A predictive dynamic traffic assignment model in congested capacity-constrained road networks

In this paper, a predictive dynamic traffic assignment model in congested capacity-constrained road networks is formulated. A traffic simulator is developed to incrementally load the traffic demand onto the network, and updates the traffic conditions dynamically. A time-dependent shortest path algorithm is also given to determine the paths with minimum actual travel time from an origin to all the destinations. The traffic simulator and time-dependent shortest path algorithm are employed in a method of successive averages to solve the dynamic equilibrium solution of the problem. A numerical example is given to illustrate the effectiveness of the proposed method.     

An empirical study of simulation-based dynamic traffic assignment procedures

Abstract

Under Intelligent Transportation Systems (ITS), real-time operations of traffic management measures depend on long-term planning results, such as the origin–destination (OD) trip distribution; however, results from current planning procedures are unable to provide fundamental data for dynamic analysis. In order to capture dynamic traffic characteristics, transportation planning models should play an important role to integrate basic data with real-time traffic management and control. In this paper, a heuristic algorithm is proposed to establish the linkage between daily OD trips and dynamic traffic assignment (DTA) procedures; thus results from transportation planning projects, in terms of daily OD trips, can be extended to estimate time-dependent OD trips. Field data from Taiwan are collected and applied in the calibration and validation processes. Dynamic Network Assignment-Simulation Model for Advanced Road Telematics (DYNASMART-P), a simulation-based DTA model, is applied to generate time-dependent flows. The results from the validation process show high agreement between actual flows from vehicle detectors (VDs) and simulated flows from DYNAMSART-P.     

W-SPSA in practice: Approximation of weight matrices and calibration of traffic simulation models

The development and calibration of complex traffic models demands parsimonious techniques, because such models often involve hundreds of thousands of unknown parameters. The Weighted Simultaneous Perturbation Stochastic Approximation (W-SPSA) algorithm has been proven more efficient than its predecessor SPSA (Spall, 1998), particularly in situations where the correlation structure of the variables is not homogeneous. This is crucial in traffic simulation models where effectively some variables (e.g. readings from certain sensors) are strongly correlated, both in time and space, with some other variables (e.g. certain OD flows). In situations with reasonably sized traffic networks, the difference is relevant considering computational constraints. However, W-SPSA relies on determining a proper weight matrix (W) that represents those correlations, and such a process has been so far an open problem, and only heuristic approaches to obtain it have been considered.This paper presents W-SPSA in a formally comprehensive way, where effectively SPSA becomes an instance of W-SPSA, and explores alternative approaches for determining the matrix W. We demonstrate that, relying on a few simplifications that marginally affect the final solution, we can obtain W matrices that considerably outperform SPSA. We analyse the performance of our proposed algorithm in two applications in motorway networks in Singapore and Portugal, using a dynamic traffic assignment model and a microscopic traffic simulator, respectively.     

The estimation of a time-dependent OD trip table with vehicle trajectory samples

Abstract

In this paper we discuss a dynamic origin–destination (OD) estimation problem that has been used for identifying time-dependent travel demand on a road network. Even though a dynamic OD table is an indispensable data input for executing a dynamic traffic assignment, it is difficult to construct using the conventional OD construction method such as the four-step model. For this reason, a direct estimation method based on field traffic data such as link traffic counts has been used. However, the method does not account for a logical relationship between a travel demand pattern and socioeconomic attributes. In addition, the OD estimation method cannot guarantee the reliability of estimated results since the OD estimation problem has a property named the ‘underdetermined problem.’ In order to overcome such a problem, the method developed in this paper makes use of vehicle trajectory samples with link traffic counts. The new method is applied to numerical examples and shows promising capability for identifying a temporal and spatial travel demand pattern.     

Eco-system optimal time-dependent flow assignment in a congested network

This research addresses the eco-system optimal dynamic traffic assignment (ESODTA) problem which aims to find system optimal eco-routing or green routing flows that minimize total vehicular emission in a congested network. We propose a generic agent-based ESODTA model and a simplified queueing model (SQM) that is able to clearly distinguish vehicles’ speed in free-flow and congested conditions for multi-scale emission analysis, and facilitates analyzing the relationship between link emission and delay. Based on the SQM, an expanded space-time network is constructed to formulate the ESODTA with constant bottleneck discharge capacities. The resulting integer linear model of the ESODTA is solved by a Lagrangian relaxation-based algorithm. For the simulation-based ESODTA, we present the column-generation-based heuristic, which requires link and path marginal emissions in the embedded time-dependent least-cost path algorithm and the gradient-projection-based descent direction method. We derive a formula of marginal emission which encompasses the marginal travel time as a special case, and develop an algorithm for evaluating path marginal emissions in a congested network. Numerical experiments are conducted to demonstrate that the proposed algorithm is able to effectively obtain coordinated route flows that minimize the system-wide vehicular emission for large-scale networks.     

A theory and implications on dynamic marginal cost

This paper extends the conventional static marginal cost analysis to the dynamic one based on the time-dependent queueing analysis at a bottleneck. First, the supply function is reformulated so as to incorporate dynamically congestion phenomena. And, the marginal cost is shown to be more closely related to the duration of congestion rather than the personal cost, since a slight change of demand at one time affects an entire traffic condition thereafter. Next, the analysis is extended so as to include the departure time choice using previous departure time choice theory. Several implications such as road pricing schemes and ramp control strategies are also discussed.     

Investigations of interactions between bus rapid transit and general traffic flows

Bus rapid transit (BRT) is a popular strategy to increase transit attraction because of its high‐capacity, comfortable service, and fast travel speed with the exclusive right‐of‐way. Various engineering designs of right‐of‐way and the violation enforcement influence interactions between BRT and general traffic flows. An empirical assessment framework is proposed to investigate traffic congestion and lane‐changing patterns at one typical bottleneck along a BRT corridor. The BRT bottleneck consists of bus lane, BRT station, video enforcement zone, and transit signal priority intersection. We analyze oblique cumulative vehicle counts and oblique cumulative lane‐changing maneuvers extracted from videos. The cumulative vehicle counts method widely applied in revealing queueing dynamics at freeway bottlenecks is extended to an urban BRT corridor. In the study site, we assume four lane‐changing patterns, three of which are verified by the empirical measurements. Investigations of interactions between buses and general traffic show that abnormal behaviors (such as lane violations and slow moving of the general traffic) induce 16% reduction in the saturation rate of general traffic and 17% increase in bus travel time. Further observations show that the BRT station and its induced increasing lane‐changing maneuvers increase the downstream queue discharge flows of general traffic. The empirical results also contribute to more efficient strategies of BRT planning and operations, such as alternative enforcement methods, various lane separation types, and optimized traffic operations. Copyright © 2014 John Wiley & Sons, Ltd.     

The construction and use of continuous autoregressive models for traffic indices

This article discusses the use of continuous autoregressive models to describe the behavior of traffic indices. From discretely sampled data, second-order differential equation models are constructed to represent dynamic traffic fluctuations as the response of a linear system to a stochastic forcing function. The results are compared to the more common M/G/∞ queueing model approach, and the analysis is demonstrated on time series of aircraft concentration in thirty-one enroute air traffic control sectors.     

Surrogate‐based optimization of cordon toll levels in congested traffic networks

The benefit, in terms of social surplus, from introducing congestion charging schemes in urban networks is depending on the design of the charging scheme. The literature on optimal design of congestion pricing schemes is to a large extent based on static traffic assignment, which is known for its deficiency in correctly predict travel times in networks with severe congestion. Dynamic traffic assignment can better predict travel times in a road network, but are more computational expensive. Thus, previously developed methods for the static case cannot be applied straightforward. Surrogate‐based optimization is commonly used for optimization problems with expensive‐to‐evaluate objective functions. In this paper, we evaluate the performance of a surrogate‐based optimization method, when the number of pricing schemes, which we can afford to evaluate (because of the computational time), are limited to between 20 and 40. A static traffic assignment model of Stockholm is used for evaluating a large number of different configurations of the surrogate‐based optimization method. Final evaluation is performed with the dynamic traffic assignment tool VisumDUE, coupled with the demand model Regent, for a Stockholm network including 1240 demand zones and 17 000 links. Our results show that the surrogate‐based optimization method can indeed be used for designing a congestion charging scheme, which return a high social surplus. Copyright © 2016 John Wiley & Sons, Ltd.     

A phenomenological model for dynamic traffic flow in networks

A macroscopic model for dynamic traffic flow is presented. The main goal of the model is the real time simulation of large freeway networks with multiple sources and sinks. First, we introduce the model in its discrete formulation and consider some of its properties. It turns out, that our non-hydrodynamical ansatz for the flows results in a very advantageous behavior of the model. Next the fitting conditions at junctions of a traffic network are discussed. In the following sections we carry out a continuous approximation of our discrete model in order to derive stationary solutions and to consider the stability of the homogeneous one. It turns out, that for certain conditions unstable traffic flow occurs. In a subsequent section, we compare the stability of the discrete model and the corresponding continuous approximation. This confirms in retrospection the close similarities of both model versions. Finally we compare the results of our model with the results of another macroscopic model, that was recently suggested by Kerner and Konhäuser [Phys. Rev. E 48, 2335–2338 (1993)].     

A dynamic traffic assignment model for the assessment of moving bottlenecks

Moving bottlenecks in highway traffic are defined as a situation in which a slow-moving vehicle, be it a truck hauling heavy equipment or an oversized vehicle, or a long convey, disrupts the continuous flow of the general traffic. The effect of moving bottlenecks on traffic flow is an important factor in the evaluation of network performance. This effect, though, cannot be assessed properly by existing transportation tools, especially when the bottleneck travels relatively long distances in the network.This paper develops a dynamic traffic assignment (DTA) model that can evaluate the effects of moving bottlenecks on network performance in terms of both travel times and traveling paths. The model assumes that the characteristics of the moving bottleneck, such as traveling path, physical dimensions, and desired speed, are predefined and, therefore, suitable for planned conveys.The DTA model is based on a mesoscopic simulation network-loading procedure with unique features that allow assessing the special dynamic characteristics of a moving bottleneck. By permitting traffic density and speed to vary along a link, the simulation can capture the queue caused by the moving bottleneck while preserving the causality principles of traffic dynamics.     

Reverse time-restricted shortest paths: Application to air traffic management

In this paper, we consider a particular class of network flow problems that seeks a shortest path, if it exists, between a source node s and a destination node d in a connected digraph, such that we arrive at node d at a specified time τ while leaving node s no earlier than a lower-bounding time LB, and where the availability of each network link is time-dependent in the sense that it can be traversed only during specified intervals of time. We refer to this problem as the reverse time-restricted shortest path problem (RTSP), and it arises, for example, in the context of generating flight plans within air traffic management approaches under severe convective weather conditions. We show that this problem is NP-hard in general, but is polynomially solvable under a special regularity condition. A pseudo-polynomial time dynamic programming algorithm is developed to solve Problem RTSP, along with an effective heap implementation strategy. Computational results using real flight generation test cases as well as random simulated problems are presented.     

A chance-constrained based stochastic dynamic traffic assignment model: Analysis, formulation and solution algorithms

This paper is concerned with the system optimum-dynamic traffic assignment (SO-DTA) problem when the time-dependent demands are random variables with known probability distributions. The model is a stochastic extension of a deterministic linear programming formulation for SO-DTA introduced by Ziliaskopoulos (Ziliaskopoulos, A.K., 2000. A linear programming model for the single destination system optimum dynamic traffic assignment problem, Transportation Science, 34, 1–12). The proposed formulation is chance-constrained based and we demonstrate that it provides a robust SO solution with a user specified level of reliability. The model provides numerous insights and can be a useful tool in producing robust control and management strategies that account for uncertainty in applications where SO-DTA is relevant (e.g. evacuation modeling, computing alternate routes around freeway incidents and establishing lower bounds on network performance).     

Network models in traffic management and control

Abstract

The context for network modelling in traffic management and control is described in terms of the current area‐wide nature of traffic management and the range of objectives to which it can contribute. Representation of a road system and traffic management measures in terms of nodes and links and parameters associated with them is described. It is shown that the pattern of traffic has to be represented not only in terms of flows on links of the network but also in terms of numbers of movements per unit time between points of entry to and points of exit from the area being modelled. In modelling so far, these numbers of movements are regarded as given, but the routes taken are estimated by traffic assignment. Models can so far be used for comparison of a range of given schemes and for optimization of traffic control within a scheme. Variation over time is a central feature of the modelling, and this requires the use of time‐dependent queueing theory, and the specification of numbers of movements for a succession of periods of between 10 and 30 minutes. Theoretical approaches to the resulting problems of modelling and optimization are discussed, and the ways in which these are supplemented by heuristic methods in currently available models is described. Some requirements‐for further research are outlined.     

A queueing based traffic flow model

The assessment of uninterrupted traffic flow is traditionally based on empirical methods. We develop some analytic queueing models based on traffic counts and we model the behavior of traffic flows as a function of some of the most relevant determinants. These analytic models allow for parameterized experiments, which pave the way towards our research objectives: assessing what-if scenario’s and sensitivity analysis for traffic management, congestion control, traffic design and the environmental impact of road traffic (e.g. emission models). The impact of some crucial modeling parameters is studied in detail and links with the broader research objectives are given. We illustrate our results for a highway, based on counted traffic flows in Flanders.     

Route swapping in dynamic traffic networks

A dynamic traffic assignment (DTA) model typically consists of a traffic performance model and a route choice model. The traffic performance model describes how traffic propagates (over time) along routes connecting origin-destination (OD) pairs, examples being the cell transmission model, the vertical queueing model and the travel time model. This is implemented in a dynamic network loading (DNL) algorithm, which uses the given route inflows to compute the link inflows (and hence link costs), which are then used to compute the route travel times (and hence route costs). A route swap process specifies the route inflows for tomorrow (at the next iteration) based on the route inflows today (at the current iteration). A dynamic user equilibrium (DUE), where each traveller on the network cannot reduce his or her cost of travel by switching to another route, can be sought by iterating between the DNL algorithm and the route swap process. The route swap process itself takes up very little computational time (although route set generation can be very computationally intensive for large networks). However, the choice of route swap process dramatically affects convergence and the speed of convergence. The paper details several route swap processes and considers whether they lead to a convergent system, assuming that the route cost vector is a monotone function of the route inflow vector.     

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

Abstract

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

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

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

Quasi-dynamic traffic assignment with residual point queues incorporating a first order node model

Static traffic assignment models are still widely applied for strategic transport planning purposes in spite of the fact that such models produce implausible traffic flows that exceed link capacities and predict incorrect congestion locations. There have been numerous attempts to constrain link flows to capacity. Capacity constrained models with residual queues are often referred to as quasi-dynamic traffic assignment models. After reviewing the literature, we come to the conclusion that an important piece of the puzzle has been missing so far, namely the inclusion of a first order node model. In this paper we propose a novel path-based static traffic assignment model for finding a stochastic user equilibrium in general transportation networks. This model includes a first order (steady-state) node model that yields more realistic turn capacities, which are then used to determine consistent capacity constrained traffic flows, residual point (vertical) queues (upstream bottleneck links), and path travel times consistent with queuing theory. The route choice part of the model is specified as a variational inequality problem, while the network loading part is formulated as a fixed point problem. Both problems are solved using existing techniques to find a solution. We illustrate the model using hypothetical examples, and also demonstrate feasibility on large-scale networks.     

A kinematic wave theory of lane-changing traffic flow

Frequent lane-changes in highway merging, diverging, and weaving areas could disrupt traffic flow and, even worse, lead to accidents. In this paper, we propose a simple model for studying bottleneck effects of lane-changing traffic and aggregate traffic dynamics of a roadway with lane-changing areas. Based on the observation that, when changing its lane, a vehicle affects traffic on both its current and target lanes, we propose to capture such lateral interactions by introducing a new lane-changing intensity variable. With a modified fundamental diagram, we are able to study the impacts of lane-changing traffic on overall traffic flow. In addition, the corresponding traffic dynamics can be described with a simple kinematic wave model. For a location-dependent lane-changing intensity variable, we discuss kinematic wave solutions of the Riemann problem of the new model and introduce a supply–demand method for its numerical solutions. With both theoretical and empirical analysis, we demonstrate that lane-changes could have significant bottleneck effects on overall traffic flow. In the future, we will be interested in studying lane-changing intensities for different road geometries, locations, on-ramp/off-ramp flows, as well as traffic conditions. The new modeling framework could be helpful for developing ramp-metering and other lane management strategies to mitigate the bottleneck effects of lane-changes.     

Integrating mesoscopic dynamic traffic assignment with agent-based travel behavior models for cumulative land development impact analysis

A number of approaches have been developed to evaluate the impact of land development on transportation infrastructure. While traditional approaches are either limited to static modeling of traffic performance or lack a strong travel behavior foundation, today’s advanced computational technology makes it feasible to model an individual traveler’s response to land development. This study integrates dynamic traffic assignment (DTA) with a positive agent-based microsimulation travel behavior model for cumulative land development impact studies. The integrated model not only enhances the behavioral implementation of DTA, but also captures traffic dynamics. It provides an advanced yet practical approach to understanding the impact of a single or series of land development projects on an individual driver’s behavior, as well as the aggregated impacts on the demand pattern and time-dependent traffic conditions. A simulation-based optimization (SBO) approach is proposed for the calibration of the modeling system. The SBO calibration approach enhances the transferability of this integrated model to other study areas. Using a case study that focuses on the cumulative land development impact along a congested corridor in Maryland, various regional and local travel behavior changes are discussed to show the capability of this tool for behavior side estimations and the corresponding traffic impacts.