Online traffic flow model applying the dynamic flow-density relation

Kim, Young‐Ho

doi:10.1049/cp:20020221

Cited by 24 publications

(9 citation statements)

References 29 publications

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“…Kim and Keller [27] and Pohlmann and Friedrich [28] introduced the CTM to the problem of traffic control in urban networks. They use the CTM to model the effects of different signal settings.…”

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

CTM Based Real-Time Queue Length Estimation at Signalized Intersection

Zhao

Liang

Liu

et al. 2015

Mathematical Problems in Engineering

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Queue length is an important index of the efficiency of urban transport system. The traditional approaches seem insufficient for the estimation of the queue length when the traffic state fluctuates greatly. In this paper, the problem is solved by introducing the Cell Transmission Model, a macroscopic traffic flow, to describe the vehicles aggregation and discharging process at a signalized intersection. To apply the model to urban traffic appropriately, some of its rules were improved accordingly. Besides, we can estimate the density of each cell of the road in a short time interval. We, first, identify the cell, where the tail of the queue is located. Then, we calculate the exact location of the rear of the queue. The models are evaluated by comparing the estimated maximum queue length and average queue length with the results of simulation calibrated by field data and testing of queue tail trajectories. The results show that the proposed model can estimate the maximum and average queue length, as well as the real-time queue length with satisfactory accuracy.

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Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

CTM Based Real-Time Queue Length Estimation at Signalized Intersection

Zhao

Liang

Liu

et al. 2015

Mathematical Problems in Engineering

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“…This need for non-homogeneous control in turn spawns the need for an additional innovation: we require a traffic flow model that permits nonhomogeneous time steps and properly models the travel time delay between lights. To this end, we might consider CTM extensions such as the variable cell length CTM (19), stochastic CTM (20,21), CTM extensions for better modeling freeway-urban interactions (22) including CTM hybrids with link-based models (23), assymmetric CTMs for better handling flow imbalances in merging roads (24), the situational CTM for better modeling of boundary conditions (25), and the lagged CTM for improved modeling of the flow density relation (26). However, despite the widespread varieties of the CTM and usage for a range of applications (27), there seems to be no extension that permits non-homogeneous time steps as proposed in our novel MILP-based control approach.…”

Section: Introductionmentioning

confidence: 99%

Nonhomogeneous Time Mixed Integer Linear Programming Formulation for Traffic Signal Control

Guilliard¹,

Sanner

Trevizan³

et al. 2016

Transportation Research Record: Journal of the Transportation R

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As urban traffic congestion is on the increase worldwide, it is critical to maximize capacity and throughput of existing road infrastructure through optimized traffic signal control. To this end, we build on the body of work in mixed integer linear programming (MILP) approaches that attempt to jointly optimize traffic signal control over an entire traffic network and specifically on improving the scalability of these methods for large numbers of intersections. Our primary insight in this work stems from the fact that MILP-based approaches to traffic control used in a receding horizon control manner (that replan at fixed time intervals) need to compute high fidelity control policies only for the early stages of the signal plan; therefore, coarser time steps can be employed to "see" over a long horizon to preemptively adapt to distant platoons and other predicted long-term changes in traffic flows. To this end, we contribute the queue transmission model (QTM) which blends elements of cell-based and link-based modeling approaches to enable a non-homogeneous time MILP formulation of traffic signal control. We then experiment with this novel QTM-based MILP control in a range of traffic networks and demonstrate that the non-homogeneous MILP formulation achieves (i) substantially lower delay solutions, (ii) improved per-vehicle delay distributions, and (iii) more optimal travel times over a longer horizon in comparison to the homogeneous MILP formulation with the same number of binary and continuous variables.

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“…"Macroscopic" theory of traffic flows can also be developed as the hydrodynamic theory of fluids. First time hydrodynamic theory was presented by Lighthill-Whitham and Richards model [1,3,4,6,7]. They presented a one-dimensional model in analogue to fluid stream model.…”

Section: Introductionmentioning

confidence: 99%

Investigation of Traffic Flow Dynamic Processes Using Discrete Model

Bogdevičius

Junevičius

2014

Journal of KONES. Powertrain and Transport

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Modelling the process of traffic flow was previously studied from different points of view and different mathematical methods where used to describe the same process. All authors have an agreement on basic traffic flow parameters like, traffic flow density, traffic flow rate or the average speed of traffic flow. Besides, a lot of different investigations into the use of traffic flow models to deal with various problems of engineering are carried out. A comparison of different continuum models has drawn that a number of scientific works were based on fluid dynamic theory and gas-kinetic traffic flow theory. The kinetic traffic flow theory is used in 'microscopic' or "macroscopic", traffic flow models. The kinetic traffic flow theory is used in Flötteröd G., Nagel K., Ging A., Li L., Li-qun X., Prigogine I., Herman R. works where various approaches to the similar method are discussed. The 'macroscopic' theory of traffic flows also can be developed as the hydrodynamic theory of fluids that was first introduced by Lighthill-Whitham and Richards's model. Plenty of traffic flow models are based on car-following theories supported by the analogues to Newton's equation for each individual vehicle interacting in a system of vehicles on the road. Different forms of the equation of motion give different versions of car-following models. This work presents research of traffic flow dynamic processes, as nonlinear dynamic system, by using a discrete model of traffic flow (DMTF). The main variables in DMTF are traffic flow density and speed. DMTF can be used to describe various traffic flow situations in the roads. The mathematical simulation of traffic flow is made when constant value of traffic flow speed and traffic flow rate is entered. Numerical results of traffic flow dynamics are obtained.

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Online traffic flow model applying the dynamic flow-density relation

Cited by 24 publications

References 29 publications

CTM Based Real-Time Queue Length Estimation at Signalized Intersection

CTM Based Real-Time Queue Length Estimation at Signalized Intersection

Nonhomogeneous Time Mixed Integer Linear Programming Formulation for Traffic Signal Control

Investigation of Traffic Flow Dynamic Processes Using Discrete Model

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