Submission to the DTA2012 special issue: Convergence of time discretization schemes for continuous-time dynamic network loading models.

*(English)*Zbl 1338.90111Summary: Dynamic Network Loading (DNL) is an essential component of Dynamic Traffic Assignment (DTA) and Dynamic User Equilibrium (DUE). Most DNL models are formulated in continuous time but solved in discrete time to obtain numerical solutions. This paper discusses the importance of choosing proper discretization schemes to numerically solve continuous-time DNL models and further to obtain convergence and other desirable properties of the discretization schemes. We use the recently developed \(\alpha\) point-queue model as an example. We first develop theoretical results to prove the consistency, stability and convergence of the implicit and explicit discretization schemes for solving the \(\alpha\) point-queue model. We then conduct numerical experiments to show such results accordingly. We also discuss the implications of the implicit and explicit discretization schemes to the developments of DNL and DTA/DUE solution algorithms.

##### MSC:

90B20 | Traffic problems in operations research |

65K05 | Numerical mathematical programming methods |

93B40 | Computational methods in systems theory (MSC2010) |

##### Keywords:

discretization scheme; dynamic traffic assignment; dynamic network loading; point-queue model; ordinary differential equation; convergence analysis
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\textit{R. Ma} et al., Netw. Spat. Econ. 15, No. 3, 419--441 (2015; Zbl 1338.90111)

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