A NEW DYNAMIC TRAFFIC MODEL AND THE EXISTENCE AND CALCULATION OF DYNAMIC USER EQUILIBRIA ON CONGESTED CAPACITY-CONSTRAINED ROAD NETWORKS

M J Smith

A NEW DYNAMIC TRAFFIC MODEL AND THE EXISTENCE AND CALCULATION OF DYNAMIC USER EQUILIBRIA ON CONGESTED CAPACITY-CONSTRAINED ROAD NETWORKS

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

This paper presents a new dynamic model of peak period traffic flows on congested capacity-constrained urban road networks. While respecting the first in, first out (FIFO) discipline of road traffic queues and the exit capacities of road links, the model determines the (time-varying) costs incurred in traversing the various routes when (time-varying) route inflows are specified. It is proved that if this model is used to find route costs then a dynamic user equilibrium exists. The paper also gives four optimisation formulations of the dynamic user equilibrium problem. A descent algorithm is suggested; there is, as yet, no proof that the algorithm converges to an equilibrium. Finally, the paper introduces a family of alternative methods of determining dynamic flows which (almost) satisfy FIFO, and specifies one member of this family in some detail. These alternative methods arise as a consequence of using different ways of specifying the priority of a vehicle or a group of vehicles.

Original language	English
Pages (from-to)	49-63
Number of pages	15
Journal	Transportation Research Part B: Methodological
Volume	27
Issue number	1
Publication status	Published - Feb 1993

Keywords

ASSIGNMENT
STABILITY

Cite this

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title = "A NEW DYNAMIC TRAFFIC MODEL AND THE EXISTENCE AND CALCULATION OF DYNAMIC USER EQUILIBRIA ON CONGESTED CAPACITY-CONSTRAINED ROAD NETWORKS",

abstract = "This paper presents a new dynamic model of peak period traffic flows on congested capacity-constrained urban road networks. While respecting the first in, first out (FIFO) discipline of road traffic queues and the exit capacities of road links, the model determines the (time-varying) costs incurred in traversing the various routes when (time-varying) route inflows are specified. It is proved that if this model is used to find route costs then a dynamic user equilibrium exists. The paper also gives four optimisation formulations of the dynamic user equilibrium problem. A descent algorithm is suggested; there is, as yet, no proof that the algorithm converges to an equilibrium. Finally, the paper introduces a family of alternative methods of determining dynamic flows which (almost) satisfy FIFO, and specifies one member of this family in some detail. These alternative methods arise as a consequence of using different ways of specifying the priority of a vehicle or a group of vehicles.",

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