Highlights ► The continuous-time point-queue model is an ODE with a discontinuous right-hand side. ► The original point-queue model may lead to negative queue length during discretization. ► Two modified point-queue models are proposed to ensure physical realism. ► Both modified point-queue models are superior to the original model. ► Convergent discretization schemes are developed to solve the modified models.

    Abstract Extending a recent work () pertaining to a simple single-bottleneck model, this paper is the first of a two-part research wherein we undertake a mathematically rigorous study of the continuous-time dynamic user equilibrium (DUE) problem using the recently introduced mathematical paradigm of differential complementarity systems (DCSs) (). The first step in this comprehensive research is to gain a thorough understanding of some continuous-time point-queue models, which will be used as the building block of a computationally tractable model for the continuous-time DUE problem that we will study in detail in the accompanying paper (). Starting with the original point-queue model introduced by , we summarize some desirable properties that a continuous-time point-queue model should possess, and show that one of these properties—the nonnegativity of the queue lengths—is violated by Vickrey’s original model. As a remedy to this drawback of Vickrey’s model and with the goal of extending it to a continuous-time setting, we introduce two continuous-time point-queue models and show that they satisfy the properties we propose. Discretizations of the continuous-time models are discussed and construction of numerical trajectories is presented; convergence of such trajectories as the time step approaches zero is established; regularity of a solution to the continuous-time problem is clarified, and numerical results are presented.


    Access

    Check access

    Check availability in my library

    Order at Subito €


    Export, share and cite



    Title :

    Continuous-time point-queue models in dynamic network loading


    Contributors:

    Published in:

    Publication date :

    2011-11-10


    Size :

    21 pages




    Type of media :

    Article (Journal)


    Type of material :

    Electronic Resource


    Language :

    English




    Continuous-time point-queue models in dynamic network loading

    Ban, Xuegang (Jeff) | Online Contents | 2012


    Queue Spillback and Demand Uncertainty in Dynamic Network Loading

    Boyles, Stephen D. / Ruiz Juri, Natalia | Transportation Research Record | 2019


    Point queue models: A unified approach

    Jin, Wen-Long | Online Contents | 2015


    Point queue models: A unified approach

    Jin, Wen-Long | Elsevier | 2015