Flow-density Relation Research Articles

Pedestrian Flow Characteristics Analysis and Model Parameter Calibration in Comprehensive Transport Terminal

Pedestrian flow characteristics analysis and model calibration constitute the base and key processes of pedestrian simulation. Field data of pedestrian flow was collected in Chinese comprehensive passenger transport terminal—Xizhimen underground station using video recording, and then selected and analyzed by statistic analysis software SPSS. Parameters relation models for pedestrian flow on different terminal facilities were established based on data statistics. The results show that the pedestrian flow-density relation model is quadratic equation in corridor; the flow-space relation model is quadratic equation when space is below a certain value and is logarithmic equation when space is above the value; the speed-density relation model is linear equation. The models on stairs show the similar characteristics, but the eigenvalue is different. Parameters of social force model were acquired based on these models. Range of semi-major axis of pedestrian ellipse in social force model was ascertained. Considering time pressure as a factor pattern, expect speed in social force model was obtained by multiplying this factor and speed-density function together.

Validation of Van Aerde's simplified steadystate car-following and traffic stream model

The research reported in this paper validates Van Aerde's simplified steady-state car-following and traffic stream motion model, identifies valid input parameter ranges, and compares the model performance to other single and multi-regime models. In addition, the paper demonstrates that the Pipes linear car-following model produces the commonly known inverted V-shaped flow-density relationship. The paper also derives the relationship between the kinematic wave speed and the facility capacity, jam density, and free-flow speed for the Pipes and Van Aerde models. The study demonstrates that the Van Aerde functional form offers a superior fit to field data when compared to Newell's nonlinear single-regime model and Pipes linear dual-regime model. Specifically, the Van Aerde model is shown to fit data from different roadway types using different data aggregation intervals with a quality of fit that is superior to multi-regime models, without the need to deal with the complexities associated with the selection of regime break points.

The mathematical solution of a cellular automaton model which simulates traffic flow with a slow-to-start effect

In this paper we investigate a cellular automaton model associated with traffic flow and of which the mathematical solution is unknown before. We classify all kinds of stationary states and show that every state finally evolves to a stationary state. The obtained flow-density relation shows multiple branches corresponding to the stationary states in congested phases, which are essentially due to the slow-to-start effect introduced into this model. The stability of these states is formulated by a series of lemmas, and an algorithm is given to calculate the stationary state that the current state finally evolves to. This algorithm has a computational requirement in proportion to the number of cars.

Trafficlike Collective Movement of Ants on Trails: Absence of a Jammed Phase

We report experimental results on unidirectional trafficlike collective movement of ants on trails. Our work is primarily motivated by fundamental questions on the collective spatiotemporal organization in systems of interacting motile constituents driven far from equilibrium. Making use of the analogies with vehicular traffic, we analyze our experimental data for the spatiotemporal organization of ants on a trail. From this analysis, we extract the flow-density relation as well as the distributions of velocities of the ants and distance headways. Some of our observations are consistent with our earlier models of ant traffic, which are appropriate extensions of the asymmetric simple exclusion process. In sharp contrast to highway traffic and most other transport processes, the average velocity of the ants is almost independent of their density on the trail. Consequently, no jammed phase is observed.

Fundamental Diagram Modelling and Analysis Based NGSIM Data

Abstract Traffic control requires looking at traffic models of all types in finer details. This paper is to investigate lane-wise flow-density (or equivalently speed-density) relationship which is traditionally called Fundamental Diagram (FD) over a stretch of homogeneous freeway section using the microscopic NGSIM data. Particularly, it investigates how a homogenous traffic further drop (breakdown) through data analysis and modeling. The breakdown of a homogenous traffic is understood as the significant flow drop and density increase with noticeable shock-wave back-propagation. The corresponding density is a generalization of the critical density for traffic breakdown from free-flow. Variable structure models with two limbs of the inverse λ – shape are proposed to model the homogenous flow and its further drop. A special Generalized Polynomial Model (with fraction coefficients) is also proposed for the right limb. Properly aggregated NGSIM data are used to fit the model with results compared with some other models over time at fixed location using Root Mean Square Errors (RMSE) as measure. Principles for time/distance aggregation of individual vehicle trajectories to macroscopic traffic state parameters are proposed.

Consistency of Input-Output Model and Shockwave Analysis in Queue and Delay Estimations

This paper investigates the consistency between the simple input-output model and the shockwave analysis method as applied to traffic bottleneck problems. Mathematical derivations considering changes in arriving demand and discharge rate have shown that these models are consistent in queue and delay estimations, as both methods produce identical results at anytime during the congestion propagation and dissipation processes. Earlier findings on the inconsistency of these two methods are attributed to the lack of consideration of the baseline factor, which is dependent on the level of background traffic. Numerical examples are presented to illustrate the importance of the baseline factor, to ensure consistency regardless of the use of different flow-density relationships.

Consistent node arrival order in dynamic network loading models

Dynamic network loading (DNL) models need to address both the behavior of traffic at different roadway elements (sections, merges and diverges) as well as the propagation of flows along routes. Most models presented so far devote more attention to one of the two issues. This paper aims to achieve consistent integration between the two components, focusing in particular on the order of arrival to nodes. A novel concept of anticipated arrival order (AAO) is proposed to describe the number of vehicles expected to choose a certain downstream link at a diverge road-node as a function of the total number of vehicles that arrived at this road-node. An iterative procedure is proposed. In each iteration, a route flow propagation model is used to determine the AAO for the entire modeling horizon; then, a traffic behavior model uses the AAO to determine cumulative volumes for the entire horizon. Computational results show that this unique non-chronological heuristic approach to DNL can indeed provide consistent solutions so that residual FIFO violation is monitored. The proposed model is an analytic macroscopic model with continuous flows. We chose to examine the AAO concept using a traffic flow behavior that follows the kinematic waves model with a triangular flow–density relationship. The single-link model is converted to an equivalent variations problem and solved on a dense discrete intra-link time–space mesh by a standard least-cost-path algorithm for acyclic graphs.

Analysis of Characteristics of the Dynamic Flow-Density Relation and its Application to Traffic Flow Models

Online traffic flow modeling is of increasing importance due to intelligent transport systems and technologies. The flow-density relation plays an important role in traffic flow modeling and provides a basic way to illustrate traffic flow behavior under different traffic flow and traffic density conditions. Until now the research effort has focused mainly on the shape of the relation. The time series of the relation has not been identified clearly, even though the time series of the relation reflects the upstream/downstream traffic conditions and should be considered in the traffic flow modeling. In this paper, the dynamic flow-density relation is identified based on the classification of traffic states and is quantified employing fuzzy logic. The quantified dynamic flow-density relation builds the basis for online application of a macroscopic traffic flow model. The new approach to online modeling of traffic flow applying the dynamic flow-density relation alleviates parameter calibration problems stemming from the static flow-density relation.

New insights into traffic dynamics: a weighted probabilistic cellular automaton model

From the macroscopic viewpoint for describing the acceleration behaviour of drivers, a weighted probabilistic cellular automaton model (the WP model, for short) is proposed by introducing a kind of random acceleration probabilistic distribution function. The fundamental diagrams, the spatiotemporal patterns, are analysed in detail. It is shown that the presented model leads to the results consistent with the empirical data rather well, nonlinear flow–density relationship existing in lower density regions, and a new kind of traffic phenomenon called neo-synchronized flow. Furthermore, we give the criterion for distinguishing the high-speed and low-speed neo-synchronized flows and clarify the mechanism of this kind of traffic phenomenon. In addition, the result that the time evolution of distribution of headways is displayed as a normal distribution further validates the reasonability of the neo-synchronized flow. These findings suggest that the diversity and the randomicity of drivers and vehicles have indeed a remarkable effect on traffic dynamics.

Estimation of speed–flow and flow–density relations on the motorway network in the greater Copenhagen region

The speed-flow and flow-density relations at the motorway network of the greater Copenhagen region are explored based on a large data sample consisting of a total of 5.3 million observations at 398 locations. It is concluded that the US Bureau of Public Road (BPR) speed-flow formula from 1964 is an adequate average description of the non-queuing conditions in static assignment models, while the variation of travel speed should be taken into account in meso- and micro-simulation models. The variance of the variation of the non-queuing conditions appears to be fairly independent of the flow. The flow-density curve for the non-queuing conditions should according to theory have a convex shape to be consistent with the speed-flow curve. This was confirmed by the data. It was also shown that the variance hereby is linearly increasing with density. A linearly decreasing relationship between density and flow may be assumed for the queuing situation. Data confirmed this, although less clearly than for the non-queuing situation. This equals a derived curved formulation of the speed-flow relationship. Data for the queuing situation revealed more variance in driving speed. The variance of the variation may be assumed constant in the flow-density curves, meaning an increasing variance of speed. Finally, it was concluded, that the speeds at the capacity limit is highly unstable, within a range from 30 to 90 km/h. The transition point between the non-queuing and queuing conditions was more clearly defined in the flow-density curves than in the speed- flow curves.

Behavioural Issues in Pedestrian Speed Choice and Street Crossing Behaviour: A Review

This paper discusses issues that are encountered in the modelling of the operational behaviour of pedestrians such as the representation of pedestrian street crossing movements and speed choice at a micro‐scale. A comprehensive literature review is undertaken for various parameters of pedestrian movement that are of fundamental importance in any pedestrian modelling approach. These parameters are pedestrian speeds, pedestrian speed–flow–density relationships, pedestrian compliance to traffic signals, and pedestrian gap acceptance while crossing the road. Based on the research evidence from the literature, a modelling framework for examining pedestrian speed choice is presented that postulates that pedestrian speed is a function of a pedestrian’s value of time, risk and capabilities.

From Existing Accident-Free Car-Following Models to Colliding Vehicles

The study explores the specifications of microscopic traffic models that could capture congestion dynamics and model accident-prone behaviors on a highway section in greater realism than existing models currently used in practice (commercial software). A comparative assessment of several major acceleration models is conducted, especially for congestion formation and incident modeling. On the basis of this assessment, alternative specifications for car-following and lane-changing models are developed and implemented in a microscopic simulation framework. The models are calibrated and compared for resulting vehicle trajectories and macroscopic flow-density relationships. Experiments are conducted with the models under different degrees of relaxation of the safety constraints typically applied in conjunction with simulation codes used in practice. The ability of the proposed specifications to capture traffic behavior in extreme situations is examined. The results suggest that these specifications offer an improved basis for microscopic traffic simulation for situations that do not require an accident-free environment. As such, the same basic behavior model structure could accommodate both extreme situations (evacuation scenarios, oversaturated networks) as well as normal daily traffic conditions.

Enhanced Lagged Cell-Transmission Model for Dynamic Traffic Assignment

The lagged cell-transmission model (L-CTM) is an enhanced version of the CTM. Both can be incorporated into a dynamic traffic assignment framework for offline transport planning and policy evaluation and online intelligent transportation system applications. In contrast to the CTM, the L-CTM adopts a nonconcave flow-density relation, which can be used to predict the existence of rather dense traffic in queues coasting toward the end of the queue or to help disprove the existence of this phenomenon. However, this study shows that the L-CTM can yield unrealistic densities, namely, negative densities and densities higher than theoretical jam density, the former of which has not been addressed in the literature. To cope with these unrealistic results, this study improves the L-CTM by introducing one more term in each sending and receiving function of the model. The improved model, the enhanced L-CTM (EL-CTM), is proved to yield nonnegative densities not greater than the jam density but can still allow the use of nonconcave density relations. The EL-CTM yields Lighthill-Whitham-Richards solutions when cell lengths and time intervals tend to zero and includes the CTM and the L-CTM as special cases. The EL-CTM is also shown to give more accurate solutions than the L-CTM (and hence also the CTM) does under a small increase in computation time. Hence the EL-CTM is believed to be more suitable for both online and offline applications in the future.

Explicit construction of entropy solutions for the Lighthill–Whitham–Richards traffic flow model with a piecewise quadratic flow–density relationship

In this paper we explicitly construct the entropy solutions for the Lighthill–Whitham–Richards (LWR) traffic flow model with a flow–density relationship which is piecewise quadratic, continuous, concave, but not differentiable at the junction points where two quadratic polynomials meet, and with piecewise linear initial condition and piecewise constant boundary conditions. The proposed model is a generalization of the well-known piecewise linear flow–density relationship in the LWR model. As observed traffic flow data can be well fitted with such continuous piecewise quadratic functions, the explicitly constructed solutions provide a fast and accurate solution tool which may be used for predicting traffic or as a diagnosing tool to test the performance of numerical schemes. We implement these explicit entropy solutions for two representative traffic flow cases and also compare them with numerical solutions obtained by a high order weighted essentially non-oscillatory (WENO) scheme.

A new stochastic cellular automaton model on traffic flow and its jamming phase transition

A general stochastic traffic cellular automaton (CA) model, which includes the slow-to-start effect and driver's perspective, is proposed in this paper. It is shown that this model includes well-known traffic CA models such as the Nagel?Schreckenberg model, the quick-start model and the slow-to-start model as specific cases. Fundamental diagrams of this new model clearly show metastable states around the critical density even when the stochastic effect is present. We also obtain analytic expressions of the phase transition curve in phase diagrams by using approximate flow-density relations at boundaries. These phase transition curves are in excellent agreement with numerical results.

Synchronized flow and wide moving jams from balanced vehicular traffic

Recently we proposed an extension to the traffic model of Aw, Rascle, and Greenberg. The extended traffic model can be written as a hyperbolic system of balance laws and numerically reproduces the reverse-lambda shape of the fundamental diagram of traffic flow. In the current work we analyze the steady-state solutions of the model and their stability properties. In addition to the equilibrium flow curve the trivial steady-state solutions form two additional branches in the flow-density diagram. We show that the characteristic structure excludes parts of these branches, resulting in the reverse-lambda shape of the flow-density relation. The upper branch is metastable against the formation of synchronized flow for intermediate densities and unstable for high densities, whereas the lower branch is unstable for intermediate densities and metastable for high densities. Moreover, the model can reproduce the typical speed of the downstream front of wide moving jams. It further reproduces a constant outflow from wide moving jams, which is far below the maximum free flow. Applying the model to simulate traffic flow at a bottleneck we observe a general pattern with wide moving jams traveling through the bottleneck.

Reproducibility of Flow-Density Relations in Heavily Congested Flow Based on Individual Vehicle Data

The flow-density relations represent equilibrium relations between flow and density in the stationary state. Using individual vehicle data, this paper extends to heavily congested flow the reproducibility of the flow-density relations found by Cassidy. A new filtering method using standard deviations of traffic variables in a vehicle group built from individual vehicle data is proposed to distinguish the nearly stationary state from the nonstationary state. The traffic data collected from the nearly stationary state with this filtering method show significantly smaller data scattering than do those without filtering in heavily congested flow, even though the data aggregation interval is kept at the same level. This fact indicates that a reproducible flow-density relation also exists in heavily congested flow if the traffic data are collected in the nearly stationary state

Reproducibility of Flow–Density Relations in Heavily Congested Flow Based on Individual Vehicle Data

The flow-density relations represent equilibrium relations between flow and density in the stationary state. Using individual vehicle data, this paper extends to heavily congested flow the reproducibility of the flow-density relations found by Cassidy. A new filtering method using standard deviations of traffic variables in a vehicle group built from individual vehicle data is proposed to distinguish the nearly stationary state from the nonstationary state. The traffic data collected from the nearly stationary state with this filtering method show significantly smaller data scattering than do those without filtering in heavily congested flow, even though the data aggregation interval is kept at the same level. This fact indicates that a reproducible flow-density relation also exists in heavily congested flow if the traffic data are collected in the nearly stationary state

A SYSTEMS THEORY APPROACH TO THE DEVELOPMENT OF TRAFFIC FLOW-DENSITY MODELS

This paper presents the derivation of macroscopic speed-density and flow-density relations based on the statistic average behaviors of microscopic driver-vehicle cells. The microscopic model for a single vehicle introduces a systemic approach of the human in the loop represented by a cascade control structure. When in a constrained situation, by the presence of other vehicles, the distance regulation performed by the human driver is proposed to have a proportional-derivative action, not integral, which results in a tracking error that is linearly dependent with speed. This relation is the base for the speed-density curve for each vehicle. The paper presents a methodology, based on statistic data of road usage, to build the fundamental diagram for traffic control developments.

A variational formulation of kinematic waves: Solution methods

This paper presents improved solution methods for kinematic wave traffic problems with concave flow-density relations. As explained in part I of this work, the solution of a kinematic wave problem is a set of continuum least-cost paths in space-time. The least cost to reach a point is the vehicle number. The idea here consists in overlaying a dense but discrete network with appropriate costs in the solution region and then using a shortest-path algorithm to estimate vehicle numbers. With properly designed networks, this procedure is more accurate than existing methods and can be applied to more complicated problems. In many important cases its results are exact.