Theory of Traffic Assignment Through Absorbing Markov Process

Sasaki, Tsuna

doi:10.2208/jscej1949.1965.121_28

Cited by 9 publications

(3 citation statements)

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“…Thus, we think that it is valuable to try the new definition and to investigate the properties. Note, also, that the definition is same as the implicit one in Sasaki's assignment model through the Markov process (Sasaki, 1965), which has been applied in various practical networks.…”

Section: Logit Type Assignment With Infinite Cyclesmentioning

confidence: 99%

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Cyclic flows, Markov process and stochastic traffic assignment

Akamatsu

1996

Transportation Research Part B: Methodological

177

107

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Dial's stochastic assignment algorithm restricts the assignment path set to "efficient path." As a result, it sometimes produces the unrealistic flow pattern that no flow is loaded on some paths where many vehicles are running in reality. To remove the drawback of Dial's algorithm, this paper presents the LOGIT type assignment that does not restrict the assignment paths. We first show the theoretical relation between the proposed model and Sasaki's assignment model through Markov process. This analysis makes it clear that the proposed assignment model can be calculated by some matrix operations. Next, we propose an efficient algorithm that does not require the matrix operation nor path enumeration over a network. The algorithm solves an equivalent program based on the entropy decomposition derived from the Markov property of LOGIT model. Finally, it is shown that the proposed approach can be easily extended to the flow dependent case,(i.e. stochastic equilibrium assignment).

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Section: Logit Type Assignment With Infinite Cyclesmentioning

confidence: 99%

“…Takashi Akamatsu the calculation method of the proposed assignment model using the absorbing Markov chain theory: it is first demonstrated that the proposed model has some theoretical relationships to the assignment model through Markov process (Sasaki, 1965). Moreover, the precise procedure for solving the model is derived.…”

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confidence: 99%

Cyclic flows, Markov process and stochastic traffic assignment

Akamatsu

1996

Transportation Research Part B: Methodological

177

107

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“…In this study, OD flows were estimated by an absorbing Markov chain model [43]. This is a simple model based on the traffic generation and transition probabilities.…”

Section: Overview Of Absorbing Markov Chain Modelmentioning

confidence: 99%

Estimation of Origin-Destination Flows of Passenger Cars in 1925 in Old Tokyo City, Japan

Ishikawa

Nakayama

2019

IJGI

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In recent years, surveys of personal travel behavior have been conducted around the world and these surveys have been used for understanding the characteristics of people flow. However, it is impossible to acquire people and traffic flows for the modern era . In modern era Japan, some traffic surveys were conducted, and that records still persist. The purpose of this study was to estimate origin-destination (OD) flows in old Tokyo in 1925 based on the historical traffic census record. In this study, OD flows were estimated using an absorbing Markov chain model, which is a simple model based on traffic generation and transition probabilities. Transition probabilities in unobserved nodes were estimated using genetic algorithms (GA). The result of OD distributions is clearly different in the eastern part of Tokyo City, the Shitamachi area, from the western part, the Yamanote area. The traffic was very busy in Shitamachi, an area which included terminal stations and a central business district. In Yamanote, major traffic generation and absorption points were distributed along the main streets to the Shinjuku or Shibuya areas. These results are affected by the distribution of main roads and the locations of residences or workplaces of car owners.

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Analysis of the congestion detecting system by slow vehicle detection

Hamba

Kushiya²

1977

Electrical Engineering Japan

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Theory of Traffic Assignment Through Absorbing Markov Process

Cited by 9 publications

References 0 publications

Cyclic flows, Markov process and stochastic traffic assignment

Cyclic flows, Markov process and stochastic traffic assignment

Estimation of Origin-Destination Flows of Passenger Cars in 1925 in Old Tokyo City, Japan

Analysis of the congestion detecting system by slow vehicle detection

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