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.     

A traffic assignment model for a ridesharing transportation market

A nascent ridesharing industry is being enabled by new communication technologies and motivated by the many possible benefits, such as reduction in travel cost, pollution, and congestion. Understanding the complex relations between ridesharing and traffic congestion is a critical step in the evaluation of a ridesharing enterprise or of the convenience of regulatory policies or incentives to promote ridesharing. In this work, we propose a new traffic assignment model that explicitly represents ridesharing as a mode of transportation. The objective is to analyze how ridesharing impacts traffic congestion, how people can be motivated to participate in ridesharing, and, conversely, how congestion influences ridesharing, including ridesharing prices and the number of drivers and passengers. This model is built by combining a ridesharing market model with a classic elastic demand Wardrop traffic equilibrium model. Our computational results show that (i) the ridesharing base price influences the congestion level, (ii) within a certain price range, an increase in price may reduce the traffic congestion, and (iii) the utilization of ridesharing increases as the congestion increases. Copyright © 2014 John Wiley & Sons, Ltd.     

A cell-based Merchant-Nemhauser model for the system optimum dynamic traffic assignment problem

A cell-based variant of the Merchant-Nemhauser (M-N) model is proposed for the system optimum (SO) dynamic traffic assignment (DTA) problem. Once linearized and augmented with additional constraints to capture cross-cell interactions, the model becomes a linear program that embeds a relaxed cell transmission model (CTM) to propagate traffic. As a result, we show that CTM-type traffic dynamics can be derived from the original M-N model, when the exit-flow function is properly selected and discretized. The proposed cell-based M-N model has a simple constraint structure and cell network representation because all intersections and cells are treated uniformly. Path marginal costs are defined using a recursive formula that involves a subset of multipliers from the linear program. This definition is then employed to interpret the necessary condition, which is a dynamic extension of the Wardrop’s second principle. An algorithm is presented to solve the flow holding back problem that is known to exist in many discrete SO-DTA models. A numerical experiment is conducted to verify the proposed model and algorithm.     

A dynamic behavioural traffic assignment model with strategic agents

Foresee traffic conditions and demand is a major issue nowadays that is very often approached using simulation tools. The aim of this work is to propose an innovative strategy to tackle such problem, relying on the presentation and analysis of a behavioural dynamic traffic assignment.The proposal relies on the assumption that travellers take routing policies rather than paths, leading us to introduce the possibility for each simulated agent to apply, in real time, a strategy allowing him to possibly re-route his path depending on the perceived local traffic conditions, jam and/or time already spent in his journey.The re-routing process allows the agents to directly react to any change in the road network. For the sake of simplicity, the agents’ strategy is modelled with a simple neural network whose parameters are determined during a preliminary training stage. The inputs of such neural network read the local information about the route network and the output gives the action to undertake: stay on the same path or modify it. As the agents use only local information, the overall network topology does not really matter, thus the strategy is able to cope with large and not previously explored networks.Numerical experiments are performed on various scenarios containing different proportions of trained strategic agents, agents with random strategies and non strategic agents, to test the robustness and adaptability to new environments and varying network conditions. The methodology is also compared against existing approaches and real world data. The outcome of the experiments suggest that this work-in-progress already produces encouraging results in terms of accuracy and computational efficiency. This indicates that the proposed approach has the potential to provide better tools to investigate and forecast drivers’ choice behaviours. Eventually these tools can improve the delivery and efficiency of traffic information to the drivers.     

Multiple equilibria in a dynamic traffic network

This study provides an example in which the dynamic user equilibrium (DUE) assignment of a congested road network with bottlenecks is non-unique. In previous studies, the uniqueness of DUE assignments with the bottleneck model has been shown in limited cases such as single-origin and single-destination networks. Consequently, it is still an important issue whether or not uniqueness is a general property of DUE assignments. The present study describes a network in which multiple patterns of link travel time are found, thus providing a negative answer to this question. The network has a loopy structure with multiple bottlenecks and multiple origin-destination (OD) pairs. Given a certain demand pattern of departure times for vehicles leaving their origins, a non-convex set of equilibria with a non-unique pattern of link travel times is shown to exist.     

Integrating a simplified emission estimation model and mesoscopic dynamic traffic simulator to efficiently evaluate emission impacts of traffic management strategies

This paper presents a computationally efficient and theoretically rigorous dynamic traffic assignment (DTA) model and its solution algorithm for a number of emerging emissions and fuel consumption related applications that require both effective microscopic and macroscopic traffic stream representations. The proposed model embeds a consistent cross-resolution traffic state representation based on Newell’s simplified kinematic wave and linear car following models. Tightly coupled with a computationally efficient emission estimation package MOVES Lite, a mesoscopic simulation-based dynamic network loading framework DTALite is adapted to evaluate traffic dynamics and vehicle emission/fuel consumption impact of different traffic management strategies.     

Computing dynamic user equilibria for large-scale transportation networks

In this paper, we present an approach for determining dynamic user equilibria. The method is suitable for disaggregated microscopic and mesoscopic simulation-based models. It is a modification of the convex-simplex method, which disposes with the line search step, and controls the subset of travelers to be re-routed at each step while updating the link travel times after each assignment. To guarantee finite termination, a suitable stopping criterion is adopted. The proposed method is implemented within TRANSIMS, the Transportation Analysis and Simulation System, as a two-stage process that employs a combined use of link performance functions and a microsimulator in order to design a framework suitable for application to real transportation systems. To demonstrate this capability, we apply the developed methodology to a large-scale network, Bignet, which is part of the transportation city network of Portland, Oregon; and a medium-scale network, Blacksburg, Virginia; and provide some comparative analyses. Our results exhibit that an improved distribution of travelers is obtained while consuming less than 17–33% of the effort required by the current version of TRANSIMS.     

Urban university campus transportation and parking planning through a dynamic traffic simulation and assignment approach

Abstract

Many urban university campuses are considered major trip attractors. Considering the multimodal and complex nature of university campus transportation planning and operation, this paper proposes a dynamic traffic simulation and assignment analysis approach and demonstrates how such a methodology can be successfully applied. Central to the research is the estimation of trip origin–destinations and the calibration of a parking lot choice model. Dynamic simulation is utilized to simulate multiple modes of transportation within the transportation network while further assigning these modes with respect to various mode-specific roadway accessibilities. A multiple vehicle-class simulation analysis for planning purposes becomes a critical capability to predict how faculty and staff who once parked within the campus core choose other nearby alternate parking lots. The results highlight the effectiveness of the proposed approach in providing integrated and reliable solutions for challenging questions that face urban university campus planners and local transportation jurisdictions.     

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.     

Stochastic cell transmission model (SCTM): A stochastic dynamic traffic model for traffic state surveillance and assignment

The paper proposes a first-order macroscopic stochastic dynamic traffic model, namely the stochastic cell transmission model (SCTM), to model traffic flow density on freeway segments with stochastic demand and supply. The SCTM consists of five operational modes corresponding to different congestion levels of the freeway segment. Each mode is formulated as a discrete time bilinear stochastic system. A set of probabilistic conditions is proposed to characterize the probability of occurrence of each mode. The overall effect of the five modes is estimated by the joint traffic density which is derived from the theory of finite mixture distribution. The SCTM captures not only the mean and standard deviation (SD) of density of the traffic flow, but also the propagation of SD over time and space. The SCTM is tested with a hypothetical freeway corridor simulation and an empirical study. The simulation results are compared against the means and SDs of traffic densities obtained from the Monte Carlo Simulation (MCS) of the modified cell transmission model (MCTM). An approximately two-miles freeway segment of Interstate 210 West (I-210W) in Los Ageles, Southern California, is chosen for the empirical study. Traffic data is obtained from the Performance Measurement System (PeMS). The stochastic parameters of the SCTM are calibrated against the flow-density empirical data of I-210W. Both the SCTM and the MCS of the MCTM are tested. A discussion of the computational efficiency and the accuracy issues of the two methods is provided based on the empirical results. Both the numerical simulation results and the empirical results confirm that the SCTM is capable of accurately estimating the means and SDs of the freeway densities as compared to the MCS.     

Development of a delay model for unsignalized intersections applicable to traffic assignment

Abstract

This paper develops a model for estimating unsignalized intersection delays which can be applied to traffic assignment (TA) models. Current unsignalized intersection delay models have been developed mostly for operational purposes, and demand detailed geometric data and complicated procedures to estimate delay. These difficulties result in unsignalized intersection delays being ignored or assumed as a constant in TA models.

Video and vehicle license plate number recognition methods are used to collect traffic volume data and to measure delays during peak and off-peak traffic periods at four unsignalized intersections in the city of Tehran, Iran. Data on geometric design elements are measured through field surveys. An empirical approach is used to develop a delay model as a function of influencing factors based on 5- and 15-min time intervals. The proposed model estimates delays on each approach based on total traffic volumes, rights-of-way of the subject approach and the intersection friction factor. The effect of conflicting traffic flows is considered implicitly by using the intersection friction factor. As a result, the developed delay model guarantees the convergence of TA solution methods.

A comparison between delay models performed using different time intervals shows that the coefficients of determination, R ², increases from 43.2% to 63.1% as the time interval increases from 5- to 15-min. The US Highway Capacity Manual (HCM) delay model (which is widely used in Iran) is validated using the field data and it is found that it overestimates delay, especially in the high delay ranges.     

A generic class of first order node models for dynamic macroscopic simulation of traffic flows

Node models for macroscopic simulation have attracted relatively little attention in the literature. Nevertheless, in dynamic network loading (DNL) models for congested road networks, node models are as important as the extensively studied link models. This paper provides an overview of macroscopic node models found in the literature, explaining both their contributions and shortcomings. A formulation defining a generic class of first order macroscopic node models is presented, satisfying a list of requirements necessary to produce node models with realistic, consistent results. Defining a specific node model instance of this class requires the specification of a supply constraint interaction rule and (optionally) node supply constraints. Following this theoretical discussion, specific macroscopic node model instances for unsignalized and signalized intersections are proposed. These models apply an oriented capacity proportional distribution of the available supply over the incoming links of a node. A computationally efficient algorithm to solve the node models exactly is included.     

A linear programming formulation for autonomous intersection control within a dynamic traffic assignment and connected vehicle environment

This paper develops a novel linear programming formulation for autonomous intersection control (LPAIC) accounting for traffic dynamics within a connected vehicle environment. Firstly, a lane based bi-level optimization model is introduced to propagate traffic flows in the network, accounting for dynamic departure time, dynamic route choice, and autonomous intersection control in the context of system optimum network model. Then the bi-level optimization model is transformed to the linear programming formulation by relaxing the nonlinear constraints with a set of linear inequalities. One special feature of the LPAIC formulation is that the entries of the constraint matrix has only {−1, 0, 1} values. Moreover, it is proved that the constraint matrix is totally unimodular, the optimal solution exists and contains only integer values. It is also shown that the traffic flows from different lanes pass through the conflict points of the intersection safely and there are no holding flows in the solution. Three numerical case studies are conducted to demonstrate the properties and effectiveness of the LPAIC formulation to solve autonomous intersection control.     

Multimodal,multiclass stochastic dynamic traffic assignment for evaluating information provision strategies

A multimodal, multiclass stochastic dynamic traffic assignment model was developed to evaluate pre‐trip and enroute travel information provision strategies. Three different information strategies were examined: user optimum [UO], system optimum [SO] and mixed optimum [MO]. These information provision strategies were analyzed based on the levels of traffic congestion and market penetration rate for the information equipment. Only two modes, bus and car, were used for evaluating and calculating the modal split ratio. Several scenarios were analyzed using day‐to‐day and within day dynamic models. From the results analyzed, it was found that when a traffic manager provides information for drivers using the UO strategy and drivers follow the provided information absolutely, the total travel time may increases over the case with no information. Such worsening occurs when drivers switch their routes and face traffic congestion on the alternative route. This phenomenon is the 'Braess Paradox'.     

Development and calibration of a long-distance passenger traffic assignment model

This paper studies the assignment of long-distance passenger traffic on a highway corridor network. First, we propose a traditional model for the long-distance traffic assignment considering interactions with local commuter traffic. It addresses the effect of local networks on highway corridors. An iterative algorithm is developed to solve for the exact solution. Then, to address the potential computational issues that arise therein, a decomposition method is proposed by introducing a new concept of corridor elasticity. An assignment procedure for long-distance passenger traffic is developed accordingly. Numerical tests show that the proposed decomposition method makes significant improvements in computational performance at a small loss of optimality. This decomposition method well approximates the exact assignment from the traditional formulation, especially when the highway corridors are near-saturation. The proposed decomposition method appears practical for application.     

An integrated framework for embedding large-scale dynamic traffic assignment models in advanced traveler information systems

In recent years, increasing attention has been drawn to the development of various applications of intelligent transportation systems (ITS), which are credited with the amelioration of traffic conditions in urban and regional environments. Advanced traveler information systems (ATIS) constitute an important element of ITS by providing potential travelers with information on the network's current performance both en-route and pre-trip. In order to tackle the complexity of such systems, derived from the difficulty of providing real-time estimations of current as well as forecasts of future traffic conditions, a series of models and algorithms have been initiated. This paper proposes the development of an integrated framework for real-time ATIS and presents its application on a large-scale network, that of Thessaloniki, Greece, concluding with a discussion on development and implementation challenges as well as on the advantages and limitations of such an effort.     

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.     

A methodology to estimate travel time using dynamic traffic assignment (DTA) under incident conditions

This paper presents results from a research case study that examined the distribution of travel time of origin–destination (OD) pairs on a transportation network under incident conditions. Using a transportation simulation dynamic traffic assignment (DTA) model, incident on a transportation network is executed under normal conditions, incident conditions without traveler information availability, and incident conditions assuming that users had perfect knowledge of the incident conditions and could select paths to avoid the incident location. The results suggest that incidents have a different impact on different OD pairs. The results confirm that an effective traveler information system has the potential to ease the impacts of incident conditions network wide. Yet it is also important to note that the use of information may detriment some OD pairs while benefiting other OD pairs. The methodology demonstrated in this paper provides insights into the usefulness of embedding a fully calibrated DTA model into the analysis tools of a traffic management and information center.     

Dynamic traffic assignment of cooperative adaptive cruise control

Advances in connected and automated vehicle technologies have resulted in new vehicle applications, such as cooperative adaptive cruise control (CACC). Microsimulation models have shown significant increases in capacity and stability due to CACC, but most previous work has relied on microsimulation. To study the effects of CACC on larger networks and with user equilibrium route choice, we incorporate CACC into the link transmission model (LTM) for dynamic network loading. First, we derive the flow-density relationship from the MIXIC car-following model of CACC (at 100% CACC market penetration). The flow-density relationship has an unusual shape; part of the congested regime has an infinite congested wave speed. However, we verify that the flow predictions match observations from MIXIC modeled in VISSIM. Then, we use the flow-density relationship from MIXIC in LTM. Although the independence of separate links restricts the maximum congested wave speed, for common freeway link lengths the congested wave speed is sufficiently high to fit the observed flows from MIXIC. Results on a freeway and regional networks (with CACC-exclusive lanes) indicate that CACC could reduce freeway congestion, but naïve deployment of CACC-exclusive lanes could cause an increase in total system travel time.     

A model and solution algorithm for dynamic deterministic user equilibrium assignment

Abstract

In this paper a route-based dynamic deterministic user equilibrium assignment model is presented. Some features of the linear travel time model are first investigated and then a divided linear travel time model is proposed for the estimation of link travel time: it addresses the limitations of the linear travel time model. For the application of the proposed model to general transportation networks, this paper provides thorough investigations on the computational issues in dynamic traffic assignment with many-to-many OD pairs and presents an efficient solution procedure. The numerical calculations demonstrate that the proposed model and solution algorithm produce satisfactory solutions for a network of substantial size with many-to-many OD pairs. Comparisons of assignment results are also made to show the impacts of incorporation of different link travel time models on the assignment results.