### Abstract

The paper considers a dynamic traffic assignment model with deterministic queueing and inelastic demand for each origin-destination (OD) pair in the network. Two types of time-varying behaviour are modelled. First, within-day time is regarded as a continuous variable. During each day, flows propagating through routes connecting OD pairs are represented by non-negative, essentially bounded and measurable functions. Also, day-to-day time is (slightly surprisingly) modelled as if it were continuous. The day-to-day dynamical system that is adopted is derived naturally from the usual user equilibrium condition. The route cost is shown to be a Lipschitz continuous function of route flow in the single bottleneck per route case. Global convergence to equilibrium is shown to be guaranteed when the route cost vector is a non-decreasing (monotone) function of the route flow vector. In the single bottleneck per route case, the route cost function is shown to be a monotone function of the route flow if the bottleneck capacities are all non-decreasing as functions of within-day time. Monotonicity of the route cost function is also shown to hold when each bottleneck has at most one route passing through it.

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

Pages (from-to) | 779-791 |

Number of pages | 13 |

Journal | Transportation Research Part B: Methodological |

Volume | 40 |

Issue number | 9 |

Early online date | 10 Jan 2006 |

DOIs | |

Publication status | Published - 1 Nov 2006 |

### Fingerprint

### Keywords

- Bottleneck
- Dynamic traffic assignment
- Monotonicity
- Queueing

### ASJC Scopus subject areas

- Management Science and Operations Research
- Transportation

### Cite this

**Convergence in a continuous dynamic queueing model for traffic networks.** / Mounce, Richard.

Research output: Contribution to journal › Article

*Transportation Research Part B: Methodological*, vol. 40, no. 9, pp. 779-791. https://doi.org/10.1016/j.trb.2005.10.004

}

TY - JOUR

T1 - Convergence in a continuous dynamic queueing model for traffic networks

AU - Mounce, Richard

PY - 2006/11/1

Y1 - 2006/11/1

N2 - The paper considers a dynamic traffic assignment model with deterministic queueing and inelastic demand for each origin-destination (OD) pair in the network. Two types of time-varying behaviour are modelled. First, within-day time is regarded as a continuous variable. During each day, flows propagating through routes connecting OD pairs are represented by non-negative, essentially bounded and measurable functions. Also, day-to-day time is (slightly surprisingly) modelled as if it were continuous. The day-to-day dynamical system that is adopted is derived naturally from the usual user equilibrium condition. The route cost is shown to be a Lipschitz continuous function of route flow in the single bottleneck per route case. Global convergence to equilibrium is shown to be guaranteed when the route cost vector is a non-decreasing (monotone) function of the route flow vector. In the single bottleneck per route case, the route cost function is shown to be a monotone function of the route flow if the bottleneck capacities are all non-decreasing as functions of within-day time. Monotonicity of the route cost function is also shown to hold when each bottleneck has at most one route passing through it.

AB - The paper considers a dynamic traffic assignment model with deterministic queueing and inelastic demand for each origin-destination (OD) pair in the network. Two types of time-varying behaviour are modelled. First, within-day time is regarded as a continuous variable. During each day, flows propagating through routes connecting OD pairs are represented by non-negative, essentially bounded and measurable functions. Also, day-to-day time is (slightly surprisingly) modelled as if it were continuous. The day-to-day dynamical system that is adopted is derived naturally from the usual user equilibrium condition. The route cost is shown to be a Lipschitz continuous function of route flow in the single bottleneck per route case. Global convergence to equilibrium is shown to be guaranteed when the route cost vector is a non-decreasing (monotone) function of the route flow vector. In the single bottleneck per route case, the route cost function is shown to be a monotone function of the route flow if the bottleneck capacities are all non-decreasing as functions of within-day time. Monotonicity of the route cost function is also shown to hold when each bottleneck has at most one route passing through it.

KW - Bottleneck

KW - Dynamic traffic assignment

KW - Monotonicity

KW - Queueing

UR - http://www.scopus.com/inward/record.url?scp=33745056186&partnerID=8YFLogxK

U2 - 10.1016/j.trb.2005.10.004

DO - 10.1016/j.trb.2005.10.004

M3 - Article

AN - SCOPUS:33745056186

VL - 40

SP - 779

EP - 791

JO - Transportation Research Part B: Methodological

JF - Transportation Research Part B: Methodological

SN - 0191-2615

IS - 9

ER -