Dynamic User Equilibrium Traffic Assignment Research Articles

Development, Calibration, and Validation of a Large-Scale Traffic Simulation Model: Belgium Road Network

Development of large-scale traffic simulation models have always been challenging for transportation researchers. One of the essential steps in developing traffic simulation models, which needs lots of resources, is travel demand modeling. Therefore, proposing travel demand models that require less data than classical travel demand models is highly important, especially in large-scale networks. This paper first presents a travel demand model named as probabilistic travel demand model, then it reports the process of development, calibration and validation of Belgium traffic simulation model. The probabilistic travel demand model takes cities' population, distances between the cities, yearly vehicle-kilometer traveled, and yearly truck trips as inputs. The extracted origin-destination matrices are imported into the SUMO traffic simulator. Mesoscopic traffic simulation and the dynamic user equilibrium traffic assignment are used to build the base case model. This base case model is calibrated using the traffic count data. Al-so, the validation of the model is performed by comparing the real (extracted from Google Map API) and simulated travel times between the cities. The validation results ensure that the model is a superior representation of reality with a high level of accuracy. The model will be helpful for road authorities, planners, and decision-makers to test different scenarios, such as the im-pact of abnormal conditions or the impact of connected and autonomous vehicles on the Belgium road network.

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.

A real-time vehicle-specific eco-routing model for on-board navigation applications capturing transient vehicle behavior

The paper develops a real-time vehicle-specific eco-routing model for use in on-board navigation systems for both conventional fuel- and battery-powered electric vehicles. The model uses a novel link cost function that retains all microscopic transient behavior along a link by capturing within-link speed, acceleration, and road grade variations. Specifically, eight vehicle-agnostic link-specific variables are transmitted to the cloud and fused with information received from other connected vehicles. The fused data are then sent back to the connected vehicles and used to compute vehicle-specific eco-routes (edge computing). The solution produces an energy-efficient dynamic user-equilibrium traffic assignment that is solved incrementally. A numerical experiment is first designed to test the model, demonstrating the benefits associated with vehicle-specific eco-routes compared to those produced by traditional models. The model is then implemented in a micro-simulation framework to evaluate the network-wide impacts of the proposed energy-efficient user-optimum incremental traffic assignment for different traffic demand levels. Results demonstrate that the proposed model produces lower network-wide energy consumption levels compared to traditional energy-efficient and travel time user-optimum traffic assignment methods for both conventional fuel and electric vehicles. Conventional fuel savings relative to travel time routing decrease with increasing traffic demand levels, while electric power savings do not vary monotonically with congestion levels. Energy savings relative to traditional eco-routing are also demonstrated to not vary monotonically with demand levels. Results of the study also demonstrate that the transportation network layout significantly affects the eco-routing system performance. Finally, the feasibility of the proposed model in real-world applications is discussed and presented.

An informed user equilibrium dynamic traffic assignment problem in a multiple origin-destination stochastic network

We develop in this paper a comprehensive linear mathematical framework to study the benefit of real-time information and the impact of resulting user adaptive route choice behaviours on network performance. The framework formulates the information-based stochastic user equilibrium (ISUE) dynamic traffic assignment (DTA) problem for a multiple origin-destination (OD) network. Using the framework, we prove the linkage between the user equilibrium (UE) and system optimal (SO) solutions underpinned by the first-in-first-out (FIFO) principle. This important property then enables us to develop an incremental loading method to obtain the ISUE solutions efficiently by solving a sequence of linear programs. Moreover, the proposed method is more scalable that avoids a huge enumeration of paths in large-scale networks as done in path-based methods of the existing literature on this topic. We show via numerical examples the impact of information on both route choices and network performance, and demonstrate the significant improvements in the obtained ISUE solution both in terms of accuracy and computational complexity.

A linear framework for dynamic user equilibrium traffic assignment in a single origin-destination capacitated network

The dynamic traffic assignment (DTA) problem has been studied intensively in the literature. However, there is no existing linear framework to solve the user equilibrium (UE) DTA problem. In this paper, we develop a novel linear programming framework to solve the UE-DTA problem in a dynamic capacity network that exploits the linkage between the UE and system optimal (SO) solutions underpinned by a first-in-first-out (FIFO) principle. This important property enables us to develop an incremental loading method to obtain the UE solutions efficiently by solving a sequence of linear programs. The proposed solution methodology possesses several nice properties such as a predictable number of iterations before reaching the UE solution, and a linear system of equations to be solved in each of the iterations.In contrast to the related iterative methods, such as Frank–Wolfe algorithm, successive average (MSA) or projection and their extensions where the purpose of iteration is to seek the solution convergence, whereas ours is to solve a linear problem over multiple iterations but only for a single unit of demand in each iteration. Furthermore, we provide a theoretical proof that in the limit, the SO objective can be used to obtain the UE solution as the system time step goes to zero given the satisfaction of the FIFO constraint. We show via numerical examples the significant improvements in the obtained UE solutions both in terms of accuracy and computational complexity.

Activity-Based Model with Dynamic Traffic Assignment and Consideration of Heterogeneous User Preferences and Reliability Valuation

To forecast the impact of congestion pricing schemes, it is essential to capture user responses to these schemes and the resulting dynamics of traffic flow on the network. The responses of users must include route, departure time, and mode choices. To capture the effects of these decisions, this paper lays out a framework for the integration of the relevant elements of an activity-based model (ABM) with a dynamic traffic assignment (DTA) model and a simulation framework to support the analysis and evaluation of various pricing schemes. In this paper, a multicriterion dynamic user equilibrium traffic assignment model is used; the model explicitly considers heterogeneous users who seek to minimize travel time, out-of-pocket cost, and travel time reliability in the underlying route choice framework. In addition to the methodological developments, various demand and supply parameters are estimated and calibrated for the selected application network (the Greater Chicago, Illinois, network). This paper showcases the integration of ABM components and a DTA in one coherent modeling framework for the implementation and evaluation of congestion pricing in an actual large-scale network.

Flow Equilibrium Under Dynamic Traffic Assignment and Signal Control—An Illustration of Pretimed and Actuated Signal Control Policies

Under intelligent transportation systems, the interaction between signal setting and traffic assignment is an important issue in designing efficient advanced traffic management systems. Most of the studies only describe the interaction under static assumptions, which do not consider possible temporal flow distribution. These assumptions limit the applicability in real-time management and control. This paper focuses on finding equilibrium under the interaction of signal setting and traffic assignment. The problem is constructed and solved through a bi-level framework. The upper level solves for signal setting parameters based on flow distributions, including cycle length and green splits. The lower level solves for user equilibrium dynamic traffic assignment (UEDTA) flows in a traffic network. The signal setting parameters are adjusted through pretimed and actuated signal controls. UEDTA flow patterns are generated through a simulation-based dynamic traffic assignment (DTA) model, DynaTAIWAN. Numerical experiments based on a real network in Kaohsiung City, Taiwan, are conducted to study the dynamic equilibrium. The numerical results indicate the existence of equilibrium flow under signal control and route assignment in a dynamic aspect. The results show that the average travel times under the pretimed signal policy are, in general, better than the times under the actuated signal policy.

A framework for user equilibrium dynamic traffic assignment

Several analytic approaches have been developed to describe or predict traffic flows on networks with time-varying (dynamic) travel demands, flows and travel times. A key component of these models lies in modelling the flows and/or travel times on the individual links, but as this is made more realistic or accurate it tends to make the overall model less computationally tractable. To help overcome this, and for other reasons, we develop a bi-level user equilibrium (UE) framework that separates the assignment or loading of flows on the time–space network from the modelling of flows and trip times within individual links. We show that this model or framework satisfies appropriate definitions of UE satisfies a first-in-first-out (FIFO) property of road traffic, and has other desirable properties. The model can be solved by iterating between (a) a linear network-loading model that takes the lengths of time–space links as fixed (within narrow ranges), and (b) a set of link flow sub-models which update the link trip times to construct a new time–space network. This allows links to be processed sequentially or in parallel and avoids having to enumerate paths and compute path flows or travel times. We test and demonstrate the model and algorithms using example networks and find that the algorithm converges quickly and the solutions behave as expected. We show how to extend the model to handle elastic demands, multiple destinations and multiple traffic types, and traffic spillback within links and from link to link.

A bi-criterion dynamic user equilibrium traffic assignment model and solution algorithm for evaluating dynamic road pricing strategies

To support the evaluation of dynamic road pricing strategies in a network context, this study develops a bi-criterion dynamic user equilibrium (BDUE) model, which aims to capture users’ path choices in response to time-varying toll charges, and hence explicitly considers heterogeneous users with different value of time (VOT) preferences in the underlying path choice decision framework. The VOT is represented as a continuously distributed random variable across the population of trips, and an infinite dimensional variational inequality formulation is established to characterize the solutions to the BDUE problem. This study proposes a simulation-based heuristic approach to find the BDUE path flow patterns. Specifically, embedded in the algorithmic framework are (i) a bi-criterion time-dependent least generalized cost path algorithm applied to generate the extreme efficient path set and the corresponding set of breakpoints that naturally defines the multiple user classes, thereby generating the descent direction from a multi-class auxiliary path flow vector, and (ii) a traffic simulator used to describe the traffic flow propagation and determine experienced travel times and costs. To circumvent the difficulty of storing the memory-intensive path set and routing policies for large-scale network applications, a vehicle-based implementation technique is proposed to use the vehicle path set as a proxy for keeping track of the path assignment results. A set of numerical experiments are conducted on several real road networks to explore the convergence behavior and solution quality of the BDUE algorithm, as well as to investigate how VOT distributions affect the path flow pattern and toll road usage under dynamic road pricing scenarios.

Dynamic User Equilibrium Traffic Assignment on Congested Multidestination Network

This paper presents the development of a dynamic user equilibrium (DUE) traffic-assignment model for the congested urban road network with signalized intersections. A simulation-based approach is employed for the case of multiple-origin multiple-destination traffic flows. The modified method of successive averages (MSA) is developed to arrive at the user equilibrium condition. The proposed method is applied to an example network, and its results are compared with the results obtained by using the artificial intelligence technique of genetic algorithms (GAs). It is concluded that the formulated DUE model avoids the all-or-nothing type of assignment and gives results closer to the equilibrium condition, and the modified MSA gives better results with lesser computation time as compared to GAs.

The existence, uniqueness and computation of an arc-based dynamic network user equilibrium formulation

In this paper, a dynamic user equilibrium traffic assignment model with simultaneous departure time/route choices and elastic demands is formulated as an arc-based nonlinear complementarity problem on congested traffic networks. The four objectives of this paper are (1) to develop an arc-based formulation which obviates the use of path-specific variables, (2) to establish existence of a dynamic user equilibrium solution to the model using Brouwer's fixed-point theorem, (3) to show that the vectors of total arc inflows and associated minimum unit travel costs are unique by imposing strict monotonicity conditions on the arc travel cost and demand functions along with a smoothness condition on the equilibria, and (4) to develop a heuristic algorithm that requires neither a path enumeration nor a storage of path-specific flow and cost information. Computational results are presented for a simple test network with 4 arcs, 3 nodes, and 2 origin–destination pairs over the time interval of 120 periods.

Are the objective and solutions of dynamic user-equilibrium models always consistent?

Existing dynamic user-equilibrium traffic assignment (DUETA) models are mostly expanded from the static user-equilibrium traffic assignment model by introducing the time dimension along with a group of additional constraints. Whereas the equivalency between the solution to the traffic assignment model and the user-equilibrium condition as defined by Wardrop is well established in the static case, the same may not be true for the dynamic case. This paper examines the general form of DUETA models as proposed in previous research and shows that, if queuing behavior is represented in the model at a minimal level, the solution to conventional DUETA models with an objective function of the form adopted by most existing formulations may not necessarily converge to or approximate the Wardropian user-equilibrium condition in the dynamic sense as defined by many researchers.