Static Traffic Assignment Model Research Articles

Flow count data-driven static traffic assignment models through network modularity partitioning

AbstractAccurate static traffic assignment models are important tools for the assessment of strategic transportation policies. In this article we present a novel approach to partition road networks through network modularity to produce data-driven static traffic assignment models from loop detector data on large road systems. The use of partitioning allows the estimation of the key model input of Origin–Destination demand matrices from flow counts alone. Previous network tomography-based demand estimation techniques have been limited by the network size. The amount of partitioning changes the Origin–Destination estimation optimisation problems to different levels of computational difficulty. Different approaches to utilising the partitioning were tested, one which degenerated the road network to the scale of the partitions and others which left the network intact. Applied to a subnetwork of England’s Strategic Road Network and other test networks, our results for the degenerate case showed flow and travel time errors are reasonable with a small amount of degeneration. The results for the non-degenerate cases showed that similar errors in model prediction with lower computation requirements can be obtained when using large partitions compared with the non-partitioned case. This work could be used to improve the effectiveness of national road systems planning and infrastructure models.

An Efficient LP-Based Approach for Spatial-Temporal Coordination of Electric Vehicles in Electricity-Transportation Nexus

A growing integration of electric vehicles (EV) and fast charging stations (FCS) has paved the way for the emergence of transportation and power distribution networks. However, previous work on the coordination of EV in the transportation system mainly focuses on static traffic assignment (STA) models which are unable to characterize the temporal evolution of EV flows on traffic links. Meanwhile, limited prior effort in dynamic traffic assignment (DTA) employs a static FCS model which is unable to describe the temporal evolution of charging and discharging (C&D) behavior of EV flows, while respecting the state-of-charge (SoC) related operating constraints, hindering full exploitation of EV flexibility potentials. To bridge the knowledge gap, this paper proposes a novel DTA model to optimize the spatial-temporal distribution of EV flows on roads and at FCSs, taking into account their flexible C&D options and SoC-related constraints, through the solution of only a single linear program. Case studies validate the effectiveness of the proposed DTA model by benchmarking its performance against traditional STA models, and corroborate the core benefits from the proposed spatial-temporal coordination of EV C&D demand in the power distribution network in terms of peak demand reduction, improved RES absorption, reduced carbon emission as well as more efficient network congestion management.

General solution scheme for the static link transmission model

Most static traffic assignment models, both in the literature and in practice, are neither capacity constrained nor storage constrained. They allow flows to exceed the link capacity and/or queues to exceed the link length. Recent studies in this area have resulted in novel approaches that do consider capacity constraints, resulting in residual queues, and sometimes even storage constraints, resulting in possible queue spillback. We build upon the results of these works and in particular on the model formulated in Bliemer and Raadsen (2020) that introduced a static network loading model formulation that is both capacity constrained as well as storage constrained. Their static network loading model formulation is derived from – and consistent with - the link transmission model, a well-established dynamic network loading model. It is referred to as the static link transmission model (sLTM) in this paper. This model considers a general concave fundamental diagram for each link and a general first order node model. It is well known that ignoring queue spillback can result in significant underestimation of path travel times. This is especially true for paths that do not traverse any of the bottleneck(s) directly, but that are affected by space occupied by queues that are spilling back. The prospect of being able to capture queuing and spillback effects in static assignment provides new opportunities for improving the modelling capabilities of this paradigm. In this paper, we propose a solution scheme to sLTM capable of finding a solution on large scale networks. This is the first time that an algorithm is proposed for solving an analytical static model with queue spillback. The inclusion of a node model in a static context - while enhancing the model's capabilities – generally results in the absence of a guaranteed convergent algorithm, and introducing spillback exacerbates the issue. Given the challenges of finding a stable solution, we discuss a base solution scheme and three (configurable) extensions. Further, we investigate algorithmic settings with respect to convergence and its impact on computational cost. A large-scale case study demonstrates the feasibility of the proposed scheme by finding solutions under the most challenging of conditions in a real-world setting. We show that improving convergence capabilities negatively affects computational efficiency. To this end, several potential improvements based on our findings are discussed. Lastly, we discuss the potential of this line of research in more general terms, highlighting strengths and weaknesses following our experiences.

InfraRisk: An open-source simulation platform for resilience analysis in interconnected power–water–transport networks

Integrated simulation models are emerging as an alternative for analyzing large-scale interdependent infrastructure networks due to their modeling advantages over traditional interdependency models. This paper presents an open-source integrated simulation package for the asset-level analysis of interdependent infrastructure systems. The simulation platform, named 'InfraRisk' and developed in Python, can simulate disaster-induced infrastructure failures and subsequent post-disaster restoration in interconnected water-, power-, and road networks. InfraRisk consists of an infrastructure module, a hazard module, a recovery module, a simulation module, and a resilience quantification module. The infrastructure module integrates existing infrastructure network packages (wntr for water networks, pandapower for power systems, and a static traffic assignment model for transportation networks) through an interface that facilitates the network-level simulation of interdependent failures. The hazard module generates infrastructure component failure sequences based on various disaster characteristics. The recovery module determines repair sequences and assigns repair crews based on predefined heuristics-based recovery strategies or model predictive control (MPC) based optimization. Based on the schedule, the simulation module implements the network-wide simulation of the consequences of the disaster impacts and the recovery actions. The resilience quantification module offers system-level and consumer-level metrics to quantify both the risks and resilience of the integrated infrastructure networks against disaster events. InfraRisk provides a virtual platform for decision-makers to experiment and develop region-specific pre-disaster and post-disaster policies to enhance the overall resilience of interdependent urban infrastructure networks.

Congestion and environmental impacts of short car trip replacement with micromobility modes

Transportation is a basic social need, but most trips are done by private vehicles, which is not environmentally sustainable with growing urban populations. Micromobility (e.g., shared bikes) represents a significant opportunity to replace short private vehicles trips (0–3 miles) and reduce transportation sector emissions. This paper uses Seattle as a case study and estimates that up to 18% of short car trips could be replaced by micromobility. A static traffic assignment model is developed to simulate and compare the results of peak hour traffic under a base case scenario (2014 traffic conditions) to scenarios where a portion of short car trips are substituted by micromobility. Results indicate that micromobility could reduce congestion on heavily congested corridors and wide-scale bike lane deployment can maximize congestion benefits, but the impacts to energy use and emissions are disproportionately low and other measures (e.g., vehicle electrification) are needed to meet climate change emissions targets.

A link-based semi-dynamic user equilibrium traffic assignment model considering signal effect

In most cities, traffic conditions vary significantly during the day. A static traffic assignment model may not adequately represent time-dependent congestion phenomena in traffic network analysis. Moreover, a dynamic traffic assignment model is too complex and is computationally intensive. As effective alternatives, various semi-dynamic traffic assignment models have been proposed. This paper develops a link-based semi-dynamic user equilibrium traffic assignment model and extends it to consider the signal delay time. In many cities, the signal cycle length changes during the day related to traffic volume, so its consideration is essential. We have previously reported that if the signal stop time is not considered, the route travel time will be underestimated. Furthermore, the effectiveness of this model is illustrated by applying it to the Kanazawa urban area network.

A Data-Driven Quasi-Dynamic Traffic Assignment Model Integrating Multi-Source Traffic Sensor Data on the Expressway Network

Static traffic assignment (STA) models have been widely utilized in the field of strategic transport planning. However, STA models cannot fully represent the dynamic road conditions and suffer from inaccurate assignment during traffic congestion. At the same time, an increasing number of installed sensors have become an important means of detecting dynamic road conditions. To address the shortcomings of STA models, we integrate multi-source traffic sensor datasets and propose a novel data-driven quasi-dynamic traffic assignment model, named DQ-DTA. In this model, records of toll stations are used for time-varying travel demand estimation. GPS trajectory datasets of vehicles are further used to calculate the dynamic link costs of the road network, replacing the imprecise Bureau of Public Roads (BPR) function. Moreover, license plate recognition (LPR) data are used to design a statistical probability-based multipath assignment method to capture travelers’ route choices. The expressway network in the Hunan province is selected as the study area, and several classic STA models are also chosen for performance comparison. Experimental results demonstrate that the accuracy of the proposed DQ-DTA model is about 6% higher than that of the chosen STA models.

Dynamic feedback control of day-to-day traffic disequilibrium process

In the literature, networks are usually assumed to operate at their steady states in static traffic assignment models. Given a set of demand management and supply regulation strategies, whether the vehicular traffic on a network would approach or not to a steady state under certain assumptions of behavioral realism is of importance and great interest in practice. Moreover, one primary reason for understanding the long-term traffic evolution dynamics is to control or influence the system trajectory in an efficient manner. To address these problems, we focus on a dynamic feedback control design and its subsequent steady-state analysis for a class of day-to-day (DTD) disequilibrium process so that the network traffic would evolve towards the desired stable traffic equilibrium. We propose an interconnected dynamic system framework for the stability and convergence analysis of DTD traffic adjustment process under the dynamic feedback control. Distinguished from the existing studies, we introduce a notion of output stability as well as the Lyapunov-like conditions to carry out the investigation noting that the steady states of the dynamic tolls that correspond to the Lagrange multipliers of the traffic equilibrium problem can be non-unique. The proposed method gives rise to a new approach to selecting pricing strategy. The proposed method involves only two adjustment parameters with well-identified physical meanings while the requirement on adjustment parameters for convergence and stability is mild. Finally, several numerical examples are presented to illustrate the insightful findings. It is found that, with dynamic feedback control, the network traffic state can converge to the desired equilibrium in a much faster manner than the case without control. The dynamic feedback controller can be implemented as demand management and supply regulation strategies such as road pricing and signal control.

Estimating Emissions from Static Traffic Models: Problems and Solutions

In large urban areas, the estimation of vehicular traffic emissions is commonly based on the outputs of transport planning models, such as Static Traffic Assignment (STA) models. However, such models, being used in a strategic context, imply some important simplifications regarding the variation of traffic conditions, and their outputs are heavily aggregated in time. In addition, dynamic traffic flow phenomena, such as queue spillback, cannot be captured, leading to inaccurate modelling of congestion. As congestion is strongly correlated with increased emission rates, using STA may lead to unreliable emission estimations. The first objective of this paper is to identify the errors that STA models introduce into an emission estimation. Then, considering the type and the nature of the errors, our aim is to suggest potential solutions. According to our findings, the main errors are related to STA inability of accurately modelling the level and the location of congestion. For this reason, we suggest and evaluate the postprocessing of STA outputs through quasidynamic network loading. Then, we evaluate our suggested approach using the HBEFA emission factors and a 19 km long motorway segment in Stockholm as a case study. Although, in terms of total emissions, the differences compared to the simple static case are not so vital, the postprocessor performs better regarding the spatial distribution of emissions. Considering the location-specific effects of traffic emissions, the latter may lead to substantial improvements in applications of emission modelling such as dispersion, air quality, and exposure modelling.

A Hybrid Method for Predicting Traffic Congestion during Peak Hours in the Subway System of Shenzhen.

Traffic congestion, especially during peak hours, has become a challenge for transportation systems in many metropolitan areas, and such congestion causes delays and negative effects for passengers. Many studies have examined the prediction of congestion; however, these studies focus mainly on road traffic, and subway transit, which is the main form of transportation in densely populated cities, such as Tokyo, Paris, and Beijing and Shenzhen in China, has seldom been examined. This study takes Shenzhen as a case study for predicting congestion in a subway system during peak hours and proposes a hybrid method that combines a static traffic assignment model with an agent-based dynamic traffic simulation model to estimate recurrent congestion in this subway system. The homes and work places of the residents in this city are collected and taken to represent the traffic demand for the subway system of Shenzhen. An origin-destination (OD) matrix derived from the data is used as an input in this method of predicting traffic, and the traffic congestion is presented in simulations. To evaluate the predictions, data on the congestion condition of subway segments that are released daily by the Shenzhen metro operation microblog are used as a reference, and a comparative analysis indicates the appropriateness of the proposed method. This study could be taken as an example for similar studies that model subway traffic in other cities.

Optimal Power and Semi-Dynamic Traffic Flow in Urban Electrified Transportation Networks

The increasing penetration of electric vehicles (EVs) and emerging dynamic wireless charging techniques have strengthened the coupling between traffic networks and power distribution networks. This increased coupling necessitates greater coordination between the two networks. This paper proposes a multi-period optimal traffic and power flow model that considers time-varying electricity and traffic demands. The distribution of traffic flow is represented by a semi-dynamic traffic assignment (SDTA) model, which considers flow propagation between adjacent periods. Combined second-order cone, convex hull, and McCormick envelope relaxations are employed to convexify the power and traffic flow model. Optimization-based bound tightening (OBBT) method combined with a heuristic sequential bound tightening (SBT) method is employed to improve the tightness of the relaxation. The modeling of multi-period scheduling provided by the SDTA model is thoroughly compared with that provided by the conventional static traffic assignment model. In addition, the proposed traffic and power flow model is employed to conduct congestion analysis of the coupled networks. Numerical results on two test systems demonstrate both the spatial and temporal impacts of congestion on each of the coupled networks. Moreover, numerical results verify that the proposed OBBT-SBT-based convex relaxation is sufficiently tight.

Regrets in Routing Networks

The impact of the recent increase in routing apps usage on road traffic remains uncertain to this day. The article introduces, for the first time, a criterion to evaluate a distance between an observed state of traffic and the user equilibrium of the traffic assignment: the average marginal regret . The average marginal regret provides a quantitative measure of the impact of routing apps on traffic using only link flows, link travel times, and travel demand. In non-atomic routing games (or static traffic assignment models), the average marginal regret is a measure of selfish drivers’ behaviors. Unlike the price of anarchy , the average marginal regret in the routing game can be computed in polynomial time without any knowledge of user equilibria and socially optimal states of traffic. First, this article demonstrates on a small example that the average marginal regret is more appropriate to define proximity between an observed state of traffic and an user equilibrium state of traffic than comparing flows, travel times, or total cost. Then, experiments on two different models of app usage and three networks (including the whole L.A. network with more than 50,000 nodes) demonstrate that the average marginal regret decreases with an increase of app usage. Sensitivity analysis of the equilibrium state with respect to the app usage ratio proves that the average marginal regret monotonically decreases to 0 with an increase of app usage. Finally, using a toy example, the article concludes that app usage could become the new Braess paradox.

Static traffic assignment with residual queues and spillback

In this paper we propose a novel static traffic assignment model where the network loading component accounts for non-stationary residual queues as well as spillback effects by explicitly adding capacity and storage constraints. This is achieved by deriving a static version of the dynamic general link transmission model that describes average link inflow and outflow rates during a given time period under simplified temporal assumptions. The resulting model adopts the same concave fundamental diagram and first order node model used in state-of-the-art macroscopic dynamic network loading without the need to explicitly describe time. We show that our mathematical problem formulation is an extension of several other models described in the literature, including the traditional capacity restrained static modelling paradigm. The equilibrium problem is formulated as a variational inequality problem while the network loading problem can be formulated as a fixed point problem. We prove that a solution exists to each problem as long as all traffic is loaded onto the network (i.e., no queue spillback into an origin). The model is illustrated via numerical examples on several hypothetical transport networks.

Static traffic assignment with residual queues and spillback

Abstract In this paper we propose a novel static traffic assignment model where the network loading component accounts for non-stationary residual queues as well as spillback effects by explicitly adding capacity and storage constraints. This is achieved by deriving a static version of the dynamic general link transmission model that describes average link inflow and outflow rates during a given time period under simplified temporal assumptions. The resulting model adopts the same concave fundamental diagram and first order node model used in state-of-the-art macroscopic dynamic network loading without the need to explicitly describe time. We show that our mathematical problem formulation is an extension of several other models described in the literature, including the traditional capacity restrained static modelling paradigm. The equilibrium problem is formulated as a variational inequality problem while the network loading problem can be formulated as a fixed point problem. We prove that a solution exists to each problem as long as all traffic is loaded onto the network (i.e., no queue spillback into an origin). The model is illustrated via numerical examples on several hypothetical transport networks.

Dynamic User Equilibrium of Mobility-on-Demand System with Linear Programming Rebalancing Strategy

Mobility-on-demand (MoD) services are provided by multiple competing companies. In their competition for travelers, they need to provide minimum travel costs, or travelers will switch to competitors. This study developed a dynamic traffic assignment of MoD systems. A static traffic assignment (STA) model is first defined. When demand is asymmetric, empty rebalancing trips are required to move vehicles to traveler origins, and the optimal rebalancing flows are found by a linear program. Because of the time-dependent nature of traveler demand, the model was converted to dynamic traffic assignment (DTA). The method of successive averages, which is provably convergent for STA, was used to find dynamic user equilibrium (DUE). The simulation was conducted on two networks. The MoD system was simulated with different fleet sizes and demands. The results showed that the average total delay and travel distance decreased with the increase in fleet size whereas the average on-road travel time increased with the fleet size. The result of traffic assignment of one network with MoD system was compared with a network where all travelers use private vehicles. The results showed that the network with MoD system created more trips but less traffic congestion.

Modeling the Enveloping Macroscopic Fundamental Diagram Based on the Traffic Assignment With Deterministic User Equilibrium

This paper aims to propose a new analytical method of deriving the enveloping macroscopic fundamental diagram (MFD) in the light of the well-defined sufficient condition and the route choice criterion in a general network. The enveloping MFD is defined to describe the boundary of all scatter points relating the flow rate (vehicles per unit time) to the vehicle accumulation (vehicles) in a road network. The theoretical framework consists of two parts. The first part is a static congested traffic assignment model which is based on the congested link performance function and the deterministic user equilibrium principle under the entirely congested condition. The second part is the new analytical method which is proposed based on the static uncongested and congested traffic assignments with the deterministic user equilibrium, in which the well-defined sufficient condition is satisfied by employing the static traffic assignment models, and the route choice criterion is fulfilled by the deterministic user equilibrium condition (Wardrop's principle). The main findings of this paper are summarized as follows: 1) the enveloping MFD delimits a region where all scatter points are located; 2) the existence and reproducibility of the enveloping MFD in a general network are verified through numerical examples; 3) the proposed method is suggested to be applied to transportation planning for describing and evaluating the macro-characteristics and the performance of road networks and evaluating whether the OD pattern is congruous with the network topology.

A path marginal cost approximation algorithm for system optimal quasi-dynamic traffic assignment

This study introduces an efficient path-based System-Optimal Quasi-Dynamic Traffic Assignment (SOQDTA) framework that benefits from the computational efficiency of static traffic assignment models, yet captures the realism of traffic flow, with less complexity and a lower computational burden, compared to dynamic traffic assignment models.To solve the proposed SOQDTA problem, we have developed a novel Path Marginal Cost (PMC) approximation algorithm, based on a Quasi-Dynamic Network Loading (QDNL) procedure (Bliemer et al., 2014), that incorporates a first order node model, and thus produces realistic path travel times consistent with queuing theory, and similar to those of dynamic network loading models, but at a lower computational cost. The model considers capacity constrained static flows, residual vertical/point queues and no spillback.The proposed SOQDTA model is applied to the test network of Sioux Falls and is demonstrated to result in system optimal traffic flow patterns that improve total system travel times compared to the user equilibrium solution. In the case study experiment, the convergence of the algorithm is demonstrated using a relative gap function. A sensitivity analysis is performed to realize the impact of perturbation size on the solution quality, and a discussion is presented on the selection of perturbation size for general network applications.

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

SummaryThe 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.

Dynamic Network Loading Using Cell Transition Model

Static traffic assignment models cannot capture traffic dynamics. Time varying flows, queuing, are not accounted in static models hence traffic dynamics. Hence to replicate the real time scenario Dynamic traffic assignment models are required. Loading the network dynamically gives realistic picture of traffic dynamics which helps for an effective management of traffic congestion hence real picture of incidents all through the network. In this project Cell transmission model (CTM) which is macroscopic and dynamic in nature is used for loading the network dynamically over space and time to capture the traffic dynamics which cannot be captured by using static models to load the network. To investigate how results are affected when a natural incident occurs like sudden increase in demand, vehicle break downs on the link is modelled. Considering each link into number of cells depending upon the free flow speed of typical vehicle in a tick of clock accommodating slower vehicle in the model; the network is loaded dynamically on a three junction road study network consisting ten links to model how the traffic responds to an incident happening in next cell. Simulation for each of the ten links is done and modelled outflow is done and compared with observed outflow. Modelling is done and the network is tested for various incidents depicting the real time scenario, like when traffic enters a cell beyond the capacity flow rate how bottle necks are formed, hence performance of link can be tested. Progression of cell occupancies for different step lengths is modelled and state of a cell is also replicated which is useful to know the real time scenario at a specified cell of a road link at a particular instance of time. The links are modelled and analysed for increased inflow demand, vehicle break downs, capacity drops hence fluctuations in traffic which may be used as real time information for a commuter to make a route choice with help of a user interface. Also for traffic engineer helps in effective planning and management of traffic congestion. Finally we conclude and outline that modelling traffic dynamically effectively tests even the performance of the road network replicating realism which would not be possible with static dynamics, moreover cell transmission model is easier to implement for its simple calculations of linear relationships. Testing and analyzing road network is effectively done.

Emission-based static traffic assignment models

Tailpipe emissions in the road transportation system are a major source of air pollution and greenhouse gases. One of the possible approaches is to influence drivers’ routing decisions such that the emissions and fuel consumption is minimized. In order to evaluate such condition, we develop environmental traffic assignment (E-TA) models based on user equilibrium (UE) and system optimal (SO) behavioral principles. Extending the traditional travel time-based UE and SO principles to E-TA is not straightforward because, unlike travel time, the rate of emissions increases with the increase in vehicle speed beyond a certain point. The results of various TA models show a network-wide traffic control strategy in which vehicles are routed according to SO-based E-TA, can reduce system-wide emissions. However, a system in which drivers make routing decisions to minimize their own emissions (E-UE system) results in a paradoxical situation of increased individual as well as system-wide emissions.