Steady-state and N-stages control for isolated controlled intersections

Haddad, Jack; Schutter, Bart De; Mahalel, David; Gutman, Per‐Olof

doi:10.1109/acc.2009.5159957

Cited by 9 publications

(4 citation statements)

References 26 publications

(31 reference statements)

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“…Most of the past work related to traffic signal control design is based on the assumption that traffic flow is deterministic. Paper [6] proposes FFM with a discrete-event max-plus model while an FFM with the stochastic hybrid model is proposed in [7]. The FFM in [6] does not consider a random variation of the flow rates, whereas the FFM in [7] assumes that the evolution of arrival flow rate and departure flow rate are well defined by the parameters of the certain stochastic processes that have the capability to describe varying of intensity flow.…”

Section: A Stochastic Hybrid Models: Fluid Flow Approachmentioning

confidence: 99%

Developing a Stochastic Model of Queue Length at a Signalized Intersection

Sutarto¹,

Joelianto²,

Nugroho³

2017

International Journal on Advanced Science, Engineering and Information Technology

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This paper proposes a stochastic hybrid dynamic model of the queue-length at a signalized intersection. The flow rate along with traffic light variables are used to define the evolution of the queue-lengths and it evolves as a piecewise linear function, being the integral of the difference between arrival and departure rate; these arrival and departure rates are described by stochastic AR model with mode-dependent parameters. The mode changes are modeled by a first order 2 or 3-state Markov process. The traffic flow rate is described using a mode-dependent first autoregressive (AR) stochastic process. The technique is applied to actual traffic flow data from the city of Jakarta, Indonesia and synthetic data from VISSIM traffic simulator. The model thus obtained via EM parameter estimation is validated by using the online particle filter. This technique can be useful and practical for periodically updating the parameters of hybrid model leading to an adaptive traffic flow state estimator as crucial part for the synthesis of traffic light control.

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Section: A Stochastic Hybrid Models: Fluid Flow Approachmentioning

confidence: 99%

Developing a Stochastic Model of Queue Length at a Signalized Intersection

Sutarto¹,

Joelianto²,

Nugroho³

2017

International Journal on Advanced Science, Engineering and Information Technology

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“…For presentation simplicity, this subsection only handles the case of increasing the green ratios after the switch. The adjustment to the other case is similar except for some details; see Algorithm 1, lines (9)- (20). This adjustment can be viewed as a gradient descent approach to gradually reduce the total delay.…”

Section: The Adjustment Around the Switchmentioning

confidence: 99%

“…The corresponding design problem can then be formulated as a linear programming (LP) problem [20][21][22][23][24][25]. One interesting question that naturally arises is how to depict the difference and connection between the discrete-time model and the continuous-time model.…”

Section: Introductionmentioning

confidence: 99%

Continuous and Discrete-Time Optimal Controls for an Isolated Signalized Intersection

Tan

Shi

et al. 2017

Journal of Sensors

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A classical control problem for an isolated oversaturated intersection is revisited with a focus on the optimal control policy to minimize total delay. The difference and connection between existing continuous-time planning models and recently proposed discrete-time planning models are studied. A gradient descent algorithm is proposed to convert the optimal control plan of the continuous-time model to the plan of the discrete-time model in many cases. Analytic proof and numerical tests for the algorithm are also presented. The findings shed light on the links between two kinds of models.

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“…This approach makes it possible to simplify the mathematical description of the traffic flow process without the use of switching variables. In this paper we consider the isolated controlled intersection as a switching system, as was done in [2], [3], [7], [8], and the optimization of the traffic signal switching sequences will be performed with a discrete-event max-plus model.…”

Section: Discrete-event Models For Isolated Controlled Intersectmentioning

confidence: 99%

Optimal Steady-State Control for Isolated Traffic Intersections

Haddad

Schutter

Mahalel

et al. 2010

IEEE Trans. Automat. Contr.

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Abstract-A simplified isolated controlled vehicular traffic intersection with two movements is considered. A discreteevent max-plus model is proposed to formulate an optimization problem for the green-red switching sequence. In the case when the criterion is a strictly increasing, linear function of the queue lengths, the problem becomes a linear programming (LP) problem. Also, in this case, the steady-state control problem can be solved analytically. A sufficient and necessary condition for steady-state control is derived, and the structure of optimal steady-state traffic control is revealed. Our condition is the same as the necessary condition in [5] for both queue lengths to be non-increasing at an isolated intersection.

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Steady-state and N-stages control for isolated controlled intersections

Cited by 9 publications

References 26 publications

Developing a Stochastic Model of Queue Length at a Signalized Intersection

Developing a Stochastic Model of Queue Length at a Signalized Intersection

Continuous and Discrete-Time Optimal Controls for an Isolated Signalized Intersection

Optimal Steady-State Control for Isolated Traffic Intersections

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