Advanced

The Prigogine-Herman kinetic model predicts widely scattered flow data at high concentrations

Nelson, P. and Sopasakis, Alexandros LU (1998) In Transportation Research. Part B: Methodological 32(8). p.589-604
Abstract
The classical derivation of a traffic stream model (e.g. speed/concentration relation) from the equilibrium solutions of the Prigogine–Herman kinetic equation invokes the nontrivial assumption that the underlying distribution of desired speeds is nonzero for vanishingly small speeds. In this paper we investigate the situation when this assumption does not hold. It is found that the Prigogine–Herman kinetic equation has a one-parameter family of equilibrium solutions, and hence an associated traffic stream model, only for traffic concentrations below some critical value; at higher concentrations there is a two-parameter family of solutions, and hence a continuum of mean velocities for each concentration. This result holds for both constant... (More)
The classical derivation of a traffic stream model (e.g. speed/concentration relation) from the equilibrium solutions of the Prigogine–Herman kinetic equation invokes the nontrivial assumption that the underlying distribution of desired speeds is nonzero for vanishingly small speeds. In this paper we investigate the situation when this assumption does not hold. It is found that the Prigogine–Herman kinetic equation has a one-parameter family of equilibrium solutions, and hence an associated traffic stream model, only for traffic concentrations below some critical value; at higher concentrations there is a two-parameter family of solutions, and hence a continuum of mean velocities for each concentration. This result holds for both constant values of the passing probability and the relaxation time, and for values that depend on concentration in the manner assumed by Prigogine and Herman. It is hypothesized that this result reflects the well-known tendency toward substantial scatter in observational data of traffic flow at high concentrations. (Less)
Please use this url to cite or link to this publication:
author
publishing date
type
Contribution to journal
publication status
published
subject
keywords
traffic flow, kinetic theory of vehicular traffic, Prigogine-Hermar model, traffic stream models, unstable flow
in
Transportation Research. Part B: Methodological
volume
32
issue
8
pages
589 - 604
publisher
Elsevier
external identifiers
  • scopus:0032219179
ISSN
0191-2615
DOI
10.1016/S0191-2615(98)00020-4
language
English
LU publication?
no
id
111efbcc-b9a0-4854-aa3b-d3a23a5f58fe (old id 2201947)
date added to LUP
2012-01-03 10:33:49
date last changed
2017-08-06 03:41:42
@article{111efbcc-b9a0-4854-aa3b-d3a23a5f58fe,
  abstract     = {The classical derivation of a traffic stream model (e.g. speed/concentration relation) from the equilibrium solutions of the Prigogine–Herman kinetic equation invokes the nontrivial assumption that the underlying distribution of desired speeds is nonzero for vanishingly small speeds. In this paper we investigate the situation when this assumption does not hold. It is found that the Prigogine–Herman kinetic equation has a one-parameter family of equilibrium solutions, and hence an associated traffic stream model, only for traffic concentrations below some critical value; at higher concentrations there is a two-parameter family of solutions, and hence a continuum of mean velocities for each concentration. This result holds for both constant values of the passing probability and the relaxation time, and for values that depend on concentration in the manner assumed by Prigogine and Herman. It is hypothesized that this result reflects the well-known tendency toward substantial scatter in observational data of traffic flow at high concentrations.},
  author       = {Nelson, P. and Sopasakis, Alexandros},
  issn         = {0191-2615},
  keyword      = {traffic flow,kinetic theory of vehicular traffic,Prigogine-Hermar model,traffic stream models,unstable flow},
  language     = {eng},
  number       = {8},
  pages        = {589--604},
  publisher    = {Elsevier},
  series       = {Transportation Research. Part B: Methodological},
  title        = {The Prigogine-Herman kinetic model predicts widely scattered flow data at high concentrations},
  url          = {http://dx.doi.org/10.1016/S0191-2615(98)00020-4},
  volume       = {32},
  year         = {1998},
}