Link Travel Time Estimation in Double-Queue-Based Traffic Models

  • Xia Yang Tongji University, College of Transportation Engineering, Shanghai, China
  • Rui Ma University of Alabama in Huntsville, Huntsville, AL, USA
  • Peng Yang Hunan University of Finance and Economics, Changsha, Hunan, China
  • Xuegang Jeff Ban University of Washington, Seattle, WA
Keywords: double queue model, dynamic user equilibrium, dynamic network loading, travel time estimation, first-in-first-out (FIFO)


Double queue concept has gained its popularity in dynamic user equilibrium (DUE) modeling because it can properly model real traffic dynamics. While directly solving such double-queue-based DUE problems is extremely challenging, an approximation scheme called first-order approximation was proposed to simplify the link travel time estimation of DUE problems in a recent study without evaluating its properties and performance. This paper focuses on directly investigating the First-In-First-Out property and the performance of the first-order approximation in link travel time estimation by designing and modeling dynamic network loading (DNL) on single-line stretch networks. After model formulation, we analyze the First-In-First-Out (FIFO) property of the first-order approximation. Then a series of numerical experiments is conducted to demonstrate the FIFO property of the first-order approximation, and to compare its performance with those using the second-order approximation, a point queue model, and the cumulative inflow and exit flow curves. The numerical results show that the first-order approximation does not guarantee FIFO and also suggest that the second-order approximation is recommended especially when the link exit flow is increasing. The study provides guidance for further study on proposing new methods to better estimate link travel times.


Peeta S, Ziliaskopoulos AK. Foundations of dynamic traffic assignment: The past, the present and the future. Networks and Spatial Economics. 2001;1(3): 233–265.

Friesz TL, Kim T, Kwon C, Rigdon MA. Approximate network loading and dual-time-scale dynamic user equilibrium. Transportation Research Part B: Methodological. 2011;45(1): 176–207.

Ban X, Pang JS, Liu HX, Ma R. Modeling and solving continuous-time instantaneous dynamic user equilibria: A differential complementarity systems approach. Transportation Research Part B: Methodological. 2012;46(3): 389–408.

Daganzo CF. The cell-transmission model: A dynamic representation of highway traffic consistent with the hydrodynamic theory. Transportation Research Part B: Methodological. 1994;28(40): 269-287.

Ziliaskopoulos A. A linear programming model for the single destination system optimum dynamic traffic assignment problem. Transportation Science. 2000;34(1): 37–49.

Zheng H, Chiu Y. A network flow algorithm for the cell-based single-destination system optimal dynamic traffic assignment problem. Transportation Science. 2011;45(1): 121–137.

Yperman I. The Link Transmission Model for Dynamic Network Loading. Katholieke Universiteit Leuven, Belgium; 2007.

Gentile G. Using the general link transmission model in a dynamic traffic assignment to simulate congestion on urban networks. Transportation Research Procedia. 2015;5: 66–81.

Osorio C, Flotterod G, Bierlaire M. Dynamic network loading: A stochastic differentiable model that derives link state distributions. Transportation Research Part B. 2011;45(9): 1410–1423.

Osorio C, Flötter G. Capturing dependency among link boundaries in a stochastic dynamic network loading model. Transportation Science. 2014;49(2): 420–431.

Ma R, Ban XJ, Pang JS. A Link-Based Dynamic Complementarity System Formulation for Continuous-time Dynamic User Equilibria with Queue Spillbacks. Transportation Science. 2017;52(3): 564–592.

Ma R, Ban XJ, Pang JS. Continuous-time dynamic system optimum for single-destination traffic networks with queue spillbacks. Transportation Research Part B. 2014;68: 98–122.

Han K, Friesz TL, Yao T. Existence of simultaneous route and departure choice dynamic user equilibrium. Transportation Research Part B. 2012;53: 17–30.

Jin WL, Zhang HM. On the distribution schemes for determining flows through a merge. Transportation Research Part B. 2003;37(6): 521–540.

Yang X. Modeling multi-modal transportation network emergency evacuation considering evacuees’ cooperative behavior. Transportation Research Part A. 2018;114: 380–397.

Ban X, Liu HX, Liu MC, Ferris MC, Ran B. A link-node complementarity model and solution algorithm for dynamic user equilibria with exact flow propagations. Transportation Research Part B: Methodological. 2008;42: 823–842.

Ran B, Boyce D. Modeling dynamic transportation networks: An intelligent transportation system oriented approach. Berlin Heidelberg: Springer-Verlag; 1996.

Kucharski R, Gentile G. Simulation of rerouting phenomena in Dynamic Traffic Assignment with the Information Comply Model. Transportation Research Part B: Methodological. 2019;126: 414–441.

Ban XJ, Pang S, Liu HX, Ma R. Continuous-time point-queue models in dynamic network loading. Transportation Research Part B: Methodological. 2012;46(3): 360–380.

Ma R, Ban XJ, Pang JS, Liu H. Convergence of Time Discretization Schemes for Continuous-Time Dynamic Network Loading Models. Networks and Spatial Economics. 2014;15(3): 419–441.

How to Cite
Yang X, Ma R, Yang P, Ban XJ. Link Travel Time Estimation in Double-Queue-Based Traffic Models. Promet - Traffic&Transportation. 2021;33(3):387-9. DOI: 10.7307/ptt.v33i3.3515