## 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.

### Citations

281 | cars on smart roads: Problems of control - Varaiya, Smart - 1993 |

266 | Model predictive control: Theory and practice – A survey - Garcia, Prett, et al. - 1989 |

95 | Generalized predictive control. Part I: The basic algorithm - Clarke, Mothadi, et al. - 1987 |

66 | The extended linear complementarity problem
- Schutter, Moor
- 1995
(Show Context)
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... |

39 | Control issues in automated highway systems - Hedrick, Tomizuka, et al. - 1994 |

37 |
Max-algebraic system theory for discrete event systems
- Schutter
- 1996
(Show Context)
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... |

19 |
Traffic flow fundamentals. Englewood Cliffs
- May
(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... |

16 |
Intelligent control for urban traffic systems
- Kashani, Saridis
- 1983
(Show Context)
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... |

15 |
Modelling and hierarchical optimization of oversaturated urban traffic networks
- Singh, Tamura
- 1974
(Show Context)
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... |

12 | Application of prediction-error minimization and maximum likelihood to estimate intersection o-d matrices from traffic counts - Nihan, Davis - 1989 |

11 |
Simultaneous optimization of offsets, splits, and cycle time
- Gartner, Little, et al.
- 1976
(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... |

9 |
Hierarchical optimal control of oversaturated urban networks
- Lim, Hwang, et al.
- 1981
(Show Context)
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... |

9 |
Hierarchical optimal control of urban traffic networks
- Park, Lim, et al.
- 1984
(Show Context)
Citation Context |

7 | Parameter optimization methods for estimating dynamic origin-destination trip tables - Sherali, Arora, et al. - 1997 |

5 |
Hierarchical techniques in traffic control
- Lin, Ulrich, et al.
- 1976
(Show Context)
Citation Context |

4 |
Optimal traffic signal control for a single intersection
- Schutter, Moor
- 1996
(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... |

4 | Optimal trac light control for a single intersection: Addendum - Schutter, Moor - 1998 |

3 | Simultaneous optimization of osets, splits, and cycle time - Gartner, Little, et al. - 1976 |

3 | Hierarchical optimal control of urban trac networks - Park, Lim, et al. - 1984 |

2 | Hierarchical techniques in trac control - Lin, Ulrich, et al. - 1976 |

2 | Schuppen, “Routing control of a motorway network: A summary - Huijberts, van - 1995 |

2 | Tra��c Flow Fundamentals. Englewood Clis - May - 1990 |

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

1 | Intelligent control for urban tra��c systems - Kashani, Saridis - 1983 |

1 | Fuzzy tra��c control: Adaptive strategies - Favila, Machion, et al. - 1993 |

1 | Singapore's road tra��c control and management - Kahaner - 1996 |