Journal ArticleDOI
A stochastic model of traffic flow: Theoretical foundations
Saif Eddin Jabari,Henry X. Liu +1 more
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TLDR
In this paper, the authors proposed a new stochastic model of traffic flow that addresses the uncertainty inherent in driver gap choice, which is represented by random state dependent vehicle time headways.Abstract:
In a variety of applications of traffic flow, including traffic simulation, real-time estimation and prediction, one requires a probabilistic model of traffic flow. The usual approach to constructing such models involves the addition of random noise terms to deterministic equations, which could lead to negative traffic densities and mean dynamics that are inconsistent with the original deterministic dynamics. This paper offers a new stochastic model of traffic flow that addresses these issues. The source of randomness in the proposed model is the uncertainty inherent in driver gap choice, which is represented by random state dependent vehicle time headways. A wide range of time headway distributions is allowed. From the random time headways, counting processes are defined, which represent cumulative flows across cell boundaries in a discrete space and continuous time conservation framework. We show that our construction implicitly ensures non-negativity of traffic densities and that the fluid limit of the stochastic model is consistent with cell transmission model (CTM) based deterministic dynamics.read more
Citations
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Journal ArticleDOI
Traffic state estimation on highway: A comprehensive survey
TL;DR: A survey of highway TSE methods is conducted, and the recent usage of detailed disaggregated mobile data for the purpose of TSE is summarized, showing two possibilities in order to solve this problem: improvement of theoretical models and the use of data-driven or streaming-data-driven approaches, which recent studies have begun to consider.
Journal ArticleDOI
Optimal vehicle speed trajectory on a signalized arterial with consideration of queue
TL;DR: In this paper, a multi-stage optimal control formulation is proposed to obtain the optimal vehicle trajectory on signalized arterials, where both vehicle queue and traffic light status are considered, and a constrained optimization model is proposed as an approximation approach, which can be solved much quicker.
Journal ArticleDOI
Genealogy of traffic flow models
TL;DR: An historical overview of the development of traffic flow models is proposed in the form of a model tree that shows the genealogy of four families: the fundamental relation, microscopic, mesoscopic and macroscopic models.
Journal ArticleDOI
On the Stochastic Fundamental Diagram for Freeway Traffic: Model Development, Analytical Properties, Validation, and Extensive Applications
Xiaobo Qu,Jin Zhang,Shuaian Wang +2 more
TL;DR: In this article, the authors apply a new calibration approach to generate stochastic traffic flow fundamental diagrams, which have continuity, differentiability and convexity properties so that it can be easily solved by Gauss-Newton method.
Journal ArticleDOI
A stochastic model of traffic flow: Gaussian approximation and estimation
Saif Eddin Jabari,Henry X. Liu +1 more
TL;DR: Model validation was carried out in a real-world signalized arterial setting, where cycle-by-cycle maximum queue sizes were estimated using the Gaussian model as a description of state dynamics and results indicate very good agreement between estimated and observed queue sizes.
References
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Stochastic Differential Equations
TL;DR: In this paper, the authors return to the possible solutions X t (ω) of the stochastic differential equation where W t is 1-dimensional "white noise" and where X t satisfies the integral equation in differential form.
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TL;DR: In this paper, the authors describe the derivation of conservation laws and apply them to linear systems, including the linear advection equation, the Euler equation, and the Riemann problem.
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Shock Waves on the Highway
TL;DR: In this article, a simple theory of traffic flow is developed by replacing individual vehicles with a continuous fluid density and applying an empirical relation between speed and density, which is a simple graph-shearing process for following the development of traffic waves.
Journal ArticleDOI
Traffic and related self-driven many-particle systems
Dirk Helbing,Dirk Helbing +1 more
TL;DR: This article considers the empirical data and then reviews the main approaches to modeling pedestrian and vehicle traffic, including microscopic (particle-based), mesoscopic (gas-kinetic), and macroscopic (fluid-dynamic) models.