The Aw–Rascle and Zhang’s model: Vacuum problems,existence and regularity of the solutions of the Riemann problem

In this paper we will discuss some aspects of the recent macroscopic models of the second-order proposed by [Aw, A., Rascle, M., 2000. Resurrection of second order models of traffic flow. SIAM Journal of Applied Mathematics 60 (3), 916–938] and [Zhang, H.M., 2002. A non-equilibrium traffic model devoid of gas-like behavior. Transportation Research Part B 36, 275–290]. These models were suggested after the publication of an article written by [Daganzo, C.F., 1995. Requiem for second-order fluid approximations of traffic flow. Transportation Research Part B 29, 277–286] showing that some classical second-order models can exhibit non-physical solutions. It is shown in this note that the ARZ (Aw–Rascle–Zhang) model respects the anisotropic character of traffic flow, that it yields physical solutions, and that vacuum problems can be solved satisfactorily, provided that the fundamental diagram (equilibrium speed–density relationship) is extended in a suitable fashion. It follows that the Riemann problem for the ARZ model with extended fundamental diagram always admits a solution, and that this solution depends continuously on the initial conditions.     

Anisotropic second-order models and associated fundamental diagrams

According to Banks [Investigation of some characteristics of congested flow. Transportation Research Record, 1999], traffic heterogeneity explains the data scattering on the flow–density plane and positive transferences within the congested phase (a transference is a line connecting adjacent points in the time series). This heterogeneity results from a traffic mixture, made up of various vehicles and drivers, or different traffic conditions such as meteorological conditions. This paper only deals with traffic mixture and more particularly with vehicle classes such as passenger car and truck, which are correlated to the vehicle length. When considering a macroscopic model, the mean vehicle length, which is measured by sensors, is associated with the truck percentage. Then the Generic Second Order Model (GSOM) by Lebacque [Lebacque, J.P., Mammar, S., Haj-Salem, H., 2007a. Generic second-order traffic flow modeling. In: Proceedings of the 17th International Symposium on Transportation and Traffic Theory, London, 23–25 July 2007, 749–770.] provides a rigorous mathematical framework for traffic heterogeneity modeling. The added value in this paper is that admissible invariants which characterize generic fundamental diagrams, possibly depending on the mean vehicle length, are interpreted and debated. Aw–Rascle–Zhang’s [Aw, A., Rascle, M., 2000. Resurrection of second-order models of traffic flow. SIAM Journal of Applied Mathematics, 60 (3), 916–938; Zhang, H.M., 2002. A non equilibrium traffic model devoid of gas-like behavior. Transportation Research Part B, 36, 275–290.] and Colombo’s [Colombo, R.M., 2002. A 2 × 2 hyperbolic traffic flow model. Mathematical and Computer Modeling, 35, 683–688.] anisotropic models are deeply analyzed from a traffic point of view. At last an extended GSOM equation system provides a full parameterization of fundamental diagrams which is needed to traffic heterogeneity modeling.     

Revisiting Jiang’s dynamic continuum model for urban cities

Jiang et al. (Jiang, Y.Q., Wong, S.C., Ho, H.W., Zhang, P., Liu, R.X., Sumalee, A., 2011. A dynamic traffic assignment model for a continuum transportation system. Transportation Research Part B 45 (2), 343–363) proposed a predictive continuum dynamic user-optimaDUO-l to investigate the dynamic characteristics of traffic flow and the corresponding route-choice behavior of travelers. Their modeled region is a dense urban city that is arbitrary in shape and has a single central business district (CBD). However, we argue that the model is not well posed due to an inconsistency in the route-choice strategy under certain conditions. To overcome this inconsistency, we revisit the PDUO-C problem, and construct an improved path-choice strategy. The improved model consists of a conservation law to govern the density, in which the flow direction is determined by the improved path-choice strategy, and a Hamilton–Jacobi equation to compute the total travel cost. The simultaneous satisfaction of both equations can be treated as a fixed-point problem. A self-adaptive method of successive averages (MSA) is proposed to solve this fixed-point problem. This method can automatically determine the optimal MSA step size using the least squares approach. Numerical examples are used to demonstrate the effectiveness of the model and the solution algorithm.     

The strategic transportation research study — Its origins and purposes

The highway industry in the United States spends about $35 to $40 billion annually. Management of the industry is almost wholly decentralized. This decentralization plus diminishing fuel tax revenues used to finance road improvements have caused road research efforts to decline to a very low level. Comparisons between funds for highway research and those spent by private firms in similar industries show that private firms spend from 5 to 12 times the rate of highway agencies. The problem of how much to spend on research is difficult both for private-sector and for public-sector enterprises. The level of research spending is shown to correlate well with both profitability and growth in U.S. firms. Four methods used for making research decisions in the private sector are discussed. The goals of the Strategic Transportation Research Study (STRS), which is being conducted by the Transportation Research Board to examine highway and transportation needs, are described.     

Traffic forecast inaccuracy in transportation: a literature review of roads and railways projects

Transportation - The inaccuracy of traffic forecasts has long stood as a central research theme in the field of infrastructure and transportation studies. The literature presents several motives...     

A chance-constrained based stochastic dynamic traffic assignment model: Analysis, formulation and solution algorithms

This paper is concerned with the system optimum-dynamic traffic assignment (SO-DTA) problem when the time-dependent demands are random variables with known probability distributions. The model is a stochastic extension of a deterministic linear programming formulation for SO-DTA introduced by Ziliaskopoulos (Ziliaskopoulos, A.K., 2000. A linear programming model for the single destination system optimum dynamic traffic assignment problem, Transportation Science, 34, 1–12). The proposed formulation is chance-constrained based and we demonstrate that it provides a robust SO solution with a user specified level of reliability. The model provides numerous insights and can be a useful tool in producing robust control and management strategies that account for uncertainty in applications where SO-DTA is relevant (e.g. evacuation modeling, computing alternate routes around freeway incidents and establishing lower bounds on network performance).     

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.     

Demand management of congested public transport systems: a conceptual framework and application using smart card data

Transportation - Transportation demand management, long used to reduce car traffic, is receiving attention among public transport operators as a means to reduce congestion in crowded public...     

A copula-based joint multinomial discrete–continuous model of vehicle type choice and miles of travel

In this paper, a joint model of vehicle type choice and utilization is formulated and estimated on a data set of vehicles drawn from the 2000 San Francisco Bay Area Travel Survey. The joint discrete–continuous model system formulated in this study explicitly accounts for common unobserved factors that may affect the choice and utilization of a certain vehicle type (i.e., self-selection effects). A new copula-based methodology is adopted to facilitate model estimation without imposing restrictive distribution assumptions on the dependency structures between the errors in the discrete and continuous choice components. The copula-based methodology is found to provide statistically superior goodness-of-fit when compared with previous estimation approaches for joint discrete–continuous model systems. The model system, when applied to simulate the impacts of a doubling in fuel price, shows that individuals are more likely to shift vehicle type choices than vehicle usage patterns.

Assessing the impacts of driving environment on driving behavior patterns

Transportation - Considering the role of behavioral and environmental factors on road accidents and traffic intensities, the characterization of vehicle use and driver behavior opens new...     

SMART: simulation model for activities, resources and travel

This paper proposes the development of an activity-based model of travel that integrates household activities, land use patterns, traffic flows, and regional demographics. The model is intended as a replacement of the traditional Urban Transportation Planning System (UTPS) modeling system now in common use. Operating in a geographic-information system (GIS) environment, the model's heart is a Household Activity Simulator that determines the locations and travel patterns of household members daily activities in 3 categories: mandatory, flexible, and optional. The system produces traffic volumes on streets and land use intensity patterns, as well as typical travel outputs. The model is particularly well suited to analyzing issues related to the Clean Air Act and the Intermodal Surface Transportation Efficiency Act (ISTEA). Implementation would, ideally, require an activity-based travel diary, but can be done with standard house-interview travel surveys. An implementation effort consisting of validation research in parallel with concurrent model programming is recommended.     

Models for optimizing transportation networks and modal split in China

This paper summarizes the research in a project entitled “The Models for Optimizing Transportation Network and Modal Split in China”. The research background, procedure, various mathematical models used in traffic demands forecasting, modal split and network design are presented with the key results. The systematic optimization approach adopted in this paper for integrated planning of transport network and the rational modal split formulation is firstly proposed in China. Finally, further discussion on the difficulties of using transport modeling techniques in Chinese conditions is given.     

Modeling stochastic perception error in the mean-excess traffic equilibrium model

In this paper, we extend the α-reliable mean-excess traffic equilibrium (METE) model of Chen and Zhou (Transportation Research Part B 44(4), 2010, 493-513) by explicitly modeling the stochastic perception errors within the travelers’ route choice decision processes. In the METE model, each traveler not only considers a travel time budget for ensuring on-time arrival at a confidence level α, but also accounts for the impact of encountering worse travel times in the (1 − α) quantile of the distribution tail. Furthermore, due to the imperfect knowledge of the travel time variability particularly in congested networks without advanced traveler information systems, the travelers’ route choice decisions are based on the perceived travel time distribution rather than the actual travel time distribution. In order to compute the perceived mean-excess travel time, an approximation method based on moment analysis is developed. It involves using the conditional moment generation function to derive the perceived link travel time, the Cornish-Fisher Asymptotic Expansion to estimate the perceived travel time budget, and the Acerbi and Tasche Approximation to estimate the perceived mean-excess travel time. The proposed stochastic mean-excess traffic equilibrium (SMETE) model is formulated as a variational inequality (VI) problem, and solved by a route-based solution algorithm with the use of the modified alternating direction method. Numerical examples are also provided to illustrate the application of the proposed SMETE model and solution method.     

Surrounding traffic complexity analysis for efficient and stable conflict resolution

The constant increase in air traffic demand increases a probability of the separation minima infringements in certain areas as a consequence of increased traffic density. The Annual Safety Report 2016 reports that in recent years the number of infringements, measured per million flight hours, had been increased at a lower rate (Eurocontrol, 2018). However, this level of infringements still generates a continuous pressure on the air traffic control (ATC) system and seeks for more control resources ready to tactically solve potential conflicts, while increasing at the same time the operational costs. Considering present air traffic management (ATM) trade-off criteria: increased airspace capacity and traffic efficiency but reducing the cost while preserving safety, new services must be designed to distribute the separation management ATC task loads among other actors. Based on the Single European Sky Air Traffic Management Research and Next Generation Air Transportation System initiatives, this paper proposes an innovative separation management service to shift the completely centralized tactical ATC interventions to more efficient decentralized tactical operations relying on an advanced surrounding traffic analysis tool, to preserve the safety indicators while considering the operational efficiency. A developed methodology for the proposed service is an application-oriented, trying to respond to characteristics and requirements of the current operational environment. The paper further analysis the traffic complexity taking into consideration the so-called domino effect, i.e. a number of the surrounding aircraft causally involved in the separation management service by the means of identification of the spatiotemporal interdependencies between them and the conflicting aircraft. This complexity is driven by the interdependencies structure and expressed as a time-criticality in quantifying the total number of the system solutions, that varies over time as the aircraft are approaching to each other. The results from two randomly selected ecosystem scenarios, extracted from a simulated traffic, illustrate different avoidance capacities for a given look-ahead time and the system solutions counts, that in discrete moments reach zero value.     

Smartphones as an integrated platform for monitoring driver behaviour: The role of sensor fusion and connectivity

Nowadays, more than half of the world’s web traffic comes from mobile phones, and by 2020 approximately 70 percent of the world’s population will be using smartphones. The unprecedented market penetration of smartphones combined with the connectivity and embedded sensing capability of smartphones is an enabler for the large-scale deployment of Intelligent Transportation Systems (ITS). On the downside, smartphones have inherent limitations such as relatively limited energy capacity, processing power, and accuracy. These shortcomings may potentially limit their role as an integrated platform for monitoring driver behaviour in the context of ITS. This study examines this hypothesis by reviewing recent scientific contributions. The Cybernetics theoretical framework was employed to allow a systematic comparison. First, only a few studies consider the smartphone as an integrated platform. Second, a lack of consistency between the approaches and metrics used in the literature is noted. Last but not least, areas such as fusion of heterogeneous information sources, Deep Learning and sparse crowd-sensing are identified as relatively unexplored, and future research in these directions is suggested.     

Construction of traffic state vector using mutual information for short-term traffic flow prediction

Short-term traffic flow prediction is an integral part in most of Intelligent Transportation Systems (ITS) research and applications. Many researchers have already developed various methods that predict the future traffic condition from the historical database. Nevertheless, there has not been sufficient effort made to study how to identify and utilize the different factors that affect the traffic flow. In order to improve the performance of short-term traffic flow prediction, it is necessary to consider sufficient information related to the road section to be predicted. In this paper, we propose a method of constructing traffic state vectors by using mutual information (MI). First, the variables with different time delays are generated from the historical traffic time series, and the spatio-temporal correlations between the road sections in urban road network are evaluated by the MI. Then, the variables with the highest correlation related to the target traffic flow are selected by using a greedy search algorithm to construct the traffic state vector. The K-Nearest Neighbor (KNN) model is adapted for the application of the proposed state vector. Experimental results on real-world traffic data show that the proposed method of constructing traffic state vector provides good prediction accuracy in short-term traffic prediction.     

Increasing the capacity of signalized intersections by allocating exit lanes to turning movements

Unconventional intersection designs have been used to increase the capacity of intersections that are over‐saturated under conventional ones. However, existing unconventional designs typically require extra land space and their effectiveness often depends on drivers' familiarity with the uncommon operating rules. To overcome these challenges, we propose a new unconventional design, where movements that are mutually incompatible under the conventional design can be made compatible of each other by allocating exit lanes to them appropriately, thereby creating opportunities for capacity improvement. We develop a lane‐based capacity optimization model that incorporates the allocation of exit lanes as decision variables. The model is formulated as a Binary Mixed Integer Linear Programming problem, which can be efficiently solved by standard branch‐and‐bound algorithms. Numerical experiments show that significant capacity improvement can be obtained under our design. Besides proposing a new unconventional design, we also contribute to the literature of lane‐based signal optimization methods by providing a novel linear formulation for the latest, yet nonlinear, model described in Wong and Heydecker [Transportation Research Part B 45(4):667–681]. This improvement is methodologically beneficial as linear models are computationally more convenient than nonlinear ones. Copyright © 2017 John Wiley & Sons, Ltd.     

The potential use of big vehicle GPS data for estimations of annual average daily traffic for unmeasured road segments

Transportation - A promising methodology is proposed to estimate reliable annual average daily traffic (AADT) volumes for no-surveyed road sections using probe volumes collected by a vehicle global...     

Modelling traffic flows and estimating road travel times in transportation network under dynamic disturbances

Transportation - Traffic congestion is a common phenomenon in road transportation networks, especially during peak hours. More accurate prediction of dynamic traffic flows is very important for...     

An analysis of weekly out-of-home discretionary activity participation and time-use behavior

Activity-travel behavior research has hitherto focused on the modeling and understanding of daily time use and activity patterns and resulting travel demand. In this particular paper, an analysis and modeling of weekly activity-travel behavior is presented using a unique multi-week activity-travel behavior data set collected in and around Zurich, Switzerland. The paper focuses on six categories of discretionary activity participation to understand the determinants of, and the inter-personal and intra-personal variability in, weekly activity engagement at a detailed level. A panel version of the Mixed Multiple Discrete Continuous Extreme Value model (MMDCEV) that explicitly accounts for the panel (or repeated-observations) nature of the multi-week activity-travel behavior data set is developed and estimated on the data set. The model also controls for individual-level unobserved factors that lead to correlations in activity engagement preferences across different activity types. To our knowledge, this is the first formulation and application of a panel MMDCEV structure in the econometric literature. The analysis suggests the high prevalence of intra-personal variability in discretionary activity engagement over a multi-week period along with inter-personal variability that is typically considered in activity-travel modeling. In addition, the panel MMDCEV model helped identify the observed socio-economic factors and unobserved individual specific factors that contribute to variability in multi-week discretionary activity participation.