### Abstract

Original language | English |
---|---|

Pages (from-to) | 535-542 |

Number of pages | 8 |

Journal | Transportation science |

Volume | 49 |

Issue number | 3 |

Early online date | 23 May 2014 |

DOIs | |

Publication status | Published - Aug 2015 |

### Fingerprint

### Keywords

- method of successive averages
- equilibrium
- traffic assignment
- step length

### Cite this

*Transportation science*,

*49*(3), 535-542. https://doi.org/10.1287/trsc.2014.0517

**On the convergence of the method of successive averages for calculating user equilibrium in traffic networks.** / Mounce, Richard; Carey, Malachy.

Research output: Contribution to journal › Article

*Transportation science*, vol. 49, no. 3, pp. 535-542. https://doi.org/10.1287/trsc.2014.0517

}

TY - JOUR

T1 - On the convergence of the method of successive averages for calculating user equilibrium in traffic networks

AU - Mounce, Richard

AU - Carey, Malachy

PY - 2015/8

Y1 - 2015/8

N2 - The traffic assignment problem aims to calculate an equilibrium route flow vector, generally by seeking a zero of an appropriate objective function. If a continuous dynamical system follows a descent direction for this objective function at each nonequilibrium route flow vector, the system converges to equilibrium. It is shown that when this dynamical system is discretized with a fixed step length, the system eventually approaches close to equilibrium provided that the objective function is continuously differentiable and that the rate of descent is bounded below. The method of successive averages is widely used in traffic assignment; it has a decreasing step size at each iteration. With the same conditions as above, it is shown that the resulting dynamical system converges to equilibrium. In the steady-state model, the necessary conditions are shown to be satisfied, provided that the route cost vector is a continuously differentiable monotone function of the route flow vector. However, continuous differentiability of the cost function is shown not to hold in the dynamic queueing model.

AB - The traffic assignment problem aims to calculate an equilibrium route flow vector, generally by seeking a zero of an appropriate objective function. If a continuous dynamical system follows a descent direction for this objective function at each nonequilibrium route flow vector, the system converges to equilibrium. It is shown that when this dynamical system is discretized with a fixed step length, the system eventually approaches close to equilibrium provided that the objective function is continuously differentiable and that the rate of descent is bounded below. The method of successive averages is widely used in traffic assignment; it has a decreasing step size at each iteration. With the same conditions as above, it is shown that the resulting dynamical system converges to equilibrium. In the steady-state model, the necessary conditions are shown to be satisfied, provided that the route cost vector is a continuously differentiable monotone function of the route flow vector. However, continuous differentiability of the cost function is shown not to hold in the dynamic queueing model.

KW - method of successive averages

KW - equilibrium

KW - traffic assignment

KW - step length

U2 - 10.1287/trsc.2014.0517

DO - 10.1287/trsc.2014.0517

M3 - Article

VL - 49

SP - 535

EP - 542

JO - Transportation science

JF - Transportation science

SN - 0041-1655

IS - 3

ER -