Freeway traffic flow simulation using the Link Node Cell transmission model

Muralidharan, Ajith; Dervisoglu, Gunes; Horowitz, Roberto

doi:10.1109/acc.2009.5160597

Cited by 28 publications

(40 citation statements)

References 4 publications

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“…The simulation step is ∆t = 5s. Parameters v f and F d are calibrated for each link on real data following the procedure in [18]. Parameters ρ max , ω and F are calibrated fitting the data with a straight line on the right part of the fundamental diagram for each link.…”

Section: Estimation Resultsmentioning

confidence: 99%

“…The function g (·) is defined according to LN-CTM [18], a model derived from CTM for general road topologies. It models the evolution of traffic as the combination of two main propagation modes: an upstream wave propagating forward with velocity v f for free flow FF (straight line with slope v f in Fig.…”

Section: Macroscopic Traffic Modeling With Ln-ctmmentioning

confidence: 99%

“…Although microscopic models have long incorporated random driver behavior [14,15,16], stochastic extensions to the cell transmission model (CTM) are relatively recent, in particular [17] contains an overview of the most relevant contributions. In this paper we add randomness to the link-node CTM (LN-CTM [18]) an application of the Godunov scheme to network topologies. Based on the modified LN-CTM, we develop a Bayesian method for the estimation of the space-time traffic evolution from sparse sensor observations.…”

Section: Introductionmentioning

confidence: 99%

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Estimation of highway traffic from sparse sensors: Stochastic modeling and particle filtering

Pascale

Gomes

Nicoli

2013

2013 IEEE International Conference on Acoustics, Speech and Signal Processing

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Traffic control is essential for the achievement of a sustainable and safe mobility. Monitoring systems deployed over the roads collect a great amount of traffic data that must be efficiently processed by statistical methods to draw traffic macroparameters that are needed for control operations. In this paper we propose a particle filtering approach to estimate the density over a road network starting from noisy and sparse measurements provided by road-embedded sensors. We propose a new Bayesian framework based on the link-node cell transmission model to take into account the stochastic behavior of traffic and the hysteresis phenomenon that are typically observed in real data. Numerical tests show that the estimation method is able to reliably reconstruct the traffic field even in case of very sparse sensor deployments.

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Section: Estimation Resultsmentioning

confidence: 99%

Section: Macroscopic Traffic Modeling With Ln-ctmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Estimation of highway traffic from sparse sensors: Stochastic modeling and particle filtering

Pascale

Gomes

Nicoli

2013

2013 IEEE International Conference on Acoustics, Speech and Signal Processing

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“…Based on this representation, Daganzo (3) proposed a discretized version of the LWR model, known as the cell-transmission model. Afterwards, many variants of the discrete first-order model have been presented in (4)(5)(6)(7).…”

Section: Introductionmentioning

confidence: 99%

New Extended Discrete First-Order Model to Reproduce Propagation of Jam Waves

Han

Yuan

Hegyi

2016

Transportation Research Record

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In this paper we propose an extension of the discrete LWR model of the cell-transmission model type, to reproduce the capacity drop and the propagation of jam waves. Recently studies have tried to incorporate the capacity drop into discrete first-order traffic flow models for traffic optimization purpose. It is found that the inflow to a discharging cell predicted by these models might have been overestimated, which will influence the propagation of a jam wave. Empirical analysis has been carried out to confirm this assumption. Furthermore, it is found that the extent of the flow reduction depends on the state difference between the targeting cell and its upstream cell. Based on these findings, a new mathematical model formulation is given. Simulations with both a hypothetical freeway stretch and a real life freeway stretch are performed to test the behaviour of the proposed model. The previously mentioned models are also simulated for comparison. Simulation results indicate that the proposed model has a better performance in reproducing jam waves. In addition, the proposed model can be used in a linear model predictive control framework, and formulated as a linear optimization problem, which may be beneficial for a real-life, real-time application.

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“…Ramp metering models have been introduced in the engineering community in a discrete setting, see [19,20] for details. In this article, we apply a continuous approach.…”

mentioning

confidence: 99%

A PDE-ODE Model for a Junction with Ramp Buffer

Monache¹,

Reilly²,

Samaranayake³

et al. 2014

SIAM J. Appl. Math.

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Abstract. We consider the Lighthill-Witham-Richards traffic flow model on a junction composed by one mainline, an onramp and an offramp, which are connected by a node. The onramp dynamics is modeled using an ordinary differential equation describing the evolution of the queue length. The definition of the solution of the Riemann problem at the junction is based on an optimization problem and the use of a right-of-way parameter. The numerical approximation is carried out using Godunov scheme, modified to take into account the effects of the onramp buffer. We present the result of some simulations and check numerically the convergence of the method.Key words. Scalar conservation laws, PDE-ODE systems, Riemann problem, Macroscopic traffic flow models AMS subject classifications. 90B20, 35L651. Introduction. Hydrodynamic models have commonly been used in the literature to describe the macroscopic evolution of vehicular traffic on roads and have been successfully generalized to networks in recent years. In the 1950s, Lighthill and Whitham [18] and Richards [21], independently, proposed a fluid dynamic model for traffic flow on an infinite single road, using a non-linear hyperbolic partial differential equation (PDE). The Cauchy problem has successfully been extended to initialboundary value problem in [1] and then developed specifically for scalar conservation laws with concave flux in [15], and for traffic applications in [22]. More recently, several authors proposed models on networks that take into account different type of solutions at the intersections, see [4,5,7,8,11,12] and the references therein.In this article, we focus on a junction model designed for a ramp metering problem. Ramp metering models have been introduced in the engineering community in a discrete setting, see [19,20] for details. In this article, we apply a continuous approach. We consider the scalar Lighthill-Whitham-Richards model on a network composed of a single junction connecting a mainline, an onramp and an offramp. The mainline evolution is described by a scalar conservation law, while the onramp dynamics is modeled by a buffer of infinite capacity, which is defined by an ordinary differential equation (ODE) depending on the difference between the incoming and outgoing fluxes at the ramp.In the following sections, we prove the existence and uniqueness of solutions of the Riemann problem at the junction. The results are obtained by solving a Linear Programming (LP ) optimization problem. Unlike [9], where the flux through the junction is maximized, our LP -optimization consists in maximizing the flux on the outgoing mainline, see Remark 3 below. The offramp is treated as a sink, and a priority parameter is introduced to ensure uniqueness of the solution. As a modeling choice, the priority is satisfied in an approximate way, i.e., the priority will not always be respected, in benefit of flux maximization.

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Freeway traffic flow simulation using the Link Node Cell transmission model

Cited by 28 publications

References 4 publications

Estimation of highway traffic from sparse sensors: Stochastic modeling and particle filtering

Estimation of highway traffic from sparse sensors: Stochastic modeling and particle filtering

New Extended Discrete First-Order Model to Reproduce Propagation of Jam Waves

A PDE-ODE Model for a Junction with Ramp Buffer

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