Dynamic Traffic Assignment Model Research Articles

Optimal design of Rapid evacuation strategies in constrained urban transport networks

Large-scale evacuations constitute common life-saving exercises that are activated in many disaster response campaigns. Their effectiveness is often inhibited by traffic congestion, disrupted and imperfect coordination mechanisms, and the poor state of the underlying transportation networks. To address this problem, this paper presents a hybrid simulation-optimisation methodology to optimise evacuation response strategies through demand staging and signal phasing. We introduce a pre-planning model that evaluates evacuation policies, using a low-level dynamic traffic assignment model that captures the effects of congestion, queuing and vehicle spillback. Optimal strategies are determined using derivative-free optimisation algorithms, applied to an evacuation problem based on a benchmark dataset. The effects of varying the number of activated paths and the frequency of departure under different network conditions are observed. Our analysis indicates that combined departure time scheduling and signal phasing is a promising method to improve evacuation efficiency when compared to a worst-case benchmark scenario.

Mode shift impacts of optimal time-dependent congestion pricing in large networks: A simulation-based case study in the greater toronto area

This paper presents a case study on commuter’s departure time, route and mode choice responses to optimized tolling in the Toronto, Ontario, Canada. The study integrates a toll optimization component into an integrated framework of econometric departure time choice, dynamic traffic assignment model, and random utility maximization (RUM) based mode choice model. An iterative optimization algorithm is used to generate optimal tolling structure which explicitly considers heterogeneous user preferences through econometric departure time choice modelling component. The mode choice component is exogenously retrofitted in an integrated econometric departure time choice modelling component and dynamic operational traffic assignment model to capture individual mode choice behaviour in response to variable congestion pricing. The integrated model results show that individuals are more likely to switch driving routes and departure times than commuting modes when making tradeoffs between schedule delay cost, travel time cost, and toll cost. It is found that the optimal toll scenario improves the network-wide travel time. The modelling framework presented in this study can test a wide range of policy scenarios including the time-variable tolling of congested highways, and high occupancy toll lanes. While the integrated framework presented here is tested at a large scale on the Greater Toronto Area (GTA), we believe the approach can be applied to large-scale networks globally where the objective is seeking the best network-wide spatial and temporal traffic distribution.

A bi-partitioning approach to congestion pattern recognition in a congested monocentric city

This paper proposes a bi-partitioning approach using link density data to identify an optimal restricted zone (RZ) in a congested monocentric city to assist with the implementation of area-wide congestion management strategies. A composite similarity measure is developed for each link in the network as a weighted average of a density similarity measure (ensuring homogeneity) and a distance similarity measure (ensuring connectivity and compactness). The resulting similarity matrix is fed into a graph clustering method termed symmetric nonnegative matrix factorization (SNMF) to bi-partition the network. To determine the optimal weight as a hyperparameter, we propose a hierarchical search algorithm (HSA) based on the concept of “knee” that is used to find the most significant solution from the Pareto front. The proposed approach is demonstrated on the Melbourne network using a simulation-based dynamic traffic assignment model. Results show that the methodology (i) can effectively capture the spatial variations of the congestion pattern in the network; (ii) is robust to moderate parameter changes; (iii) can be extended to the time-dependent case and hence inform when to activate the area control; and (iv) can perform relatively well in the presence of missing data. When varying the distance threshold as a design parameter, we can observe how the optimal RZ evolves in space, a feature that is critical to devising a double- or multi-layered RZ for hierarchical control purposes.

PEV Charging Infrastructure Siting Based on Spatial–Temporal Traffic Flow Distribution

Plug-in electric vehicles (PEVs) offer a solution to reduce greenhouse gas emissions and decrease fossil fuel consumption. PEV charging infrastructure siting must ensure not only a satisfactory charging service for PEV users but also a high utilization and profitability for the chosen facility locations. Thus, the various types of charging facilities should be located based on an accurate location estimation of the potential PEV charging demand. In this paper, we propose a spatial–temporal flow capturing location model. This model determines the locations of various types of charging facilities based on the spatial–temporal distribution of traffic flows. We utilize the dynamic traffic assignment model to estimate the time-varying traffic flows on the road transportation network. Then, we cluster the traffic flow dataset into distinct categories using the Gaussian mixture model and site each type of charging facilities to capture a specific traffic pattern. We formulate our siting model as an mixed integer linear programming optimization problem. The model is evaluated based on two benchmark transportation networks, and the simulation results demonstrate the effectiveness of the proposed model.

Path-Based Dynamic User Equilibrium Model with Applications to Strategic Transportation Planning

This study proposes an analytical capacity constrained dynamic traffic assignment (DTA) model along with an efficient path-based algorithm. The model can be applied to analyzing dynamic traffic demand management (TDM) strategies, but its specific feature is allowing for an evaluation of advanced traveler information systems (ATIS) within the strategic transportation planning framework. It is an extension of a former DTA model, where each link is given an infinite capacity and is assumed to be completely traversed inside any time interval it is reach by a path. Thereby, the length of time intervals should be very longer than the link travel times, and the link capacity constraints are overlooked. The paper rests on three key ideas to overcome these restrictions: (1) adding path-link fraction variables to the base model, allowing path flows to spread out over time intervals on long links; (2) uniformly dividing each link into smaller parts (segments), so that each part is more likely to be traversed inside a time interval; (3) imposing a dynamic penalty function on each link, thereby the capacity constraint can be included. The proposed DTA algorithm decomposes the augmented model in terms of origin-destination (OD) pairs and departure time intervals, and utilizes a dynamic column generation technique for generating active paths between the OD pairs. The optimal solution to a one-link network demonstrates that the model is able to approximate the dynamic flow propagation over a link with sensible accuracy. Besides, investigation of the results for a small test network reveals that the algorithm performs very well in computing temporal link flows and queuing delays. Finally, numerical experiments on a real life network indicate that the algorithm converges sufficiently fast and provides path information for each time interval. The network is further used to show the algorithm is capable of assessing a dynamic TDM strategy as well as an ATIS system.

A dynamic pricing scheme with negative prices in dockless bike sharing systems

To achieve bike relocation11The bike relocation mentioned in this paper is also referred as bike repositioning in the literature. through travellers’ spontaneous behaviour in dockless bike sharing systems, an innovative dynamic pricing scheme with negative prices is introduced. In normal situation, users pay a positive price to operators for using a bike. However, when imbalanced distribution of bikes occurs in the system, users who cycle from the oversupplied area to undersupplied area will receive monetary reward from the operator, i.e., negative pricing applies. A user equilibrium dynamic traffic assignment model is developed to capture travellers’ mode-path choice behaviour in response to the proposed dynamic pricing strategy. Travellers can either use a single transportation mode (e.g. walking, cycling and bus) or take multiple modes to complete their trips. The user equilibrium travel pattern is formulated as a variational inequality problem and then solved by a path-flow swapping algorithm. Two numerical examples are conducted to demonstrate that the proposed dynamic pricing strategy with negative prices is effective in terms of attracting users as well as achieving a more balanced bike repositioning, especially when the number of bikes provided in the system is limited.

Traffic State Estimation in Heterogeneous Networks with Stochastic Demand and Supply: Mixed Lagrangian–Eulerian Approach

A network fundamental diagram (NFD) represents the relationship between network-wide average flow and average density. Network traffic state estimation to observe NFD when congestion is heterogeneously distributed, as a result of a time-varying and asymmetric demand matrix, is a challenging problem. Recent studies have formulated the NFD estimation problem using both fixed measurements and probe trajectories. They are often based on a given ground-truth NFD for a single day demand. Stochastic variations in network demand and supply may significantly affect the approximation of an NFD. This study proposes a modified framework to estimate network traffic states to observe NFD while capturing the stochasticity in transportation networks. A mixed integer problem with non-linear constraints is formulated to address stochasticity in the NFD estimation problem. To solve this Nondeterministic Polynomial-hard (NP-hard) problem, a solution algorithm based on the simulated annealing method is applied. The problem is formulated and the solution algorithm is implemented to find an optimal configuration of loop detectors and probe vehicles to estimate the NFD of the Chicago downtown network and capture its day-to-day variations, considering a given available budget. Ground-truth NFDs and estimated NFDs based on a subset of loop detectors and probe vehicles are calculated using a simulation-based dynamic traffic assignment model, which is the best surrogate available to replicate real-world conditions. The main contribution of this study is to capture stochasticity in the demand and supply sides to find a more robust subset of links and trajectories to be acquired for the NFD estimation.

Evaluating Incident Responsive Signal Control Plans using Multi-Resolution Modeling

The implementation of incident responsive signal control strategies can be effective in relieving congestion during traffic incidents. The goal of this paper is to develop and evaluate a methodology to assess the impacts of incident responsive signal control. This study demonstrates the utilization of a multi-resolution and multi-scenario modeling approach to support the evaluation and design of incident management strategies and the associated incident responsive signal control. The approach utilizes the strength of mesoscopic simulation-based dynamic traffic assignment modeling to determine route diversion and microscopic simulation to estimate the traffic impacts of incident responsive signal timing. The methods also utilize detailed traffic and incident data to inform the analysis, modeling, and simulation. The utilized methods support the modeling of different traffic patterns, confirm the diversion estimated by modeling tools based on field detector data, provide estimation of capacity drop during arterial incidents with different locations from upstream and downstream signals, and address the need for accurate turning movement volumes resulting from the modeling. Results of the case study indicate that implementation of incident responsive signal control strategies provided a reduction in total delay of through movement in the incident direction of 18.5% and 24.5% for 30-min and 45-min incidents, respectively. The corresponding reductions in total delay of all movements in the segment were 7.5% and 9.5%, respectively. These values can be used to inform the return-on-investment as part of planning and operation analysis of active transportation management strategies.

PC–SPSA: Employing Dimensionality Reduction to Limit SPSA Search Noise in DTA Model Calibration

Calibration and validation have long been a significant topic in traffic model development. In fact, when moving to dynamic traffic assignment (DTA) models, the need to dynamically update the demand and supply components creates a considerable burden on the existing calibration algorithms, often rendering them impractical. These calibration approaches are mostly restricted either due to non-linearity or increasing problem dimensionality. Simultaneous perturbation stochastic approximation (SPSA) has been proposed for the DTA model calibration, with encouraging results, for more than a decade. However, it often fails to converge reasonably with the increase in problem size and complexity. In this paper, we combine SPSA with principal components analysis (PCA) to form a new algorithm, we call, PC–SPSA. The PCA limits the search area of SPSA within the structural relationships captured from historical estimates in lower dimensions, reducing the problem size and complexity. We formulate the algorithm, demonstrate its operation, and explore its performance using an urban network of Vitoria, Spain. The practical issues that emerge from the scale of different variables and bounding their values are also analyzed through a sensitivity analysis using a non-linear synthetic function.

Energy and Mobility Impacts of System Optimal Dynamic Traffic Assignment for a Mixed Traffic of Legacy and Automated Vehicles

This research develops a system optimal dynamic traffic assignment (DTA) model for mixed traffic of human drivers and automated vehicles (AVs) and investigates network level mobility and energy impacts for different market shares of AVs. A methodology based on vehicle-specific-energy is proposed to estimate the energy consumption from the embedded spatial-queuing traffic flow model within the DTA formulation. Results with a test network indicate that potential travel time and energy consumption reductions are possible with increased AV market share in transportation networks. Results also report a decrease in travel time as high as 49% and energy consumption as high as 28% at the system level. The developed DTA model will be able to assist in transportation planning and the investment decision process by estimating the mobility and energy impacts in future transportation networks with mixed traffic of human drivers and AVs.

Surrogate‐based toll optimization in a large‐scale heterogeneously congested network

AbstractToll optimization in a large‐scale dynamic traffic network is typically characterized by an expensive‐to‐evaluate objective function. In this paper, we propose two toll‐level problems (TLPs) integrated with a large‐scale simulation‐based dynamic traffic assignment model of Melbourne, Australia. The first TLP aims to control the pricing zone (PZ) through a time‐varying joint distance and delay toll such that the network fundamental diagram (NFD) of the PZ does not enter the congested regime. The second TLP is built upon the first TLP by further considering the minimization of the heterogeneity of congestion distribution in the PZ. To solve the two TLPs, a computationally efficient surrogate‐based optimization method, that is, regressing kriging with expected improvement sampling, is applied to approximate the simulation input–output mapping, which can balance well between local exploitation and global exploration. Results show that the two optimal TLP solutions reduce the average travel time in the PZ (entire network) by 29.5% (1.4%) and 21.6% (2.5%), respectively. Reducing the heterogeneity of congestion distribution achieves higher network flows in the PZ and a lower average travel time or a larger total travel time saving in the entire network.

Wireless charging utility maximization and intersection control delay minimization framework for electric vehicles

AbstractThis study presents the Wireless Charging Utility Maximization (WCUM) framework, which aims to maximize the utility of Wireless Charging Units (WCUs) for electric vehicle (EV) charging through the optimal WCU deployment at signalized intersections. Furthermore, the framework aims to minimize the control delay at all signalized intersections of the network. The framework consists of a two‐step optimization formulation, a dynamic traffic assignment model to calculate the user equilibrium, a traffic microsimulator to formulate the objective functions, and a global Mixed Integer Non‐Linear Programming (MINLP) optimization solver. An optimization problem is formulated for each intersection, and another for the entire network. The performance of the WCUM framework is tested using the Sioux Falls network. We perform a comparative study of 12 global MINLP solvers with a case study. Based on solution quality and computation time, we choose the Couenne solver for this framework.

Agent-based modeling to estimate exposures to urban air pollution from transportation: Exposure disparities and impacts of high-resolution data

Better understanding of the complex links between urban transportation, land use, air quality, and population exposure is needed to improve urban sustainability. A goal of this study was to develop an exposure modeling framework that integrates agent-based activity and travel simulation with air pollution modeling for Tampa, Florida. We aimed to characterize exposure and exposure inequality for traffic-related air pollution, and to investigate the impacts of high-resolution information on estimated exposure. To do these, we developed and applied a modeling framework that combines the DaySim activity-based travel demand model, the MATSim dynamic traffic assignment model, the MOVES mobile source emissions estimator, and the R-LINE dispersion model. Resulting spatiotemporal distributions of daily individual human activity and pollutant concentration were matched to analyze population and subgroup exposure to oxides of nitrogen (NOx) from passenger car travel for an average winter day in 2010. Four scenarios using data with different spatiotemporal resolutions were considered: a) high resolution for both activities and concentrations, b) low resolution for both activities and concentrations, c) high resolution for activities, but low resolution for concentrations, and d) vice versa. For the high-resolution scenario, the mean daily population exposure concentration of NOx from passenger cars was 10.2 μg/m3; individual exposure concentrations ranged from 0.2 to 145 μg/m3. Subgroup mean exposure was higher than the population mean for individuals living below-poverty (by ~16%), those with daily travel time over one hour (8%), adults aged 19–45 (7%), blacks (6%), Hispanics (4%), Asians (2%), combined other non-white races (2%), people from middle income households (2%), and residents of urban areas (2%). The subgroup inequality index (a measure of disparity) largely increased with concentration up to the 90th percentile level for these groups. At higher levels, disparities increased sharply for individuals from below poverty households, blacks, and Hispanics. Low-resolution simulation of both activities and concentrations decreased the exposure estimates by 10% on average, with differences ranging from eight times higher to ~90% lower.

Link-Based System Optimum Dynamic Traffic Assignment Problems in General Networks

Most current system optimum dynamic traffic assignment (SO-DTA) models do not contain first-in-first-out (FIFO) constraints and are limited to single-destination network applications. In “Link-based System Optimum Dynamic Traffic Assignment Problems in General Networks,” J. Long and W. Y. Szeto develop SO-DTA models either with or without FIFO constraints for general network applications using the concept of the link transmission model (LTM). The proposed SO-DTA problems without FIFO constraints are formulated as linear programs, and can address the vehicle holding problem by adding a penalty term to the objective function. The SO-DTA problems with FIFO constraints are formulated as nonconvex mixed-integer programs, and are solved by branch-and-bound algorithms. Two methods are developed to identify FIFO violations in feasible flow patterns and design a branching scheme for the proposed branch and bound algorithms. The authors show that the proposed LTM-based SO-DTA models are more computationally efficient than the CTM-based counterparts and maintain the same level of accuracy in terms of guaranteeing the same total system travel time in general networks.

A Dynamic Traffic Assignment Model for the Sustainability of Pavement Performance

Existing Dynamic Traffic Assignment (DTA) models assign traffic flow with the principle of travel time, which are easy to distribute most of the traffic flows on the shortest path. A serious unbalance of traffic flow in the network can speed up pavement deterioration of highways with heavy traffic, which influences the sustainability of pavement performance and increases maintenance expenditures. The purpose of this research is to obtain a more optimized traffic assignment for pavement damage reduction by establishing a multi-objective DTA model with the objectives of not only minimum travel time but minimum decline of Present Serviceability Index (PSI) for pavements. Then, teaching-learning-based optimization (TLBO) algorithm is utilized to solve the proposed model. Results of a case study indicate that a more balanced traffic flow assignment can be realized by the model, which can effectively reduce average PSI loss, save maintenance expenditures, extend pavement service life span, save fuel consumption and reduce pollutant emissions in spite of a little increase of average travel time. Additionally, sensitivity of weight factor for the two objective functions is analyzed. This research provides some insights on methods on sustainable pavement performance.

Analysis of a joint entry- and distance-based cordon pricing scheme: a dynamic modeling approach

Transportation demand management (TDM) covers strategies for reducing traffic congestion within the affected urban areas. Congestion pricing includes a branch of TDM strategies; among them, the entry-based cordon pricing, i.e., applying charge on entry, is the most popular because of practicality and social acceptance. Many researchers have investigated different second-best approaches for evaluations of cordon pricing plans, mostly by applying static traffic assignment methods. In this paper, a joint entry- and distance-based scheme is proposed to circumvent the deficiencies intrinsic to each. The optimal joint design is considered as the solution to an optimization problem, in which an equilibrium dynamic traffic assignment model is used to take account of flow variations and represent congestion effects more realistically. The problem is solved for the network of Sioux Falls by using an enumeration algorithm, and the solution is compared with those obtained for distinct entry- and distance-based schemes. Based on the results, the joint tolling has the best performance in reducing the total travel time of the travelers and in alleviating the congestion level inside the cordoned area, while generating a higher level of revenue from tolls. Furthermore, the numerical experiments show the unreliability of the results by static against dynamic modeling approach.

Consistency and Inconsistency Between the Fundamental Relationships on Which Different Traffic Assignment Models Are Based

We compare the forms and properties of different macroscopic behavioral relationships on which different static and dynamic traffic assignment models have been based, namely, travel time-flow functions, travel time-occupancy functions, and flow-occupancy functions or flow-density functions. Given any one of these three relationships we can derive the other two, so that they appear mathematically equivalent. These three behavioral relationships focus on different variables, but they are meant to be observing the same traffic and are not meant to be inconsistent or incompatible with each other. However, we see that the forms and properties usually assumed for any one of these three relationships are often inconsistent or incompatible with the forms or properties that are usually assumed for the other two, or that are considered acceptable for the other two. It might be thought that any inconsistencies between these relationships are because of modeling different phenomena, however that does not explain some of the surprising differences or inconsistencies, for example, those we find implied by linear or piecewise linear functions or by the best known travel time-flow function, the US Bureau of Public Roads function. Such differences or inconsistencies are seldom mentioned in the literature, though they are important because these models are so central in network traffic assignment. They are important when considering or comparing the solutions or predictions from the various traffic assignment models. Yet even if not comparing solutions, it seems important to know whether the model being used is inconsistent with another model that is widely accepted and widely used for similar scenarios. The results do not suggest discontinuing the use of any of the three forms of relationships or the corresponding assignment models referred to above. Rather, they suggest that more attention should be given to noting such potential inconsistencies, incompatibilities, or limitations when considering, reporting, or comparing results or predictions from traffic assignment models. In some cases the results indicate the direction in which the model biases the predictions compared to those from an alternative model that could have been used. In some cases, alternative properties or functional forms could or should be developed or used.

Continuum Dynamic Traffic Assignment Model for Autonomous Vehicles in a Polycentric Urban City with Environmental Consideration

This paper proposed a continuum dynamic model for autonomous vehicles in a polycentric urban city by considering the environment impact of traffic emission. The model assumes that homogeneous autonomous vehicles are continuously distributed over the urban areas which tend to choose a path to minimize their total travel cost from origin to destination. To describe the path choice behavior of travelers, we presented the continuum dynamic traffic assignment model which consists of a two-dimensional hyperbolic system of nonlinear conservation laws with source terms and an Eikonal-type equation. The elastic demand is considered using a function which associating each copy of flow with its total instantaneous travel cost. For the environmental impacts, here we consider the influence of CO emission and include the cost of emission into the actual transportation cost. A solution algorithm for the model is designed as a cell-centered finite volume method for conservation law equations and a fast sweeping method for Eikonal-type equations on unstructured grids. Numerical examples are given to demonstrate the model and the proposed solution algorithm. Further, the results of the travel cost considering CO emissions and not considering CO emissions are compared.

Dynamic traffic assignment using the macroscopic fundamental diagram: A Review of vehicular and pedestrian flow models

Link-level Dynamic Traffic Assignment (DTA) models of large cities may suffer from prohibitive computation times, and calibration/validation can become the major challenge faced in their real-time implementation. The empirical evidence in 2008 in support of the existence of a Macroscopic Fundamental Diagram (MFD) on urban networks led to the formulation of discrete-space DTA models, where the link-level representation of networks replaced by a zone-based representation. In parallel, a large body of DTA models based on Hughes’ pedestrian model have been formulated in continuum space as 2-dimensional conservation laws, where the speed-density relationship has been recently interpreted as a MFD. Unfortunately, today it is not clear whether the continuum-space and discrete-space approaches are consistent with each other, in the sense that a well-defined discrete-space model should correspond to the numerical solution of a continuum model. This paper aims to shed light on this matter by performing a review of the literature in both modeling approaches. We found that (i) the discrete-space DTA models are prone to stalling problem leading to unrealistic gridlocks, (ii) with the exception of Hänseler’s pedestrian models, existing discrete-space models are not guaranteed to be consistent with a continuum formulation, which presents the potential for significant biases between the two approaches although they are trying to answer the same question, (iii) the speed-density relationships used in the continuum-space literature are very simplistic and do not incorporate the effects of network, particularly the effects of intersections, which is the strong suit of the MFD, (iv) the models mostly have been applied to the cases with only one or a few destinations and do not seem to be capable of modeling large-scale networks. We also found that further research is needed to (i) incorporate departure time choice, (ii) improve existing numerical methods, possibly extending recent advances on the one-dimensional kinematic wave (LWR) model, (iii) study the properties of system optimum solutions, (iv) examine the real-time applicability of current continuum-space models compared to traditional DTA methods, and (v) formulate anisotropic models for the interaction of intersecting flows.

Analyzing the impact of a planned transit-oriented development on mode share and traffic conditions

ABSTRACTTransit-oriented development (TOD) is a popular planning strategy used to maximize accessibility to transit for various trip purposes. The quantitative effects of TOD on travel mode shift and traffic congestion have not been extensively tested in the current literature. This paper utilizes a seemingly unrelated regressions (SUR) mode share model and a mesoscopic dynamic traffic assignment (DTA) model to analyze the impact of a planned TOD in Maryland. The proposed model aims at improving the understanding of the quantitative impacts of such a TOD on mode share and traffic congestion. The main result of the mode share model indicates that the increase in transit ridership for a transit accessible shopping center is not that significant. Local traffic conditions will deteriorate due to a lack of investment in road infrastructure planned for the TOD area. The proposed method could be a valuable tool for other indicative land development or transportation policy analyses.