## Congestion redux

Venue: | SIAM J. Appl. Math |

Citations: | 8 - 1 self |

### BibTeX

@ARTICLE{Greenberg_congestionredux,

author = {J. M. Greenberg},

title = {Congestion redux},

journal = {SIAM J. Appl. Math},

year = {},

volume = {64},

pages = {1175--1185}

}

### OpenURL

### Abstract

Abstract. In this paper we analyze a class of second-order traffic models and show that these models support stable oscillatory traveling waves typical of the waves observed on a congested roadway. The basic model has trivial or constant solutions where cars are uniformly spaced and travel at a constant equilibrium velocity that is determined by the car spacing. The stable traveling waves arise because there is an interval of car spacing for which the constant solutions are unstable. These waves consist of a smooth part where both the velocity and spacing between successive cars are increasing functions of a Lagrange mass index. These smooth portions are separated by shock waves that travel at computable negative velocity.

### Citations

192 | Traffic and Related Self-Driven Many-Particle Systems
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- 2001
(Show Context)
Citation Context ...e interval (s1,s2), solutions converge to traveling waves. These simulations will be run on the follow-the-leader model (1.7)–(1.8). Comprehensive surveys on this vast subject may be found in Helbing =-=[8]-=- and Nagel, Wagner, and Woesler [9]. 2. Linear stability of (1.17). We look for solutions of (1.1)–(1.2) of the form (2.1) s = s0 + δ1A and u = V (s0)+δ1W,sCONGESTION REDUX 1179 where 0 <δ1 ≪ 1. To le... |

81 | Resurrection of ”second order” models of traffic flow
- Aw, Rascle
(Show Context)
Citation Context ...ocity. Key words. conservation laws, traffic congestion, follow-the-leader AMS subject classification. 35 DOI. 10.1137/S0036139903431737 1. Introduction. In the last several years a number of authors =-=[1, 2, 3, 4, 5, 6, 7, 8, 9]-=- have advanced “higher order” traffic models in an attempt to characterize strong permanent waves which appear in congested traffic. At the continuum level all of these authors have worked with models... |

73 |
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- 1999
(Show Context)
Citation Context ...ocity. Key words. conservation laws, traffic congestion, follow-the-leader AMS subject classification. 35 DOI. 10.1137/S0036139903431737 1. Introduction. In the last several years a number of authors =-=[1, 2, 3, 4, 5, 6, 7, 8, 9]-=- have advanced “higher order” traffic models in an attempt to characterize strong permanent waves which appear in congested traffic. At the continuum level all of these authors have worked with models... |

46 |
Requiem for second-order fluid approximations of traffic flow
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Citation Context ...ocity. Key words. conservation laws, traffic congestion, follow-the-leader AMS subject classification. 35 DOI. 10.1137/S0036139903431737 1. Introduction. In the last several years a number of authors =-=[1, 2, 3, 4, 5, 6, 7, 8, 9]-=- have advanced “higher order” traffic models in an attempt to characterize strong permanent waves which appear in congested traffic. At the continuum level all of these authors have worked with models... |

23 |
Derivation of continuum traffic flow models from microscopic follow-the-leader models
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- 2002
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19 | Extensions and amplifications of a traffic model of Aw and Rascle
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19 |
Congestion on multilane highways
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13 |
Still flowing: Approaches to traffic flow and traffic jam modeling, Op
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2 |
A rigorous treatment of a follow-the-leader traffic model with traffic lights present
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(Show Context)
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