Dynamic User Optimal Research Articles

Dynamic Assessment of Road Network Vulnerability Based on Cell Transmission Model

The road network maintaining stability is critical for guaranteeing urban traffic function. Therefore, the vulnerable links need to be identified accurately. Previous vulnerability research under static condition compared the operating states of the old equilibrium before the event and the new equilibrium after the event to assess vulnerability ignoring the dynamic variation process. Does road network vulnerability change over time? This paper combines the vulnerability assessment with the traffic flow evolution process, exploring the road network vulnerability evaluation from the perspective of time dimension. More accurate identification and evaluation of vulnerable nodes and links can help to strengthen the ability of road network resisting disturbances. A modified dynamic traffic assignment (DTA) model is established for dynamic path selection (reselect the shortest path at the end of each link) based on the dynamic user optimal (DUO) principle. A modified cell transmission model is established to simulate the traffic flow evolution processes. The cumulative and time-varying index of vulnerability assessment is established from the viewpoint of traveler’s time loss. Then the road network vulnerability assessment combined the traffic flow model with the vulnerability index. The road network vulnerability assessment of Bao’an Central District of Shenzhen, China, reveals that road network vulnerability does contain a dynamic process, and vulnerable links in each phase can be exactly identified by the model. Results showed that the road network would have a large vulnerability during the disordered phase when the main road fails. Therefore, prioritizing the smooth flow of main roads can weaken the impact of road network vulnerability exposure.

An Enhanced Dynamic User Optimal Passenger Flow Assignment Model for Metro Networks

By considering the difference between a car driver’s route choice behavior on the road and a passenger’s route choice behavior in urban rail transit (URT), this paper proposes an enhanced Dynamic User Optimal (DUO) passenger flow assignment model for metro networks. To capture realistic URT phenomena, the model has integrated the train operation disturbance constraint. Real passenger and train data are used to verify the proposed model and algorithm. The results indicate that the DUO-based model is more suitable for describing passenger route choice behavior under uncertain conditions compared to a static model. Moreover, this paper found that passengers under oversaturated conditions are more sensitive to train operation disturbances compared to undersaturated passengers.

The nonlinear equation system approach to solving dynamic user optimal simultaneous route and departure time choice problems

Dynamic user optimal simultaneous route and departure time choice (DUO-SRDTC) problems are usually formulated as variational inequality (VI) problems whose solution algorithms generally require continuous and monotone route travel cost functions to guarantee convergence. However, the monotonicity of the route travel cost functions cannot be ensured even if the route travel time functions are monotone. In contrast to traditional formulations, this paper formulates a DUO-SRDTC problem (that can have fixed or elastic demand) as a system of nonlinear equations. The system of nonlinear equations is a function of generalized origin-destination (OD) travel costs rather than route flows and includes a dynamic user optimal (DUO) route choice subproblem with perfectly elastic demand and a quadratic programming (QP) subproblem under certain assumptions. This study also proposes a solution method based on the backtracking inexact Broyden–Fletcher–Goldfarb–Shanno (BFGS) method, the extragradient algorithm, and the Frank-Wolfe algorithm. The BFGS method, the extragradient algorithm, and the Frank-Wolfe algorithm are used to solve the system of nonlinear equations, the DUO route choice subproblem, and the QP subproblem, respectively. The proposed formulation and solution method can avoid the requirement of monotonicity of the route travel cost functions to obtain a convergent solution and provide a new approach with which to solve DUO-SRDTC problems. Finally, numeric examples are used to demonstrate the performance of the proposed solution method.

Simulating the Dynamic Escape Process in Large Public Places

Pedestrian dynamics plays an important role in public facility design and evacuation management. During an escape process from a large public space, crowd behavior is a collection of pedestrian exit/route choice behavior, and movement behavior. Modelling such an escape process is an extremely complex challenge. In this paper, an integrated macro-micro approach is developed to simulate the escape process. An analysis of the simulation reveals the mechanisms of the formation of crowd congestion and flow distribution. At the macroscopic level, a mathematical model, based on the concept of the dynamic user optimal (DUO) criterion, is formulated to describe the pedestrian exit/route choice behavior. A method based on the fundamental diagram and point-queuing theory is developed to estimate the pedestrian escape time. At the microscopic level, a modified social force model is adopted to formulate pedestrians' dynamic movements during the escape process. A solution algorithm is proposed to solve the macro-micro integrated model and a series of experiments are carried out to validate the proposed model. The simulation results agree with the extracted experimental data. Finally, the integrated model and algorithm are used to simulate the escape process in a large public place. The proposed approach is able to generate the bandwagon effect, bottleneck effect, and route choice patterns.

In This Issue

In This Issue

An Intersection-Movement-Based Dynamic User Optimal Route Choice Problem

In this paper a novel variational inequality (VI) formulation of the dynamic user optimal (DUO) route choice problem is proposed using the concept of approach proportion. An approach proportion represents the proportion of travelers that select a turning or through movement when leaving a node. Approach proportions contain travelers' route information so that the realistic effects of physical queues can be captured in a formulation when a physical-queue traffic flow model is adopted, and so that route enumeration and path-set generation can be avoided in the solution procedure. In addition, the simple structure of the approach proportion representation allows us to decompose the constraint set for solving large-scale DUO route choice problems. This paper also discusses the existence and uniqueness of the solutions to the VI problem and develops a solution algorithm based on the extragradient method to solve the proposed VI problem. This solution algorithm makes use of the decomposition property of the constraint set and is convergent if the travel time functions are pseudomonotone and Lipschitz continuous. It is not necessary to know the Lipschitz constant of the travel time functions in advance. Finally, numerical examples are given to demonstrate the properties of the proposed model and the performance of the solution algorithm.

Solving the Dynamic User Optimal Assignment Problem Considering Queue Spillback

This paper studies the dynamic user optimal (DUO) traffic assignment problem considering simultaneous route and departure time choice. The DUO problem is formulated as a discrete variational inequality (DVI), with an embeded LWR-consistent mesoscopic dynamic network loading (DNL) model to encapsulate traffic dynamics. The presented DNL model is capable of capturing realistic traffic phenomena such as queue spillback. Various VI solution algorithms, particularly those based on feasible directions and a line search, are applied to solve the formulated DUO problem. Two examples are constructed to check equilibrium solutions obtained from numerical algorithms, to compare the performance of the algorithms, and to study the impacts of traffic interacts across multiple links on equilibrium solutions.

DYNAMIC TRAFFIC ASSIGNMENT: PROPERTIES AND EXTENSIONS

Dynamic Traffic Assignment (DTA) is long recognized as a key component for network planning and transport policy evaluations as well as for real-time traffic operation and management. How traffic is encapsulated in a DTA model has important implications on the accuracy and fidelity of the model results. This study compares and contrasts the properties of DTA modelled with point queues versus those with physical queues, and discusses their implications. One important finding is that with the more accurate physical queue paradigm, under certain congested conditions, solutions for the commonly adopted dynamic user optimal (DUO) route choice principle just do not exist. To provide some initial thinking to accommodate this finding, this study introduces the tolerance-based DUO principle. This paper also discusses its solution existence and uniqueness, develops a solution heuristic, and demonstrates its properties through numerical examples. Finally, we conclude by presenting some prospective future research directions.

DEVELOPMENT OF A SIMULATION ALGORITHM FOR DSO SOLUTION ON A SIMPLE NETWORK

This study develops a DSO (Dynamic System Optimum) simulation algorithm first, which can reproduce the traffic condition so as to minimize total travel time on condition that time-dependent OD demand is given. Next, the algorithm is verified by applying to a simple network with one OD pair. Recently most of dynamic traffic simulation models reproduce traffic flows dynamically under the principle of DUO (Dynamic User Optimal). On the other hand, DSO solution must provide practical information for the effective traffic control such as ramp metering control and road pricing measure. However, there is no simulation algorithm seeking for the DSO solution Therefore, in this study, DSO simulation algorithm has been developed in accordance with Dynamic Marginal Cost equilibrium principle, which equilibrates DMC of all routes. As a result of the verification, it has been confirmed that the proposed model and algorithm efficiently solved DSO solution.

A discrete time dynamic flow model and a formulation and solution method for dynamic route choice

This paper considers the ideal dynamic user optimal (DUO) route choice problem using a route-based variational inequality approach. A discrete time dynamic flow model is developed, which uses link travel time functions to determine time-dependent network states. The proposed flow model is built on discrete time flow variables, to eliminate the discretization process of continuous time based models. Continuity of route travel time functions is proven to establish the existence of a solution, on the condition that the link travel time functions are continuous. Furthermore, flow dispersion and concentration can be simulated, which is expected to enhance the ability of capturing dynamics of traffic movements. A variational inequality formulation based on an alternative cost mapping is proposed, which is derived from a route swapping heuristic approach. As a solution method, the projection-based approach is used since the route travel time functions in our model are not smooth. To increase the performance of the projection-based methods, an efficient implementation of the projection operation is developed. Computational experiences with two example networks are provided to illustrate the model.

A cell-based simultaneous route and departure time choice model with elastic demand

This paper develops a cell-based formulation for the simultaneous route and departure time choice problem with elastic demands through a variational inequality problem (VIP). This formulation follows the ideal Dynamic User Optimal (DUO) route and departure time choice principle and encapsulates a network version of the cell transmission model to improve the accuracy of dynamic traffic modeling. To solve the formulation, we adopt a descent method developed for co-coercive VIP. Two numerical studies are set up to demonstrate the quality of the solutions. The results show that the formulation correctly determines the DUO solution even in the presence of queue spillback and junction blockage. In the analysis, we prove that the origin–destination (OD) first-in-first-out (FIFO) property is only maintained under certain conditions of the travel time and schedule delay costs. These conditions on the cost parameters are, interestingly, consistent with the empirical results. Thus, the theoretical analyses together with the empirical results indicate that OD FIFO should hold in reality. This finding is a reasonable reflection of our experience, which shows that OD FIFO generally holds subject to overtaking not occurring commonly.

A cell-based dynamic traffic assignment model: Formulation and properties

This paper developed a cell-based dynamic traffic assignment (DTA) formulation that follows the ideal dynamic user optimal (DUO) principle. Through defining an appropriate gap function, we transformed a formulation based on the nonlinear complementarity problem to an equivalent mathematical program. To improve the accuracy of dynamic traffic modelling, this formulation encapsulates a network version of the cell transmission model (CTM). We set up four scenarios to evaluate the properties of this formulation, in the aspects of traffic dynamics, traffic interactions across multiple links, and the ideal DUO principle. This formulation produced outputs that are in agreement with what the results ought to be. Namely, the formulation is able to capture dynamic traffic phenomena, such as shock-waves, queue formation, and dissipation. Moreover, it is capable of capturing dynamic traffic interactions across multiple links. Both of these characteristics are inherent from the underlying traffic model adopted in this formulation. The results also demonstrate that this cell-based formulation follows the ideal DUO principle.

A cell-based variational inequality formulation of the dynamic user optimal assignment problem

This paper developed a cell-based dynamic traffic assignment formulation that follows the ideal dynamic user optimal (DUO) principle through a variational inequality approach. To improve the accuracy of dynamic traffic modeling, this formulation encapsulates a network version of the Cell Transmission Model (CTM). Moreover, this formulation satisfies the first-in-first-out (FIFO) conditions through the CTM. For solutions, we employed an alternating direction method developed for co-coercive variational inequality problems. We set up two scenarios to evaluate the properties of this formulation, in the areas of traffic dynamics and the ideal DUO principle. The results showed that the formulation was capable of capturing dynamic phenomena, such as shockwaves, queue formation and dissipation. Moreover, the results demonstrated that this cell-based formulation produced solutions that precisely followed the ideal DUO principle.

ANALYSIS OF LANE-BLOCKING EVENTS WITH AN ANALYTICAL DYNAMIC TRAFFIC ASSIGNMENT MODEL

An analytical-based dynamic traffic assignment (DTA) model intended for off-line analysis and evaluation of non-recurring lane-blocking events is proposed. Formulated as a variational inequality (VI), this model solves an ideal dynamic user-optimal (DUO) route choice problem. A diagonalization algorithm is proposed to solve the model to a prespecified convergence using a targe-scale, real-life traffic network. Adjustments of link capacities triggered by external lane-blocking events and internal modeled traffic phenomena are explicitly considered in the solution algorithm to capture queue formation and dissipation. The proposed solution procedure approximates route choices based on anticipatory and non-anticipatory traffic

A path-based analytical dynamic traffic assignment model for real time evaluation of simulation based dynamic traffic assignment models

In the development of a deployable real-time DTA system, macroscopic analytical DTA models are employed to provide credible benchmarks for evaluating simulation-based DTA models. To achieve this goal, an analytical link-based DTA model and a path-based DTA model are developed to incorporat the rolling horizon implementation, traffic control models, and on-line calibration process. A benchmark evaluation for simulation-based DTA models is the intended agenda of the proposed model, algorithm, and implementation approach. Specifically, a path-based DTA model is discussed in this paper to illustrate the complicated process of model and algorithm development. This model is formulated as a variational inequality (VI) and can be solved efficiently to convergence by the proposed relaxation algorithm. The incorporation of rolling horizon implementation, traffic control models, and on-line calibration makes the proposed model and algorithm more appropriate for bench-mark evaluation for simulation-based DTA models. According to different assumptions of travelers’ route choice behavior, travelers are classified into three different classes, including fixed (predetermined) route class stochastic dynamic user-optimal (SDUO) class, and dynamic user-optimal (DUO) class. The solution steps and the combined algorithm are discussed in detail. Computational results are also reported and analyzed.

Dynamic Analyses on Network Traffic Flow

This paper summarizes dynamic network analyses utilizing cumulative arrival and departure curves under point as well as physical queues. First, a relationship between the cumulative curve under point and physical queue concepts and time-space diagram is explained. Second, dynamic traffic assignments with three principles of DUO (Dynamic User Optimal), DUE (Dynamic User Equilibrium), and DSO (Dynamic System Optimal) are formulated. Finally, theoretical past research outcomes on departure time choice, which is as important as route choice, are reviewed.

A link-based variational inequality model for dynamic departure time/route choice

The dynamic user-optimal (DUO) departure time and route choice problem is to determine travelers' best departure times and route choices at each instant of time. In a previous paper, we presented a route-based two-level optimal control model for the DUO departure time/route choice problem. However, this model is not appropriate for large scale transportation networks because some degree of route enumeration is necessary to solve the model. In this paper, we present a link-based variational in equality (VI) formulation for the DUO departure time/route choice problem so that route enumeration can be avoided in both the formulation and the solution procedure. The model extends our previous VI model for the DUO route choice problem to the case where both departure time and route over a general road network must be chosen simultaneously. By proving the necessity and sufficiency of this VI, we establish the equivalence of the VI formulation and the link-based DUO departure time/route choice conditions.

A link-based variational inequality formulation of ideal dynamic user-optimal route choice problem

The ideal dynamic user-optimal (DUO) route choice problem is to determine vehicle flows on each link at each instant of time resulting from drivers using actual minimal-time routes. Actual route time is the travel time incurred while driving along the route. In a previous paper, we presented a route-based optimal control model for the ideal DUO route choice problem. However, this model is not appropriate for large-scale transportation networks because some degree of route enumeration is necessary to solve the model. In this paper, we first present the traffic network constraints and link-based DUO route choice conditions. Then, we introduce a link-based variational inequality (VI) formulation for the ideal DUO route choice problem so that route enumeration can be avoided in both the formulation and the solution procedure. By proving the necessity and sufficiency of this VI, we demonstrate that the VI formulation is equivalent to the link-based DUO route choice conditions.

A New Class of Instantaneous Dynamic User-Optimal Traffic Assignment Models

The instantaneous dynamic user-optimal (DUO) traffic assignment problem is to determine vehicle flows on each link at each instant of time resulting from drivers using instantaneous minimal-time routes. Instantaneous route time is the travel time incurred if traffic conditions remain unchanged while driving along the route. In this paper, we introduce a different definition of an instantaneous DUO state. Using the optimal control theory approach, we formulate two new DUO traffic assignment models for a congested transportation network. These models include new formulations of the objective function and flow propagation constraints, and are dynamic generalizations of the static user-optimal model. The equivalence of the solutions of the two optimal control programs with DUO traffic flows is demonstrated by proving the equivalence of the first-order necessary conditions of the two programs with the instantaneous DUO conditions. Since these optimal control problems are convex programs with linear constraints, they have unique solutions. A numerical example is presented indicating that this class of models yields realistic results.

Dynamic User Optimal Signal Design at Isolated Intersections

This paper presents a proposal of novel signal design problem at isolated intersections, which assumes that the effective green times assigned to each signal phase follow dynamic user optimal (DUO) principle. At the DUO state, the average delays of vehicles using the signal phases with positive additional green times (the assigned effective green times minus the minimum effective green times) are equal and maximum. The proposed signal design problem is formulated as a variational inequality (VI) problem. The point queue (PQ) model is applied to represent traffic dynamics and to generate the cumulative traffic flows, which is further used to estimate the average delay of each signal phase. The existence of the solution of the proposed VI problem is proved and a solution algorithm based on the method of successive averages (MSA) is developed to solve the proposed signal design problem. Finally, a sample intersection is used to illustrate the application of the proposed model and the solution algorithm.