## Optimal traffic light control for a single intersection (1997)

Venue: | NOLTA'97 |

Citations: | 17 - 10 self |

### BibTeX

@MISC{Schutter97optimaltraffic,

author = {Bart De Schutter and Bart De Moor},

title = {Optimal traffic light control for a single intersection},

year = {1997}

}

### OpenURL

### Abstract

We consider a single intersection of two two-way streets with controllable traffic lights on each corner. We construct a model that describes the evolution of the queue lengths in each lane as a function of time, and we discuss how (sub)optimal traffic light switching schemes for this system can be determined.

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Citation Context ...J (14) subject to Ax +B ffi + c ? 0 (15) x ? 0 (16) Ex +Dffi + f ? 0 (17) (Ax +B ffi + c) T x = 0 : (18) The system (15) -- (18) is a special case of an Extended Linear Complementarity Problem (ELCP) =-=[1, 2]-=-. In [1, 2] we have developed an algorithm to compute a parametric description of the complete solution set of an ELCP. Once this description has been obtained, we can determine the values of the para... |

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Citation Context ...J (14) subject to Ax +B ffi + c ? 0 (15) x ? 0 (16) Ex +Dffi + f ? 0 (17) (Ax +B ffi + c) T x = 0 : (18) The system (15) -- (18) is a special case of an Extended Linear Complementarity Problem (ELCP) =-=[1, 2]-=-. In [1, 2] we have developed an algorithm to compute a parametric description of the complete solution set of an ELCP. Once this description has been obtained, we can determine the values of the para... |

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(Show Context)
Citation Context ....944 177.37 δ ∗ pen 367.760 155.85 δ ∗ mul 366.715 14.69 ˜δ ∗ 364.944 0.88 δ ∗ lin 378.372 0.63 For more information on traffic modeling and traffic light control the interested reader is referred to =-=[4, 5, 6, 7, 8]-=-. 5 Conclusions We have derived a model that describes the evolution of the queue lengths at a traffic light controlled intersection of two streets. We have shown how an optimal traffic light switchin... |

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Citation Context ...r more information on other models that describe the evolution of the queue lengths at a traffic-lightcontrolled intersection and on optimal traffic light control the interested reader is referred to =-=[4, 5, 6, 7, 9, 10]-=- and the references given therein. III. Optimal traffic light control From now on we assume that the arrival and departure rates are known. We want to compute an optimal sequence t 0 , t 1 , : : : t N... |

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Citation Context ...r more information on other models that describe the evolution of the queue lengths at a traffic-lightcontrolled intersection and on optimal traffic light control the interested reader is referred to =-=[4, 5, 6, 7, 9, 10]-=- and the references given therein. III. Optimal traffic light control From now on we assume that the arrival and departure rates are known. We want to compute an optimal sequence t 0 , t 1 , : : : t N... |

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Citation Context ....944 177.37 δ ∗ pen 367.760 155.85 δ ∗ mul 366.715 14.69 ˜δ ∗ 364.944 0.88 δ ∗ lin 378.372 0.63 For more information on traffic modeling and traffic light control the interested reader is referred to =-=[4, 5, 6, 7, 8]-=-. 5 Conclusions We have derived a model that describes the evolution of the queue lengths at a traffic light controlled intersection of two streets. We have shown how an optimal traffic light switchin... |

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Citation Context ...r more information on other models that describe the evolution of the queue lengths at a traffic-lightcontrolled intersection and on optimal traffic light control the interested reader is referred to =-=[4, 5, 6, 7, 9, 10]-=- and the references given therein. III. Optimal traffic light control From now on we assume that the arrival and departure rates are known. We want to compute an optimal sequence t 0 , t 1 , : : : t N... |

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(Show Context)
Citation Context |

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Citation Context |

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(Show Context)
Citation Context ...rary index k. It is easy to verify that this equation is equivalent to: x 2k+1 \Gamma x 2k \Gamma b 1 ffi 2k ? 0 x 2k+1 ? 0 4 X i=1 (x 2k+1 \Gamma x 2k \Gamma b 1 ffi 2k ) i (x 2k+1 ) i = 0 (See also =-=[3]-=-). We can repeat this reasoning for (13) and for each k. If we define x = 2 6 4 x 1 . . . xN 3 7 5 and ffi = 2 6 4 ffi 0 . . . ffi N \Gamma1 3 7 5 , we finally get a problem of the form minimize J (14... |

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1 | Optimal trac signal control for a single intersection - Schutter, Moor - 1996 |

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