Cyclic flows, Markov process and stochastic traffic assignment

Akamatsu, Takashi

doi:10.1016/0191-2615(96)00003-3

Cited by 179 publications

(114 citation statements)

References 15 publications

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“…The definition of this dissimilarity measure relies on a model inspired by the work of Akamatsu in transportation networks [3], and extended recently by Saerens et al in [52] in the framework of network routing. Consider a graph or network G where a positive cost is associated to each arc connecting two nodes.…”

Section: Introductionmentioning

confidence: 99%

A family of dissimilarity measures between nodes generalizing both the shortest-path and the commute-time distances

Yen

Saerens

Mantrach

et al. 2008

Proceedings of the 14th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining

139

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This work introduces a new family of link-based dissimilarity measures between nodes of a weighted directed graph. This measure, called the randomized shortest-path (RSP) dissimilarity, depends on a parameter θ and has the interesting property of reducing, on one end, to the standard shortest-path distance when θ is large and, on the other end, to the commute-time (or resistance) distance when θ is small (near zero). Intuitively, it corresponds to the expected cost incurred by a random walker in order to reach a destination node from a starting node while maintaining a constant entropy (related to θ) spread in the graph. The parameter θ is therefore biasing gradually the simple random walk on the graph towards the shortest-path policy. By adopting a statistical physics approach and computing a sum over all the possible paths (discrete path integral), it is shown that the RSP dissimilarity from every node to a particular node of interest can be computed efficiently by solving two linear systems of n equations, where n is the number of nodes. On the other hand, the dissimilarity between every couple of nodes is obtained by inverting an n × n matrix. The proposed measure can be used for various graph mining tasks such as computing betweenness centrality, finding dense communities, etc, as shown in the experimental section.

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Section: Introductionmentioning

confidence: 99%

A family of dissimilarity measures between nodes generalizing both the shortest-path and the commute-time distances

Yen

Saerens

Mantrach

et al. 2008

Proceedings of the 14th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining

139

View full text Add to dashboard Cite

show abstract

“…Consequently, a one-to-one mapping exists between path and link flows for SUE solutions, making link-or path-based methods in this sense equally attractive. Many link-and path-based solution methods have been proposed for SUE (e.g., Sheffi and Powell, 1982;Damberg et al, 1996;Bekhor and Toledo, 2005;Zhou et al, 2012;Akamatsu, 1996;Bell et al, 1997;Leurent, 1997;Maher and Hughes, 1997).…”

Section: Solving In the Space Of Link-or Path Flowsmentioning

confidence: 99%

Stochastic user equilibrium with equilibrated choice sets: Part II – Solving the restricted SUE for the logit family

Rasmussen

Watling

Prato

et al. 2015

Transportation Research Part B: Methodological

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We propose a new class of path-based solution algorithms to solve the Restricted Stochastic User Equilibrium (RSUE), as introduced in Watling et al (2014). The class allows a flexible specification of how the choice sets are 'systematically' grown by considering congestion effects and how the flows are allocated among routes. The specification allows adapting traditional pathbased stochastic user equilibrium flow allocation methods (designed for pre-specified choice sets) to the generic solution algorithm. We also propose a cost transformation function and show that by using this we can, for certain Logit-type choice models, modify existing path-based Deterministic User Equilibrium solution methods to fit the RSUE solution algorithm. The transformation function also leads to a two-part relative gap measure for consistently monitoring convergence to a RSUE solution. Numerical tests are reported on two real-life cases, in which we explore convergence patterns and choice set composition and size, for alternative specifications of the RSUE solution algorithm.

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“…Akamatsu, 1996;Baillon and Cominetti, 2008), Fosgerau et al (2013) present the recursive logit (RL) model, where the path choice problem is formulated as a sequential link choice problem in a dynamic framework. The proposed technique avoids the full enumeration of paths and does not require sampling of alternatives.…”

Section: Introductionmentioning

confidence: 99%

Operational route choice methodologies for practical applications

2018

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Understanding the route choice of individuals is a key question in travel behavior research and fundamental to transportation demand management. Modeling route choice involves several challenges, pertaining to both data availability and accuracy, and model structure and computational efficiency. The main challenge related to the route choice problem, namely the generation of the choice set, has been circumvented by Fosgerau et al. (2013) through a Markovian link choice problem that is equivalent to a path-based logit model. It is called the recursive logit (RL) model and it is directly applicable for analysis at a disaggregate level. Recent methodologies are designed to simplify the structure of the model and reduce the data requirements. Kazagli et al. (2016) propose a representation of routes that is based on aggregate elements, inspired by the environmental images of the physical world formed by the individuals (Lynch, 1960), instead of links. It is called the mental representation items (MRI) model and is useful for analysis at an aggregate level. From an application point of view, both disaggregate and aggregate route choice indicators are useful. In this paper, we describe how the RL and the MRI models can be used in practice to derive link and route flows, that are the most relevant indicators for route choice applications. Our analysis identifies the advantages and the limitations of each model and allows to draw insights into the use of a specific model, depending on the needs of the application and the data availability. Finally, we investigate the performance of the two models on real data and discuss specific features of the MRI model. The results demonstrate the validity of the MRI model for the purposes of an aggregate analysis.

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Cyclic flows, Markov process and stochastic traffic assignment

Cited by 179 publications

References 15 publications

A family of dissimilarity measures between nodes generalizing both the shortest-path and the commute-time distances

A family of dissimilarity measures between nodes generalizing both the shortest-path and the commute-time distances

Stochastic user equilibrium with equilibrated choice sets: Part II – Solving the restricted SUE for the logit family

Operational route choice methodologies for practical applications

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