Index (SI) for EV charging locations at parking spots that are suitable for both EV charging and transit connections. SI can be customized for short-term and long-term planning scenarios. SI values are derived in Chicago as an example for (1) commuter rail stations (for work trips), and (2) shopping centers near transit stops as potential opportunities for additional weekday parking and EV charging (for multi-purpose trips/MPT). Furthermore, carbon emissions and vehicle miles travelled (VMT) across various travel modes and trip scenarios (i.e., work trips and MPT) are calculated. Compared to the baseline of driving a conventional vehicle, this study found that an EV PCR commuter can reduce up to 87% of personal VMT and 52% of carbon emissions. A more active role of the public sector in the PCR program development is recommended.     

Linking land use with household vehicle emissions in the central puget sound: methodological framework and findings

A leading cause of air pollution in many urban regions is mobile source emissions that are largely attributable to household vehicle travel. While household travel patterns have been previously related with land use in the literature (Crane, R., 1996. Journal of the American Planning Association 62 (1, Winter); Cervero, R. and Kockelman, C., 1997. Transportation Research Part D 2 (3), 199–219), little work has been conducted that effectively extends this relationship to vehicle emissions. This paper describes a methodology for quantifying relationships between land use, travel choices, and vehicle emissions within the Seattle, Washington region. Our analysis incorporates land use measures of density and mix which affect the proximity of trip origins to destinations; a measure of connectivity which impacts the directness and completeness of pedestrian and motorized linkages; vehicle trip generation by operating mode; vehicle miles/h of travel and speed; and estimated household vehicle emissions of nitrogen oxides, volatile organic compounds, and carbon monoxide. The data used for this project consists of the Puget Sound Transportation Panel Travel Survey, the 1990 US Census, employment density data from the Washington State Employment Security Office, and information on Seattle’s vehicle fleet mix and climatological attributes provided by the Washington State Department of Ecology. Analyses are based on a cross-sectional research design in which comparisons are made of variations in household travel demand and emissions across alternative urban form typologies. Base emission rates from MOBILE5a and separate engine start rates are used to calculate total vehicle emissions in grams accounting for fleet characteristics and other inputs reflecting adopted transportation control measures. Emissions per trip are based on the network distance of each trip, average travel speed, and a multi-stage engine operating mode (cold start, hot start, and stabilized) function.     

Transportation impacts of center-based telecommuting: Interim findings from the Neighborhood Telecenters Project

The transportation impacts of center-based telecommuting for 24 participants (representing 69 person-days of travel and 295 trips) in the California Neighborhood Telecenters Project are analyzed. Comparing non-telecommuting (NTC) day to telecommuting (TC) day travel shows that person-trips did not change significantly, whereas vehicle-trips increased significantly (by about one trip) on TC days. Both PMT and VMT decline significantly on TC days: by an average of 68 miles (74%) and 38 miles (65%), respectively. When these savings are weighted by the frequency of telecommuting, overall reductions in PMT and VMT come to 19% and 17%, respectively, of total weekday travel. Commute trips increase slightly (by 0.5 trips) but significantly, mainly due to lunch-time trips made home from the telecenter. Total non-commute travel does not increase, but there is a significant shift from other modes to driving alone on TC days. Commute mode split on NTC days is not affected by telecommuting. Travel on TC days tends to be compressed into fewer hours. Higher numbers of return home, eat meal, shopping, and social/recreational trips are made on TC days, in exchange for a reduction (to zero) in the number of change mode trips.     

Characterizing on-road variables that affect passenger vehicle modal operation

The current research direction in transportation-related air-quality modeling is towards development and implementation of modal emissions models that correlate emission rates to specific ranges of activity. This paper describes a methodology to identify roadway characteristics at signalized intersections which affect the fraction of vehicle activity spend in specific operating modes where modal emission rate models indicate elevated emissions occur to improve vehicle activity inputs to modal emissions models. Field studies using laser guns were conducted on-road collecting second-by-second activity for individual vehicles at signal-controlled intersections and roadway segments. Hierarchical tree-based regression analysis was used to identify on-road geometric and operational characteristics that influenced the fractions of vehicle activity spent in specific modes. Results indicated that queue position, grade, downstream and upstream per-lane hourly volume, distance to the nearest downstream signalized intersection, percent heavy vehicles, and posted link speed limit were the most statistically significant variables.     

The trade-off between trips and distance traveled in analyzing the emissions impacts of center-based telecommuting

Several travel indicators were compared between telecommuting (TC) days and non-telecommuting days for a sample of 72 center-based telecommuters in California. Distance traveled decreased significantly on TC days, with average reductions of 51 person-miles (58%) and 35 vehicle-miles (53%). When weighted by telecommuting frequency, average reductions of 11.9% in PMT and 11.5% in VMT were found over a five-day work week. Person-trips and vehicle-trips increased slightly (but not significantly) on TC days. This was due to statistically significant increases in commute trips by telecommuters (who more often went home for lunch on their TC days), partly counteracted by decreases in non-commute travel. The drive-alone mode share increased on TC days, both for all trips, and for commute trips in particular. Walking and biking shares also increased modestly on TC days, whereas shares of transit and ridesharing declined. Despite the increase in trip rates, TC-day reductions were found for all pollutants analyzed: 15% for total organic gas emissions, 21% for carbon monoxide, 35% for oxides of nitrogen, and 51% for particulate matter. The reduction in VMT more than compensated for the marginal increase in number of trips (and consequently, cold starts) on telecommuting days.     

Relationships between highway capacity and induced vehicle travel

The theory of induced travel demand asserts that increases in highway capacity will induce additional growth in traffic. This can occur through a variety of behavioral mechanisms including mode shifts, route shifts, redistribution of trips, generation of new trips, and long run land use changes that create new trips and longer trips. The objective of this paper is to statistically test whether this effect exists and to empirically derive elasticity relationships between lane miles of road capacity and vehicle miles of travel (VMT). An analysis of US data on lane mileage and VMT by state is conducted. The data are disaggregated by road type (interstates, arterials, and collectors) as well as by urban and rural classifications. Various econometric specifications are tested using a fixed effect cross-sectional time series model and a set of equations by road type (using Zellner’s seemingly unrelated regression). Lane miles are found to generally have a statistically significant relationship with VMT of about 0.3–0.6 in the short run and between 0.7 and 1.0 in the long run. Elasticities are larger for models with more specific road types. A distributed lag model suggests a reasonable long-term lag structure. About 25% of VMT growth is estimated to be due to lane mile additions assuming historical rates of growth in road capacity. The results strongly support the hypothesis that added lane mileage can induce significant additional travel.     

Selected node-pair analysis in dial's assignment algorithm

An algorithm is proposed to calculate the matrix of trips which use a particular link in a road network or alternatively pass through a particular set of nodes given the route-splitting assumptions inherent in the Dial assignment algorithm.     

Short trips: An opportunity for reducing mobile-source emissions?

This paper examines how conversion of automobile trips of less than 3 miles to other transportation modes reduces emissions. Short trips contribute disproportionately to emissions because of cold starts. An analysis is conducted of short-trip behavior across the US using the 1995 Nationwide Personal Transportation Survey. The data is used to develop likely scenarios of mode conversions for short trips, which are then applied to estimate emission savings using MOBILE6 cold start and running emission factors for volatile organic compounds, nitrogen oxides, carbon monoxide, and carbon dioxide. The results suggest that reducing short auto trips would modestly reduce mobile source air pollution, but emission reductions are high compared to most federally-funded surface transportation interventions aimed at improving air quality. Enhanced the community pedestrian environment to encourage short trip mode conversion also produces co-benefits such as increased physical activity and subsequent reductions in chronic diseases.     

Dynamic network equilibrium for daily activity-trip chains of heterogeneous travelers: application to large-scale networks

Applications of dynamic network equilibrium models have, mostly, considered the unit of traffic demand either as one-way trip, or as multiple independent trips. However, individuals’ travel patterns typically follow a sequence of trips chained together. In this study we aim at developing a general simulation-based dynamic network equilibrium algorithm for assignment of activity-trip chain demand. The trip chain of each individual trip maker is defined by the departure time at origin, sequence of activity destination locations, including the location of their intermediate destinations and their final destination, and activity duration at each of the intermediate destinations. Spatial and temporal dependency of subsequent trips on each other necessitate time and memory consuming calculations and storage of node-to-node time-dependent least generalized cost path trees, which is not practical for very large metropolitan area networks. We first propose a reformulation of the trip-based demand gap function formulation for the variational inequality formulation of the Bi-criterion Dynamic User Equilibrium (BDUE) problem. Next, we propose a solution algorithm for solving the BDUE problem with daily chain of activity-trips. Implementation of the algorithm for very large networks circumvents the need to store memory-intensive node-to-node time-dependent shortest path trees by implementing a destination-based time-dependent least generalized cost path finding algorithm, while maintaining the spatial and temporal dependency of subsequent trips. Numerical results for a real-world large scale network suggest that recognizing the dependency of multiple trips of a chain, and maintaining the departure time consistency of subsequent trips provide sharper drops in gap values, hence, the convergence could be achieved faster (compared to when trips are considered independent of each other).     

Traffic assignment by trip type using volume restraint and link restraint for application in small urban areas

This research involved the development of a new traffic assignment model consisting of a set of procedures for an urbanized area with a population of 172,000. Historical, social, and economic data were used as input to conventional trip generation and trip distribution models to produce a trip table for network assignment. This fixed table was divided into three trip types: external-external trips, external-internal trips, and internal-internal trips. The methodology used to develop the new traffic assignment model assigned each of the trip types by varying the diversion of trips from the minimum path. External-external trips were assigned on a minimum path routing and external-internal trips were assigned with a slight diversion from the minimum path. Internal-internal trips were assigned with more diversion than external-internal trips and adjusted by utilizing iterative volume restraint and incremental link restraint. A statistical analysis indicated that assigning trips by trip types using trip diversion and volume and link restraint produces a significant improvement in the accuracy of the assigned traffic volumes.     

How much can trip chaining reduce VMT? A simplified method

Trip chaining represents a way to reduce vehicle miles traveled (VMT) that does not require people to shift away from driving private automobiles. While the existing literature on trip chaining acknowledges this potential, little has been done by way of quantifying this. This research seeks to fill this gap by using a large travel survey from the San Francisco Bay area to model the VMT generated by automobile tours as a function of tour composition (i.e., the number and type of destinations on that tour). The model results indicate that many tours involving trips chains (i.e., those tours with more than one destination) generate significantly less VMT than would occur if the destinations in these tours were split into multiple tours with single destinations. Tours that combine a work and non-work destination (which are the most common types of trip chains) particularly demonstrate potential for VMT reduction. Adding a non-work destination to a work tour is usually (depending on the specific type of destination) predicted to result in a reduction of 6–11 VMT, or about 20–30 %. Adding two non-work destinations to a work tour is usually predicted to result in a reduction of 10–22 VMT, or about 25–50 %.     

A comparison of stochastic and deterministic traffic assignment over congested networks

The similarity between link flows obtained from deterministic and stochastic equilibrium traffic assignment models is investigated at different levels of congestion. A probit-based stochastic assignment is used (over a congested network) where the conditions for equilibrium are those given by Daganzo and Sheffi (1977). Stochastic equilibrium flows are generated using an iterative procedure with predetermined step sizes, and the resulting assignment is validated on the basis of the equilibrium criteria. The procedure is intended to assist in the choice of the most appropriate assignment algorithm for a given level of congestion.     

Multi-class percentile user equilibrium with flow-dependent stochasticity

Travelers often reserve a buffer time for trips sensitive to arrival time in order to hedge against the uncertainties in a transportation system. To model the effects of such behavior, travelers are assumed to choose routes to minimize the percentile travel time, i.e. the travel time budget that ensures their preferred probability of on-time arrival; in doing so, they drive the system to a percentile user equilibrium (UE), which can be viewed as an extension of the classic Wardrop equilibrium. The stochasticity in the supply of transportation are incorporated by modeling the service flow rate of each road segment as a random variable. Such stochasticity is flow-dependent in the sense that the probability density functions of these random variables, from which the distribution of link travel time are constructed, are specified endogenously with flow-dependent parameters. The percentile route travel time, obtained by directly convolving the link travel time distributions in this paper, is not available in closed form in general and has to be numerically evaluated. To reveal their structural properties, percentile UE solutions are examined in special cases and verified with numerical results. For the general multi-class percentile UE traffic assignment problem, a variational inequality formulation is given and solved using a route-based algorithm. The algorithm makes use of the diagonal elements in the Jacobian of percentile route travel time, which is approximated through recursive convolution. Preliminary numerical experiments indicate that the algorithm is able to achieve highly precise equilibrium solutions.     

A modeling approach for matching ridesharing trips within macroscopic travel demand models

State of the art travel demand models for urban areas typically distinguish four or five main modes: walking, cycling, public transport and car. The mode car can be further split into car-driver and car-passenger. As the importance of ridesharing may increase in the coming years, ridesharing should be addressed as an additional sub or main mode in travel demand modeling. This requires an algorithm for matching the trips of suppliers (typically car drivers) and demanders (travelers of non-car modes). The paper presents a matching algorithm, which can be integrated in existing travel demand models. The algorithm works likewise with integer demand, which is typical for agent-based microscopic models, and with non-integer demand occurring in travel demand matrices of a macroscopic model. The algorithm compares two path sets of suppliers and demanders. The representation of a path in the road network is reduced from a sequence of links to a sequence of zones. The zones act as a buffer along the path, where demanders can be picked up. The travel demand model of the Stuttgart Region serves as an application example. The study estimates that the entire travel demand of all motorized modes in the Stuttgart Region could be transported by 7% of the current car fleet with 65% of the current vehicle distance traveled, if all travelers were willing to either use ridesharing vehicles with 6 seats or traditional rail.     

Solving the User Optimum Privately Owned Automated Vehicles Assignment Problem (UO-POAVAP): A model to explore the impacts of self-driving vehicles on urban mobility

Interest in vehicle automation has been growing in recent years, especially with the very visible Google car project. Although full automation is not yet a reality there has been significant research on the impacts of self-driving vehicles on traffic flows, mainly on interurban roads. However, little attention has been given to what could happen to urban mobility when all vehicles are automated. In this paper we propose a new method to study how replacing privately owned conventional vehicles with automated ones affects traffic delays and parking demand in a city. The model solves what we designate as the User Optimum Privately Owned Automated Vehicles Assignment Problem (UO-POAVAP), which dynamically assigns family trips in their automated vehicles in an urban road network from a user equilibrium perspective where, in equilibrium, households with similar trips should have similar transport costs. Automation allows a vehicle to travel without passengers to satisfy multiple household trips and, if needed, to park itself in any of the network nodes to benefit from lower parking charges. Nonetheless, the empty trips can also represent added congestion in the network. The model was applied to a case study based on the city of Delft, the Netherlands. Several experiments were done, comparing scenarios where parking policies and value of travel time (VTT) are changed. The model shows good equilibrium convergence with a small difference between the general costs of traveling for similar families. We were able to conclude that vehicle automation reduces generalized transport costs, satisfies more trips by car and is associated with increased traffic congestion because empty vehicles have to be relocated. It is possible for a city to charge for all street parking and create free central parking lots that will keep total transport costs the same, or reduce them. However, this will add to congestion as traffic competes to access those central nodes. In a scenario where a lower VTT is experienced by the travelers, because of the added comfort of vehicle automation, the car mode share increases. Nevertheless this may help to reduce traffic congestion because some vehicles will reroute to satisfy trips which previously were not cost efficient to be done by car. Placing the free parking in the outskirts is less attractive due to the extra kilometers but with a lower VTT the same private vehicle demand would be attended with the advantage of freeing space in the city center.     

Do high income households reduce driving more when living near rail transit?

Transportation planning today requires an understanding of how income and near-rail residence jointly influence household travel behavior. This article fills a gap in the literature by showing how vehicle miles traveled (VMT) and transit trips taken (TT) vary with income and rail transit access by neighborhood type. Results indicate that, when comparing households with similar incomes and examining how the “near-rail” versus “far from rail” VMT and TT gap varies by income, the cross-sectional reduction in nominal VMT and the increase in TT on a percentage basis is generally larger for higher-income households (>$50,000), and particularly so in neighborhoods dense with both jobs and population. These findings offer support for the notion that near-transit housing targeting higher-income households can have both sustainability and transit use benefits. We note, though, that equity considerations are a strong reason to include low-income housing near rail transit, and argue that policies focusing overly singly on either low-income or high-income housing near rail transit will not be as impactful as a robust focus on mixed-income housing developments in rail transit-oriented developments (TODs).     

Designing optimal autonomous vehicle sharing and reservation systems: A linear programming approach

Autonomous vehicle (AV) technology holds great promise for improving the efficiency of traditional vehicle sharing systems. In this paper, we investigate a new vehicle sharing system using AVs, referred to as autonomous vehicle sharing and reservation (AVSR). In such a system, travelers can request AV trips ahead of time and the AVSR system operator will optimally arrange AV pickup and delivery schedules and AV trip chains based on these requests. A linear programming model is proposed to efficiently solve for optimal solutions for AV trip chains and required fleet size through constructed AVSR networks. Case studies show that AVSR can significantly increase vehicle use rate (VUR) and consequentially reduce vehicle ownership significantly. In the meantime, it is found that the actual vehicle miles traveled (VMT) in AVSR systems is not significantly more than that of conventional taxis, despite inevitable empty hauls for vehicle relocation in AVSR systems. The results imply huge potential benefits from AVSR systems on improving mobility and sustainability of our current transportation systems.     

A comparative life-cycle energy and emissions analysis for intercity passenger transportation in the U.S. by aviation,intercity bus,and automobile

Intercity passenger trips constitute a significant source of energy consumption, greenhouse gas emissions, and criteria pollutant emissions. The most commonly used city-to-city modes in the United States include aircraft, intercity bus, and automobile. This study applies state-of-the-practice models to assess life-cycle fuel consumption and pollutant emissions for intercity trips via aircraft, intercity bus, and automobile. The analyses compare the fuel and emissions impacts of different travel mode scenarios for intercity trips ranging from 200 to 1600 km. Because these modes operate differently with respect to engine technology, fuel type, and vehicle capacity, the modeling techniques and modeling boundaries vary significantly across modes. For aviation systems, much of the energy and emissions are associated with auxiliary equipment activities, infrastructure power supply, and terminal activities, in addition to the vehicle operations between origin/destination. Furthermore, one should not ignore the embodied energy and initial emissions from the manufacturing of the vehicles, and the construction of airports, bus stations, highways and parking lots. Passenger loading factors and travel distances also significantly influence fuel and emissions results on a per-traveler basis. The results show intercity bus is generally the most fuel-efficient mode and produced the lowest per-passenger-trip emissions for the entire range of trip distances examined. Aviation is not a fuel-efficient mode for short trips (<500 km), primarily due to the large energy impacts associated with takeoff and landing, and to some extent from the emissions of ground support equipment associated with any trip distance. However, aviation is more energy efficient and produces less emissions per-passenger-trip than low-occupancy automobiles for trip distances longer than 700–800 km. This study will help inform policy makers and transportation system operators about how differently each intercity system perform across all activities, and provides a basis for future policies designed to encourage mode shifts by range of service. The estimation procedures used in this study can serve as a reference for future analyses of transportation scenarios.     

Vehicle scheduling for on-demand vehicle fleets in macroscopic travel demand models

Transportation - The planning of on-demand services requires the formation of vehicle schedules consisting of service trips and empty trips. This paper presents an algorithm for building vehicle...