An Efficient Algorithm for the Continuous Network Loading Problem

Xu, Y; Wu, Jia; Florian, Michaël

doi:10.1016/b978-008043052-2/50003-2

Cited by 5 publications

(2 citation statements)

References 11 publications

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“…In the first case, route choice decisions are made for drivers entering the network at a time interval based on the experienced travel times, that is, the travel times of the previous time interval, and the link cost function is defined in terms of the average link travel times in the previous interval. Alternatively a heuristic approach to equilibrium can be based on repeating the simulation scheme a number of times and defining a link cost function including predictive terms, as proposed by Friesz et al (1) and by Xu et al (7 ).…”

Section: G I (T) S a (V(t))mentioning

confidence: 99%

Stochastic Heuristic Dynamic Assignment Based on AIMSUN Microscopic Traffic Simulator

Barceló¹,

Casas²

2006

Transportation Research Record

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The deployment of intelligent transportation systems must be assisted by suitable tools to conduct the feasibility studies required to test the designs and evaluate the expected impacts. Microscopic traffic simulation has proved to be the suitable methodological approach to achieve these goals. One of the most critical aspects of the dynamic simulation of road networks based on a microscopic approach–-namely, how to perform a heuristic dynamic assignment, the implied route choice models, and whether under certain criteria the approach can achieve stochastic user equilibrium–-is discussed.

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Section: G I (T) S a (V(t))mentioning

confidence: 99%

Stochastic Heuristic Dynamic Assignment Based on AIMSUN Microscopic Traffic Simulator

Barceló¹,

Casas²

2006

Transportation Research Record

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“…In addition, the traffic statics problem is related to special network loading problems with constant demands and route choice proportions, which have been extensively studied either by assuming link performance functions (Xu et al, 1998;Prashker and Bekhor, 1998;Wu et al, 1998;Xu et al, 1999;Chabini, 2001;Astarita et al, 2001) or with microscopic or mesoscopic models (Barcelo and Casas, 2005;Bliemer, 2007). But the new model of stationary traffic flow is both mathematically tractable and physically meaningful, since it is analytically based on network kinematic wave models, which can lead to network models .…”

Section: Introductionmentioning

confidence: 99%

On the existence of stationary states in general road networks

Jin

2015

Transportation Research Part B: Methodological

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Our daily driving experience and empirical observations suggest that traffic patterns in a road network are relatively stationary during peak periods. In numerous transportation network studies, there has been an implicit conjecture that stationary states exist in a network when origin demands, route choice proportions, and destination supplies are constant. In this study, we first rigorously formulate the conjecture within the framework of a network kinematic wave theory with an invariant junction model. After defining stationary states, we derive a system of algebraic equations in 3-tuples of stationary link flow-rates, demands, and supplies. We then introduce a new definition of junction critical demand levels based on effective demands and supplies. With a map in critical demand levels, we show that its fixed points and, therefore, stationary states exist with the help of Brouwer's fixed point theorem. For two simple road networks, we show that the map is well-defined and can be used to solve stationary states with a brute-force method. Finally we summarize the study and present some future extensions and applications.

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Models, Traffic Models, Simulation, and Traffic Simulation

Barceló

2010

International Series in Operations Research &Amp; Management Science

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An Efficient Algorithm for the Continuous Network Loading Problem

Cited by 5 publications

References 11 publications

Stochastic Heuristic Dynamic Assignment Based on AIMSUN Microscopic Traffic Simulator

Stochastic Heuristic Dynamic Assignment Based on AIMSUN Microscopic Traffic Simulator

On the existence of stationary states in general road networks

Models, Traffic Models, Simulation, and Traffic Simulation

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