Speed-density Relationship Research Articles

Novel Approach for Calibrating Freeway Highway Multi-Regimes Fundamental Diagram

For almost a century, several models have been developed to calibrate the pairwise relationship between traffic flow variables, that is, speed, density, and flow. Multi-regime models are well known for being superior over single-regime models in fitting the speed–density relationship. However, in modeling multi-regime models, breakpoints that separate the regimes are visually established based on the subjective judgment of data characteristics. Thus, this study proposes a data-driven approach to estimate the breakpoints of multi-regime models. It applies the Bayesian model for calibrating multi-regime models (two and three-regime models) for fitting traffic flow fundamental diagram. Furthermore, the analysis presented accounts for the random characteristics associated with the flow. To demonstrate the application of the proposed algorithm, traffic flow data from Interstate 10 (I-10) freeway in Jacksonville, Florida, were used in the analysis. The results demonstrate the potential benefit of using the proposed model in calibrating the fundamental diagram. The proposed approach can also quantify uncertainty and encode prior knowledge about the breakpoints in the model if the model developer wishes.

Generalized bathtub model of network trip flows

Vickrey (1991, 2020) proposed a bathtub model for the evolution of trip flows served by privately operated vehicles inside a road network based on three premises: (i) treatment of the road network as a single bathtub; (ii) the speed-density relation at the network level, also known as the network fundamental diagram of vehicular traffic, and (iii) the time-independent negative exponential distribution of trip distances. However, the distributions of trip distances are generally time-dependent in the real world, and Vickrey’s model leads to unreasonable results for other types of trip distance distributions. Thus there is a need to develop a bathtub model with more general trip distance distribution patterns.In this study, we present a unified framework for modeling network trip flows with general distributions of trip distances, including negative exponential, constant, and regularly sorting trip distances studied in the literature. In addition to tracking the number of active trips as in Vickrey’s model, this model also tracks the evolution of the distribution of active trips’ remaining distances. We derive four equivalent differential formulations from the network fundamental diagram and the conservation law of trips for the number of active trips with remaining distances not smaller than any value. Then we define and discuss the properties of stationary and gridlock states, derive the integral form of the bathtub model with the characteristic method, and present two numerical methods to solve the bathtub model based on the differential and integral forms respectively. We further study equivalent formulations and solutions for two special types of distributions of trip distances: time-independent negative exponential or deterministic. In particular, we present six equivalent conditions for Vickrey’s bathtub model to be applicable.

Cyber-Physical Interplay for Data Offloading in Vehicular Networks

This letter investigates the interplay of the speed-density relationship in transportation systems and the density-congestion relationship in communications systems, in terms of the data traffic volume offloaded. It also demonstrates that relaying, when this interplay is also taken into account, greatly enhances the forwarding potentials of vehicular terminals.

A Generic Work Zone Evaluation Tool Driven by Macroscopic Traffic Simulation Model

This study proposed a generic work zone evaluation tool driven by a dynamic macroscopic traffic model. The tool can investigate the effects of a work zone on freeway conditions. The classical freeway traffic network model METANET was extended to better capture typical work zone characteristics in terms of speed and capacity reductions through modifying its speed-density relationship functions. The tool can present profiles of traffic state variables, system-level performance indices, and annotated traffic conditions maps. It was used to develop a prototype computer-aided decision support system and applied in two simulation-based case studies. Case studies show that it is effective and useful for understanding complicated work zone impacts and can aid in better design and assessment of work zone plans. It can be integrated in a dynamic transportation management system for better communication between road operator and travellers.

Pedestrian Flow Characteristics at Upstream and Downstream of Bottleneck for Unidirectional Flow under Normal Conditions

The study of pedestrian flow characteristics at upstream and downstream of bottlenecks is important from level of service and evacuation perspective. Many controlled laboratory experiments have been conducted to study pedestrians’ behavior at bottlenecks. However, it is unclear whether experiments can reproduce real crowd flow characteristics. In this paper, real field data was collected at normal conditions for unidirectional pedestrian movement at Mahakaleshwar, a Hindu temple at Ujjain, India during Mahashivaratri, a festival day on which a large number of pilgrims visited the temple. Along the corridor there is a width reduction at a U-turn which creates a bottleneck. It is necessary to study pedestrian flow characteristics at bottlenecks to ensure desired level of service at temple premises during heavy flow. The speed-density relationships of upstream and downstream sections were compared and it was found that flow behavior at both the sections of bottleneck severely differ from each other. Pedestrians in the upstream are either at free flow speed for very low density values or moving slowly for intermediate to high range of density values. From the speed-density relationship, it can be concluded that pedestrians at upstream had visual clues of congestion ahead at bottleneck (pedestrian could also see the downstream flow through barricades). Therefore, pedestrians wait at their position, stay in their comfort zone and do not push each other. Thus, even at intermediate local density, pedestrians have such low speeds. This violates the general assumption that pedestrians change their speed only at the shockwave boundary. The movement of pedestrians at upstream is governed by local density and information of congestion status ahead, whereas pedestrian movement at downstream is governed by factors like density, side friction and pedestrians’ willingness to compensate for the delay at bottleneck. This study is expected to have application in planning and operation of pedestrian facilities.

Modelling multi-class disordered traffic streams using traversable distance: a concept analogous to fluid permeability

In multi-class disordered traffic conditions, the presence of numerous classes of vehicles having different size and operational characteristics invalidates the behaviour of lane discipline. Each vehicle traverses through a series of both viable as well as accessible gaps created by other vehicles, thus defining a permeable medium. In this paper, a plausible way to incorporate the disordered behaviour on macroscopic traffic stream modelling is discussed. A new metric termed as traversable distance has been formulated for characterising this behaviour, based on field observations. Based on class-specific traversable distances that correspond to a set of incommensurate density measures, equilibrium speed functions have been redefined. Disordered stream behaviour significantly affects the scatter in the equilibrium speed–density relationship which is a key input to macroscopic traffic flow models. Results from the modified speed functions based on traversable distance proved that the proposed methodology could considerably explain the scatter observed in the fundamental diagram.

Direction-Decision Learning Based Pedestrian Flow Behavior Investigation

To investigate the pedestrian flow behavior in corridors, a microscopic simulation model of pedestrian flow is proposed in this paper based on the desired-direction-decision learning and social force model. The proposed model is composed of two parts: direction-decision and walking behavior decision. First, the decision tree model is proposed to predict the walking direction of pedestrians by comparing the prediction and simulation performance of three different models. Then, to avoid collisions between pedestrians and obstacles, the acceleration model and the collision avoidance model are proposed to compute the walking speed. Finally, an computational experiment is conducted to simulate crowd movement in corridors. The experimental results show that the proposed model can suggest the shortest overtaking route for individual pedestrians among four models, and the speed-density relationship fits the experimental data well. The sensitive analysis shows that the lanes in bidirectional pedestrian flow can be formed much more easily if the pedestrians have higher direction changing frequency, and there is an optimal visibility field (2.8) to realize the highest traffic efficiency.

Simulation-Based Speed-Density Relationship Model of Highway Interchange

To study the law of traffic wave transmission in highway interchange, this study analysed the traffic characteristics of the interchange section, developed an improved speed-density model of highway interchange based on 5PL logistic model by modifying the turning density and the mixing rate coefficient. The correction coefficients Δ1, Δ2 related to the traffic of the ramp were introduced and quantified by the nonlinear fitting and multivariate linear regression analysis of the simulation data under different traffic volumes combinations. The actual operation data of the interchange section was collected on site, and the difference between the calculated value and the actual value of the model was compared to verify the correctness and versatility of the model.

Multiclass Speed-Density Relationship for Pedestrian Traffic

We introduce a probabilistic modeling approach for pedestrian speed-density relationship. It is motivated by a high scatter in real data that precludes the use of traditional equilibrium relationsh...

Development and assessment of free-flow speed models based on different methods of measurements for inter urban multilane highways in Malaysia

This study aims to assess and compare several free-flow speed measurement methods that are suitable for Malaysian multilane highways. Free-flow speed is defined as a speed where the driver can maintain their own desired speed without obstruction or without being influenced by other road users. Data collection was conducted at 16 sites across Peninsular Malaysia during peak and off-peak periods. The measurement methods use different criteria which includes linear speed-density relationship graphs, the average speed of vehicles recorded during low to moderate traffic volume and also the average speed of vehicles with a pre-determined headway. Subsequent analysis was conducted and compared by performing multiple regression analyses. Results indicate that measurement of freeflow speed based on pre-determined headway is the best-suited model for Malaysian multilane highways. The model was determined as the best fit due to its highest R value of 0.954 and the highest score of 12/15 for the performance indicator analysis. These findings can greatly contribute to traffic engineers of Malaysia in determining a more precise free-flow speed for the design and operational assessment of multilane highways in Malaysia.

Road users’ behavior and safety analysis of pedestrian–bike shared space: case study of Robson Street in Vancouver

This paper investigates the behavior and safety of road users at the pedestrian–bike shared space of Robson Street in Vancouver. The analysis was conducted using video data, collected during the summer of 2016. Automated video analysis techniques were used to detect different road users and extract their trajectories from video scenes. The extracted trajectories were used to evaluate the speed distributions of different categories of road users, and analyze the interactions (conflicts) between pedestrians and bikes to assess their safety. As well, the paper investigates the effect of introducing a bike dismount sign at both ends of the shared space on both the percentage of cyclists’ compliance with the sign and the frequency of pedestrian–bike interactions. Finally, the relationship between the speed of both pedestrians and bikes and the density of the shared space was investigated to develop speed–density relationships in this shared space environment.

Dynamic traffic assignment using the macroscopic fundamental diagram: A Review of vehicular and pedestrian flow models

Link-level Dynamic Traffic Assignment (DTA) models of large cities may suffer from prohibitive computation times, and calibration/validation can become the major challenge faced in their real-time implementation. The empirical evidence in 2008 in support of the existence of a Macroscopic Fundamental Diagram (MFD) on urban networks led to the formulation of discrete-space DTA models, where the link-level representation of networks replaced by a zone-based representation. In parallel, a large body of DTA models based on Hughes’ pedestrian model have been formulated in continuum space as 2-dimensional conservation laws, where the speed-density relationship has been recently interpreted as a MFD. Unfortunately, today it is not clear whether the continuum-space and discrete-space approaches are consistent with each other, in the sense that a well-defined discrete-space model should correspond to the numerical solution of a continuum model. This paper aims to shed light on this matter by performing a review of the literature in both modeling approaches. We found that (i) the discrete-space DTA models are prone to stalling problem leading to unrealistic gridlocks, (ii) with the exception of Hänseler’s pedestrian models, existing discrete-space models are not guaranteed to be consistent with a continuum formulation, which presents the potential for significant biases between the two approaches although they are trying to answer the same question, (iii) the speed-density relationships used in the continuum-space literature are very simplistic and do not incorporate the effects of network, particularly the effects of intersections, which is the strong suit of the MFD, (iv) the models mostly have been applied to the cases with only one or a few destinations and do not seem to be capable of modeling large-scale networks. We also found that further research is needed to (i) incorporate departure time choice, (ii) improve existing numerical methods, possibly extending recent advances on the one-dimensional kinematic wave (LWR) model, (iii) study the properties of system optimum solutions, (iv) examine the real-time applicability of current continuum-space models compared to traditional DTA methods, and (v) formulate anisotropic models for the interaction of intersecting flows.

Predicting Freeway Work Zone Capacity Distribution Based on Logistic Speed-Density Models

Speed-volume-density relationship and capacity are key elements in modelling traffic operations, designing roadways, and evaluating facility performance. This paper uses a modified five-parameter logistic model to describe the speed-density relationship. The calibrated speed-density models show that the stop-and-go speed (Vb) and shape parameters (θ1 and θ2) are similar for work zones and the nonwork zone site. Accordingly, an operational capacity prediction method is proposed. To demonstrate the effectiveness of the proposed method, the predicted operational capacities are compared with the field data, Highway Capacity Manual method, the output of WorkZoneQ software, and the ensemble tree approach under different work zone scenarios. Furthermore, a lifetime distribution prediction framework for stochastic capacity of work zones is proposed. The predicted lifetime distribution can well capture the tendency of the observed work zone capacities.

Adaptive neuro-fuzzy approach for modeling equilibrium speed–density relationship

ABSTRACTThis paper endeavors to model the equilibrium speed–density relationship using a new fuzzy logic-based approach. To capture the randomness in traffic flow dynamics, it develops a single-input Adaptive Neuro-Fuzzy Inference System (ANFIS) trained with a hybrid algorithm. Furthermore, it proposes a new Premise-Consequent Conjugate Effect (PCCE) relationship to estimate fundamental diagram (FD) parameters from the ANFIS model. Several options (i.e. optimal split of data into training and testing data, selection of suitable membership function) offered by ANFIS are then illustrated. An experiment is performed to determine the maximum achievable goodness of fit without the occurrence of overfitting phenomenon by changing the number of clusters. The calibrated ANFIS model is compared against traditional and advanced speed–density models for five different freeway locations. Results show that the proposed model outperforms other preceding models by attaining goodness-of-fit values within a range of 0.82–0.92. Finally, the proposed PCCE relationship shows the ANFIS model's robustness in accurate estimation of FD parameters for all freeway locations.

Task Replication for Deadline-Constrained Vehicular Cloud Computing: Optimal Policy, Performance Analysis, and Implications on Road Traffic

In vehicular cloud computing (VCC) systems, the computational resources of moving vehicles are exploited and managed by infrastructures, e.g., roadside units, to provide computational services. The offloading of computational tasks and collection of results rely on successful transmissions between vehicles and infrastructures during encounters. In this paper, we investigate how to provide timely computational services in VCC systems. In particular, we seek to minimize the deadline violation probability given a set of tasks to be executed in vehicular clouds. Due to the uncertainty of vehicle movements, the task replication methodology is leveraged which allows one task to be executed by several vehicles, and thus trading computational resources for delay reduction. The optimal task replication policy is of key interest. We first formulate the problem as a finite-horizon sampled-time Markov decision problem and obtain the optimal policy by value iterations. To conquer the complexity issue, we propose the balanced-task-assignment (BETA) policy which is proved optimal and has a clear structure: it always assigns the task with the minimum number of replicas. Moreover, a tight closed-form performance upper bound for the BETA policy is derived, which indicates that the deadline violation probability follows the Rayleigh distribution approximately. Applying the vehicle speed-density relationship in the traffic flow theory, we find that vehicle mobility benefits VCC systems more compared with road traffic systems, by showing that the optimum vehicle speed to minimize the deadline violation probability is larger than the critical vehicle speed in traffic theory which maximizes traffic flow efficiency.

Fundamental diagram of ship traffic in the Singapore Strait

The Singapore Strait plays a vital role for the international freight transportation, including containers, bulk cargo and crude oil. In view of the importance of Singapore Strait, it is of practical significance to investigate the ship traffic's speed-density relationship called the fundamental diagram in the Strait, which can be used to estimate the theoretical strait capacity. Despite the availability of large empirical ship traffic data and the long history of traffic flow modeling, the analysis of ship traffic fundamental diagram for the Singapore Strait is still highly deficient. To fill in the gap, we first develop a research framework to address the big AIS (automatic identification system) data for the ship traffic fundamental diagram building. To ensure the correctness of AIS data, a tangible error elimination method is presented. Moreover, a novel weighted least square approach is applied to develop the ship traffic speed-density formulations accurately. Meanwhile, we also show the applicability of the weighted least square approach by a theoretical investigation into the difference between the weighted and non-weighted least square approaches. Finally, we study all the fifteen legs in the Singapore Strait and propose 75 fundamental diagrams based on four classic traffic flow models through mining more than 43 million pieces of AIS data. These fundamental diagrams also indicate the theoretical capacity of each leg in the Singapore Strait.

Unifiable multi-commodity kinematic wave model

In the literature, many kinematic wave models have been proposed for multi-class vehicles on multi-lane roads; however, there lacks an explicit model of unifiable multi-commodity traffic, in which different commodity flows can have different speeds and violate the first-in-first-out (FIFO) principle, but there exists a speed-density relation for the total traffic. In this study, we attempt to fill the gap by constructing and solving a unifiable multi-commodity kinematic wave model. We first construct commodity speed-density relations based on generic generating functions. Then for two commodities we discuss the properties of the unifiable kinematic wave model and analytically solve the Riemann problem with a combination of total and commodity kinematic waves. We propose a unifiable multi-commodity Cell Transmission Model (CTM) with a general junction model for numerical simulations of network traffic flows, which are unifiable but may violate the FIFO principle. We prove that the CTM is well-defined under an extended CFL (Courant et al., 1928) condition. With examples we verify the consistency between the analytical and numerical solutions and demonstrate the convergence of the CTM. We conclude with several follow-up research directions for unifiable multi-commodity kinematic wave models.

The Simulation Model of Expressway Based on Modified Cell Transmission Model

In order to realize the reasonable planning, design and management of expressway, the modified cell transmission model is proposed considering the limitation of equal cell length of traditional cell transmission model, improving the mode of traffic transmission on expressway. The capacity and jam density is calculated and the relationship between traffic speed and density is calibrated by using the vehicle detector data. Meanwhile, the traffic speed-density relationship is refined by adopting the weighted least square method, enhancing the practicality of the model. When the modified cell transmission model is applied in the expressway, the mean percentage error of cell traffic flow can be controlled at around 12 percent, which shows that the simulation result is satisfactory.

A Novel Speed–Density Relationship Model Based on the Energy Conservation Concept

This paper makes a basic assumption that energy conservation exists, between psychological potential and a vehicle's kinetic energy, in the driver's psychological field based on the driver's mental activities. A virtual spring is used to describe the storage and release of psychological potential energy. Under the aforementioned conditions, we established a macroscopic traffic flow model with conservation law. Each parameter in the new model is physically meaningful and explicit. Additionally, the model can fit field data consistently well, both in free-flow and congested situations. The results of this paper prove the rationality of the energy conservation concept in traffic flow, which improves the understanding of traffic flow and provides a new theoretical foundation.

Determination of Observation Weight to Calibrate Freeway Traffic Fundamental Diagram Using Weighted Least Square Method (WLSM)

Due to unbalanced speed-density observations, the one-regime traffic fundamental diagram and speed-density relationship models using least square method (LSM) cannot reflect actual conditions under congested/jam traffic. In that case, it is inevitable to adopt the weighted least square method (WLSM). This paper used freeway Georgia State Route 400 observation data and proposed 5 weight determination methods except the LSM to analyse 5 wellknown one-regime speed-density models to determine the best calibrating models. The results indicated that different one-regime speed-density models have different best calibrating models, for Greenberg, it was possible to find a specific weight using LSM, which is similar for Underwood and Northwestern Models, but different for that one known as 3PL model. An interesting case is the Newell's Model which fits well with two distinct calibration weights. This paper can make contribution to calibrating a more precise traffic fundamental diagram.