Simulation-based Dynamic Traffic Assignment Research Articles

Joint Routing and Pricing Control in Bimodal Mixed Autonomy Networks with Elastic Demand and Three-Dimensional Passenger Macroscopic Fundamental Diagram

The interaction between mixed autonomy traffic and public transport vehicles competing for limited road space is a less explored area of research. To evaluate the traffic dynamics in bimodal networks, a three-dimensional (passenger) network fundamental diagram, known as 3D-NFD (3D-pNFD), can be estimated that relates the accumulation of cars (autonomous and human-driven) and buses to the network vehicular (passenger) travel production. In this study, we propose a 3D-pNFD-based congestion pricing scheme considering three vehicle classes of buses, system-optimal (SO) seeking connected and automated vehicles (CAVs), and user-equilibrium (UE) seeking human-driven vehicles (HVs). We develop an iterative tri-level modeling framework for mode choice, pricing, and route choice in a mixed autonomy network. The lower level generates mixed equilibrium traffic flow through an integrated mixed equilibrium simulation-based dynamic traffic assignment model and a transit assignment model. The mid-level finds the optimal toll rates through a 3D-pNFD feedback-based controller. A nested logit-based mode choice model is also applied to capture travelers’ preferences toward three available modes and incorporates elastic demand. To encourage CAVs to follow the SO routing mode, they are provided with a discount on the congestion toll whereas UE-seeking HVs are subject to full price toll. Buses are also entirely exempt from the toll. We explore three scenarios with different discount rates on SO-seeking CAVs to investigate the effect of the incentive plans on the mode choice behaviors of road users in the pricing zone. The performance of the proposed model is evaluated in a large-scale network in Melbourne, Australia.

Managing network congestion with link-based incentives: A surrogate-based optimization approach

Incentive-based travel demand management (IBTDM) programs endow monetary incentives to encourage travel demand redistribution across space and time. They are more appealing than alternatives such as congestion charging because commuters do not need to pay out of pocket. However, such congestion-alleviation solutions are usually managed by small private companies with constrained incentive budgets. Thus, the incentive should be wisely determined so that a limited incentive budget can be effectively used to fulfill maximum social welfare while maintaining the financial health of the IBTDM program. It is essential to know whether IBTDM is financially sound—that is, whether financial investment in IBTDM will lead to more than the equivalent value in total system travel time reduction. However, optimizing the link-based endowment scheme in a large-scale network is challenging because 1) the objective function and the budget constraint are both characterized by expensive-to-evaluate functions without closed form, and 2) it is a large-scale optimization problem that contains massive amount of decision variables. In this study, a computationally efficient surrogate-based optimization framework that is suitable for high-dimensional problems is proposed. A simulation-based dynamic traffic assignment model is used to evaluate the performance of transportation systems, and a Kriging model with partial least squares acts as the surrogate to approximate the simulation model. The results show that the optimal network-wide link-based incentive scheme improves the performance of the system. The higher the incentive budget, the more effective the incentive and the lower the marginal utility of the incentive. Furthermore, in a well-designed incentive scheme, a $1M investment in IBTDM would lead to much more than the equivalent of $1M in total system travel time reduction, which proves the economic viability of IBTDM and provides support for its promotion. IBTDM implemented within smaller regions and tighter incentive budgets produces higher utility ratios.

A multiclass simulation-based dynamic traffic assignment model for mixed traffic flow of connected and autonomous vehicles and human-driven vehicles

Connected and Autonomous Vehicles (CAVs) may exhibit different driving and route choice behaviours compared to Human-Driven Vehicles (HDVs), which can result in a mixed traffic flow with multiple classes of route choice behaviour. Therefore, it is necessary to solve the Multiclass Traffic Assignment Problem (TAP) for mixed traffic flow. However, most existing studies have relied on analytical solutions. Furthermore, simulation-based methods have not fully considered all of CAVs’ potential capabilities. This study presents an open-source solution framework for the multiclass simulation-based TAP in mixed traffic of CAVs and HDVs. The proposed model assumes that CAVs follow system optimal with rerouting capabilities, while HDVs follow user equilibrium. It also considers the impact of CAVs on road capacity at both micro and meso scales. The proposed model is demonstrated through three case studies. This study provides a valuable tool that can consider several assumptions for better understanding the impact of CAVs on mixed traffic flow.

Estimating Path Travel Costs in Large-Scale Networks Using Machine-Learning Techniques

The integration of activity-based models (ABMs) with simulation-based dynamic traffic assignment (DTA) is proposed as a prominent alternative to the traditional four-step approach to modeling transportation networks. In DTA, the least-generalized cost path-finding algorithm is executed to route travelers to their optimal paths, while ABM requires travel-cost skims of the activities, regardless of actual paths, to assess various options available to users such as destination and mode choices. These skims can be calculated either by rerunning the shortest-path-finding algorithm or storing the dynamic travel-cost skims generated at the DTA level. Having a large-scale network with multiple user classes, these methods require high memory storage and run time. Therefore, this study presents a heuristic algorithm utilizing machine-learning methods to predict origin–destination (OD) travel distances, times, and costs using historical vehicle trajectory data generated at the DTA level. This study uses an ellipse boundary around the ODs to truncate the network and extract the relevant vehicle sub-trajectories. Extracted sub-trajectories are clustered into with-toll and non-toll groups based on trip costs to estimate travel distance, time, and monetary cost accordingly. This approach can also be used in navigation systems to have a better estimate of arrival times. Numerical results for the greater Chicago network show promising performance in travel-cost measures estimation with improved solution times. To test the scalability of the proposed method for different OD pairs, the prediction of the best ellipse size is carried out using random forest and neural network methods.

Analysis of the Emergence of Autonomous Vehicles Using Simulation-based Dynamic Traffic Assignment – The Case of Budapest

Traffic and transport researchers, policymakers, and vehicle manufacturers are interested in investigating the implications and the influence of autonomous vehicles (AV) because a gradual deployment of such new technologies is expected to take place in the future. This research investigates the impacts of the AVs emergence on traffic performance for the city of Budapest in three future traffic scenarios with different AV market replacement rates for the year 2030. The network was modeled using simulation-based dynamic traffic assignment in PTV Visum software. Four traffic performance parameters were analyzed to explore the impacts of AV's emergence on the network. The results showed noticeable improvements among the four investigated traffic performance parameters.

Dynamic pedestrian traffic assignment with link transmission model for bidirectional sidewalk networks

Planning assessment of urban walking infrastructure requires appropriate modeling methodologies that capture the time-dependent and unique microscopic characteristics of bidirectional pedestrian streams. In this paper, we develop a simulation-based dynamic pedestrian traffic assignment (DPTA) model specifically formulated for walking networks (e.g. sidewalks) with bidirectional links. The model consists of a dynamic user equilibrium (DUE) based walking route choice and a link transmission model (LTM) for network loading. The formulated DUE adopts a pedestrian volume delay function (pVDF) taking into account the properties of bidirectional pedestrian streams such as self-organization. The adopted LTM uses a three-dimensional triangular bidirectional fundamental diagram as well as a generalized first-order node model. The applicability and validity of the model is demonstrated in hypothetical small networks as well as a real-world large-scale network of sidewalks in Sydney. The model successfully replicates formation and propagation of shockwaves in walking corridors and networks due to bidirectional effects.

Deriving the Value of Time for Toll Revenue Forecasting using Multiple Criteria Decision-Making

Mathematical traffic models replicate travel decisions and driver behavior. These tools have become more sophisticated, yet they remain simplified representations of more complex systems, including associated toll forecasts. A literature review shows that a substantial amount of toll revenue forecasts has fallen short of accurately representing actual road usage—by as much as 50%. In recent years, simulation-based modeling tools have emerged as an innovative approach to regional traffic forecasting. They capture time-varying traffic conditions and represent more realistic traffic flow and congestion, but this type of travel forecasting new and complex. One key variable in these traffic modeling tools is the value of time (VoT). The VoT represents how drivers perceive their willingness to pay a toll to reduce their travel time. How to properly quantify the VoT is still not completely understood, but it is the governing factor in how toll revenue forecasts are calculated. We propose three different approaches for quantifying the VoT. The first approach uses socio-economic data in terms of median income per zone. The VoT is quantified based on income levels of each origin-zone that travelers depart from. The second approach uses a traveler’s destination zone—derived based on trip purpose. The second approach uses a multiple-criteria decision-making (MCDM) methodology known as the Analytical Hierarchy Process (AHP) to develop weighting for each trip purpose. A third approach also uses AHP (combined with departure time) to derive weights for each traveler’s VoT. The three approaches were tested using a simulation-based dynamic traffic assignment (DTA) model.

Proposing a Simulation-Based Dynamic System Optimal Traffic Assignment Algorithm for SUMO: An Approximation of Marginal Travel Time

User equilibrium (UE) and system optimal (SO) are among the essential principles for solving the traffic assignment problem. Many studies have been performed on solving the UE and SO traffic assignment problem; however, the majority of them are either static (which can lead to inaccurate predictions due to long aggregation intervals) or analytical (which is computationally expensive for large-scale networks). Besides, most of the well-known micro/meso traffic simulators, do not provide a SO solution of the traffic assignment problem. To this end, this study proposes a new simulation-based dynamic system optimal (SB-DSO) traffic assignment algorithm for the SUMO simulator, which can be applied on large-scale networks. A new swapping/convergence algorithm, which is based on the logit route choice model, is presented in this study. This swapping algorithm is compared with the Method of Successive Average (MSA) which is very common in the literature. Also, a surrogate model of marginal travel time was implemented in the proposed algorithm, which was tested on real and abstract road networks (both on micro and meso scales). The results indicate that the proposed swapping algorithm has better performance than the classical swapping algorithms (e.g. MSA). Furthermore, a comparison was made between the proposed SB-DSO and the current simulation-based dynamic user equilibrium (SB-DUE) traffic assignment algorithm in SUMO. This proposed algorithm helps researchers to better understand the impacts of vehicles that may follow SO routines in future (e.g., Connected and Autonomous Vehicles (CAVs)).

Implications of the Emergence of Autonomous Vehicles and Shared Autonomous Vehicles: A Budapest Perspective

The introduction of autonomous vehicles (AVs) and shared autonomous vehicles (SAVs) is projected to enhance network performance and accessibility. The future share distribution of AV and SAV is not yet apparent, nor is which of these two future transport modes will become dominant. Therefore, this research deploys a simulation-based dynamic traffic assignment using Visum software to investigate the impact of varying the share distribution of AVs and SAVs on Budapest’s network performance and consumer surplus in three projected future traffic scenarios for the years 2030 and 2050 compared to the Base scenario for 2020. The three future scenarios are presented and characterized by different penetration rates of AVs and SAVs to reflect the uncertainty in the market share of these future cars as follows: Mix-Traffic scenario for 2030, and AV-Focused and SAV-Focused scenarios for 2050. The results revealed that the emergence of AVs and SAVs would improve the overall network performance, and better performance was observed with increasing the share distribution of SAVs. Similarly, the consumer surplus increased in all future scenarios, especially with increasing the share distribution of AVs. Consequently, the advent of AVs and SAVs will improve traffic performance and increase consumer surplus, benefiting road users and authorities.

Implications of static and dynamic road pricing strategies in the era of autonomous and shared autonomous vehicles using simulation-based dynamic traffic assignment: The case of Budapest

The advent of autonomous vehicles (AVs) and shared autonomous vehicles (SAVs) is expected to improve network performance and increase accessibility. However, the improved accessibility will most likely induce more vehicle miles traveled, which necessitates the use of travel demand management tools like road pricing (RP). This research deploys dynamic traffic assignment for Budapest network using “Visum” to investigate the impact of three RP schemes (static and dynamic) on network performance and social welfare in three proposed future traffic scenarios for the years 2030 and 2050. The 2030 scenario combines conventional cars (CC), AVs, and SAVs, where CC is the dominant private transport mode (Mix-Traffic Scenario), while the two scenarios for 2050 include AVs and SAVs only and are characterized by high adoption of AVs (AV-Focused Scenario) or wide usage of SAVs (SAV-Focused Scenario). The results revealed that the impact of RP schemes differs according to the different penetration rates of AVs and SAVs. Nevertheless, considering the social benefits gained, implementing a dynamic pricing strategy (Link-based Scheme) in the case of AV-Focused and SAV-Focused scenarios shows better outcomes compared to other pricing schemes. Conversely, the static pricing strategies (i.e., Bridge Toll and Distance-based Schemes) outperform dynamic strategies in the Mix-Traffic scenario.

Distance-based time-dependent optimal ratio control scheme (TORCS) in congested mixed autonomy networks

Connected and automated vehicle technologies provide an opportunity for a more efficient distribution of traffic in urban networks through cooperative routing behavior. Controlling the route choice of a proportion of autonomous vehicles (AVs) to establish the system optimum (SO) condition has already been investigated in static networks. This study aims to develop a time-dependent optimal ratio control scheme (TORCS) in which an optimal ratio of AVs is identified and selected to seek SO routing. The objective of the control scheme is to achieve a reasonable compromise between the system efficiency (i.e., total travel time savings) and the control cost that is proportional to the total distance traveled by SO-seeking AVs. The proposed distance-based TORCS is formulated as a bi-level optimization problem. A mixed equilibrium simulation-based dynamic traffic assignment model (SBDTA) estimates time-dependent mixed traffic patterns in the lower level based on the time-dependent optimal ratios of SO-seeking AVs obtained from the upper level. We also introduce a new concept of frequency control within the TORCS application. The frequency-based TORCS enables the central agent to control the route choice of selected AVs only in the time periods with the most significant impact on system travel time reduction. This is formulated with a binary variable within the TORCS problem indicating an action/no action regarding controlling AVs at a given assignment interval. The applicability of the model is demonstrated on a real large-scale network of Melbourne, Australia.

Impact of Different Penetration Rates of Shared Autonomous Vehicles on Traffic: Case Study of Budapest

The accelerating emergence of vehicle automation and the anticipation of the advent of shared mobility through fully autonomous vehicles indicate the beginning of a new era of mobility which has the potential to reshape the future of transport in urban areas. In light of such developments, it is important that communities prepare to adapt to the changes they might entail. Therefore, in this paper, traffic flow theory, simulation-based dynamic traffic assignment, and a computer experiment using PTV Visum software were employed to study the impact of different market penetration rates of shared autonomous vehicles (SAVs) on a city-size traffic system. The city of Budapest during morning peak period was chosen as a case study, and a simulation model was created by incorporating SAV elements and their interrelationships into the existing traffic model of the case study city; three alternative future penetration rates were examined in relation to five key performance indicators (KPIs). The simulation results indicated that the implementation of the SAV system has a positive effect on traffic performance. Based on the relationships between the modeled SAV demand shares and the network’s KPIs in the designed scenarios, the overall network performance showed improvement along with an increase in the SAV demand share.

A meso-to-macro cross-resolution performance approach for connecting polynomial arrival queue model to volume-delay function with inflow demand-to-capacity ratio

• Cross-resolution modelling approach for understanding the dynamic relationship between demand and supply and the resulting congestion. • Describe oversaturated system dynamics with parsimonious macroscopic analytical formulations with consistent mesoscopic queue vehicular fluid model. • Unified integration of multi-scale models provides city planners with a valid analytical framework to analyze queue saturation evolution process. • Estimate key model parameters from real-world data sets on heavily congested corridors. Although the macroscopic volume-delay function (VDF) has been widely used in static traffic assignment for transportation planning, the planning community has long recognized its deficiencies as a static function in capturing traffic flow dynamics and queue evolution process. In the existing literature, many queueing-based and simulation-based dynamic traffic assignment (DTA) models involving various traffic flow parameters have been proposed to capture traffic system dynamics on different spatial scales; however, how to calibrate these DTA models could still be a challenging task in its own right, especially for real-world congested networks with complex traffic dynamics. By extending the fluid-based polynomial arrival queue (PAQ) model with quadratic inflow rates proposed by Newell (1982) and cubic inflow rates by Cheng et al. (2022), this paper attempts to propose a cross-resolution Queueing-based Volume-Delay Function (QVDF) to explicitly establish a coherent connection between (a) the macroscopic average travel delay performance function in a long-term planning horizon and (b) the mesoscopic dynamic queuing model during a single oversaturated period. By introducing two types of elasticity functional forms, this paper develops a relationship from the macroscopic inflow demand-to-capacity (D/C) ratio to the congestion duration of a bottleneck, from the congestion duration to the magnitude of speed reduction. The QVDF can be directly utilized to provide closed-form expressions for both average travel delay performance and the time-dependent speed profiles. The proposed cross-resolution QVDF provides a numerically reliable and theoretically rigorous performance function to characterize oversaturated bottlenecks at both macroscopic and mesoscopic scales.

Simulation-Based Dynamic Traffic Assignment with Continuously Distributed Value of Time for Heterogeneous Users

The value of time (VOT) attribute is usually utilized to represent the trade-off between time and monetary expenses in transportation problems. A good representation of VOT is essential for evaluation of any road pricing scheme. Conventionally, in dynamic traffic assignment models, VOT is considered as either constant or finite discrete among travelers because of memory and computational limitations, which in turn could introduce bias in the results. This research explicitly models the individual bi-criteria dynamic user equilibrium (IBDUE) problem and presents a distinct simulation-based solution algorithm that enables individual-based traffic assignment within reasonable run time with a successful implementation of variable and continuously distributed VOT in a simulation-based dynamic traffic assignment package. Numerical analysis reveals that the constant and discrete VOT models tend to overestimate toll road usage compared with the continuous VOT model when the toll charge is low, and underestimate it when the toll charge is high, which reflects previous studies. In the meantime, an experiment on a real-world congestion pricing scheme demonstrates the capability of the proposed algorithm on evaluating flow-dependent pricing schemes.

Joint routing and pricing control in congested mixed autonomy networks

Routing controllability of connected and autonomous vehicles (CAVs) has been shown to reduce the adverse effects of selfish routing on the network efficiency. However, the assumption that CAV owners would readily allow themselves to be controlled externally by a central agency for the good of the system is unrealistic. In this paper, we propose a joint routing and pricing control scheme that aims to incentivize CAVs to seek centrally controlled system-optimal (SO) routing by saving on tolls while user equilibrium (UE) seeking human-driven vehicles (HVs) are subject to a congestion charge. The problem is formulated as a bi-level optimization program where the upper level optimizes the dynamic toll rates using the network fundamental diagram (NFD) and the lower level is a mixed equilibrium simulation-based dynamic traffic assignment model (SBDTA) considering different combinations of SO-seeking CAVs. We apply a feedback-based controller to solve for the optimal spatially differentiated distance-based congestion charge from which SO-seeking CAVs are exempt; but UE-seeking HVs are subject to the charge for entering the city center. To capture the distinct microscopic behavior of CAVs in the mixed autonomy traffic, we also implement an adaptive link fundamental diagram (FD) within the SBDTA model. The proposed joint control scheme encourages CAV owners to seek SO routing resulting in less total system travel time. It also discourages UE-seeking HVs from congesting the city center. We demonstrate the performance of the proposed scheme in both a small network and a large-scale network of Melbourne, Australia.

A link-to-link segment based metamodel for dynamic network loading

Dynamic network loading (DNL) is a core part of simulation-based dynamic traffic assignment (DTA) models, which describes how traffic propagates on a transportation network and usually maps a set of route departure rates to a set of route travel times. Due to the incorporation of different intra- and inter-link dynamics such as queuing, spillback, etc., DNL becomes complex, resulting in models with undesirable analytical properties (e.g., discontinuity, non-differentiability, and lack of closed-form) and requiring intensive computational efforts. Moreover, as DNL is applied repeatedly in simulation-based DTA algorithms, it often is the computational bottleneck of large-scale traffic assignment and related optimization problems. In this research, we address these problems by proposing a link-to-link segment-based Kriging metamodel for dynamic network loading. The proposed Kriging model calculates route travel time, link travel time, and link flow. It systematically approximates the traditional DNL model while being faster and maintaining some desirable analytical properties. Both temporal and spatial proximity information and the route segment incidence information are incorporated in the metamodel formulation. The models are trained using maximum likelihood estimation with different dataset sizes. In the experiments, the proposed Kriging metamodels performed better than a state-of-the-art neural network model, achieving an average error of 1.64% and 5.32% in the Nguyen Dupuis (ND) network and the Sioux Falls (SF) network, respectively, along with at least 43 times, sometimes as high as over 1300 times, improvement in computational speed. The results, however, suggest a tradeoff between efficiency and accuracy and the size of the training dataset. With balanced route demand, the model’s performance was reasonable even under congested traffic conditions. The MAPE values were at most 3% and 18% in the ND network and the SF network, respectively, for different level of congestion demonstrating the effectiveness of the proposed model.

Improving the accuracy and efficiency of online calibration for simulation-based Dynamic Traffic Assignment

Simulation-based Dynamic Traffic Assignment models have important applications in real-time traffic management and control. The efficacy of these systems rests on the ability to generate accurate estimates and predictions of traffic states, which necessitates online calibration. A widely used solution approach for online calibration is the Extended Kalman Filter (EKF), which – although appealing in its flexibility to incorporate any class of parameters and measurements – poses several challenges with regard to calibration accuracy and scalability, especially in congested situations for large-scale networks. This paper addresses these issues in turn so as to improve the accuracy and efficiency of EKF-based online calibration approaches for large and congested networks. First, the concept of state augmentation is revisited to handle violations of the Markovian assumption typically implicit in online applications of the EKF. Second, a method based on graph-coloring is proposed to operationalize the partitioned finite-difference approach that enhances scalability of the gradient computations.Several synthetic experiments and a real world case study demonstrate that application of the proposed approaches yields improvements in terms of both prediction accuracy and computational performance. The work has applications in real-world deployments of simulation-based dynamic traffic assignment systems.

Comparing Dynamic User Equilibrium and Noniterative Stochastic Route Choice in a Simulation-Based Dynamic Traffic Assignment Model: Practical Considerations for Large-Scale Networks

Simulation-based dynamic traffic assignment (DTA) models play a vital role in transportation planning and operations. While the widely studied equilibrium-seeking DTA including dynamic user equilibrium (DUE) often provides robust and consistent outcomes, their expensive computational cost for large-scale network applications has been a burden in practice. The noniterative stochastic route choice (SRC) model, as a nonequilibrium seeking DTA model, provides an alternative for specific transportation operations applications that may not require equilibrium results after all (e.g., evacuation and major network disruptions) and thus tend to be computationally less expensive, yet may suffer from inconsistent outcomes. While DUE is a widely accepted approach for many strategic planning applications, SRC has been increasingly used in practice for traffic operations purposes. This paper aims to provide a comparative and quantitative analysis of the two modeling approaches. Specifically, a comparison has been made at two levels: link-level flows and network-level congestion patterns. Results suggest that adaptive driving improves the quality of the SRC solution, but its difference from DUE still remains significant at the link level. Results have practical implications for the application of large-scale simulation-based DTA models for planning and operations purposes.

How does the value of time influence road user costs during work zone closures? A case study in El Paso, Texas, using simulation-based modeling methods

It is becoming standard practice for many departments of transportation (DOTs) to use incentive/disincentive clauses (also known as road user costs) with contractors to stay on or ahead of schedule. These road user costs are clauses that DOTs use to calculate a monetary amount to encourage contractors to complete work prior to milestone dates and/or limit the time specified on the contract. The monetary amounts are typically vehicle operating costs and vehicle delay costs encumbered by highway users resulting from construction, maintenance, or rehabilitation activity. In this paper, we propose an innovative way of calculating these costs using varied values of time based on trip purpose and departure time. In addition, we use advanced pre-trip and en route traveler information to determine the influence it has on route choice. Several scenarios are modeled using an advanced, simulation-based dynamic traffic assignment model. The goal of this paper is to identify the governing factors that contribute to road use costs by determining different approaches to derive the value one places on a trip. The approach to this study is twofold: first several research methods were used to derive the value of time. Second, the use of advanced traveler information is introduced to determine if it plays a critical role in route choice. The proposed methodology shows differences in road user cost calculations. Which approach would be more receptive to a contractor while proposing roadway construction? A case study of a roadway construction project in El Paso, Texas, is used to compare different approaches to calculate road user costs.

An Open GMNS Dataset of a Dynamic Multi-Modal Transportation Network Model of Melbourne, Australia

Simulation-based dynamic traffic assignment models are increasingly used in urban transportation systems analysis and planning. They replicate traffic dynamics across transportation networks by capturing the complex interactions between travel demand and supply. However, their applications particularly for large-scale networks have been hindered by the challenges associated with the collection, parsing, development, and sharing of data-intensive inputs. In this paper, we develop and share an open dataset for reproduction of a dynamic multi-modal transportation network model of Melbourne, Australia. The dataset is developed consistently with the General Modeling Network Specification (GMNS), enabling software-agnostic human and machine readability. GMNS is a standard readable format for sharing routable transportation network data that is designed to be used in multimodal static and dynamic transportation operations and planning models.