Decomposition of Path Choice Entropy in General Transport Networks

Akamatsu, Takashi

doi:10.1287/trsc.31.4.349

Cited by 83 publications

(59 citation statements)

References 25 publications

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“…He simply proposed to weigh the paths in a heuristic way, without trying to optimize the total expected travel cost. In a second paper, Akamatsu (1997) proved that the total entropy spread in the network is a strictly concave function with respect to the arc flows and provided an interpretation of his model in terms of a different concept, the "expected minimum cost", also called "maximum utility", which plays an important role in the random utility theory. The present work therefore provides a new interpretation for Akamatsu's model, as well as a new perspective, based on statistical physics, which allows to derive the main results in a unified way.…”

Section: Related Workmentioning

confidence: 99%

“…In a second paper, Akamatsu (1997) proved that the entropy defined by Equation (29) can be decomposed into the sum of two terms, a link-based and a node-based term. Here, we adapt his proof, as well as the work on the entropy rate of a Markov chain (Cover and Thomas (2006)), in order to show the equivalence between the entropy concepts.…”

Section: Equivalence Of the Entropy Conceptmentioning

confidence: 99%

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Randomized Shortest-Path Problems: Two Related Models

et al. 2009

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This letter addresses the problem of designing the transition probabilities of a finite Markov chain (the policy) in order to minimize the expected cost for reaching a destination node from a source node while maintaining a fixed level of entropy spread throughout the network (the exploration). It is motivated by the following scenario. Suppose you have to route agents through a network in some optimal way, for instance by minimizing the total travel cost. Nothing particular up to now -you could use a standard shortest-path algorithm. Suppose, however, that you want to avoid pure deterministic routing policies in order, for instance, to allow some continual exploration of the network, to avoid congestion, or to avoid complete predictability of your routing strategy. In other words, you want to introduce some randomness/unpredictability in the routing policy, i.e., the routing policy is randomized. This problem, which will be called the randomized shortest-path problem (RSP), is investigated in this work. The global level of randomness of the routing policy is quantified by the expected Shannon entropy spread throughout the network, and is provided a priori by the designer. Then, necessary conditions allowing to compute the optimal randomized policy -minimizing the expected routing cost -are derived. Iterating these necessary conditions, reminiscent of Bellman's value iteration equations, allows to compute an optimal policy, that is, a set of transition probabilities in each node. Interestingly and surprisingly enough, this first model, while formulated in a totally different framework, is equivalent to Akamatsu's model (Akamatsu (1996)), appearing in transportation science, for a special choice of the entropy constraint. We therefore revisit Akamatsu's model by recasting it into a sum-over-paths statistical-physics formalism allowing to easily derive all the quantities of interest in an elegant, unified, way. For instance, it is shown that the unique optimal policy can be obtained by solving a simple linear system of equations. This second * Marco Saerens is also a Research Fellow of the IRIDIA Laboratory, Université Libre de Bruxelles. 1 model is therefore more convincing because of its computational efficiency and soundness. Finally, simulation results obtained on simple, illustrative, examples show that the models behave as expected.

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Section: Related Workmentioning

confidence: 99%

Section: Equivalence Of the Entropy Conceptmentioning

confidence: 99%

Randomized Shortest-Path Problems: Two Related Models

et al. 2009

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“…However, the proposed algorithm contains both absolute cost difference and relative cost difference as shown in Eqs. (5) and (8).…”

Section: Algorithm Modification Statementmentioning

confidence: 99%

“…Bell [7] proposed two logit assignment methods as alternatives to Dial's algorithm without path enumeration. Akamatsu [8] utilized the decomposition of path choice entropy to transform path-based into link-based logit assignment. Owing to the homogeneity of variance in the logit model, Nakayama [9] and Nakayama and Chikaraishi [10] presented a q-generalization method based on generalized extreme-value distribution to the random component of utility to allow heteroscedastic variance.…”

Section: Introductionmentioning

confidence: 99%

A select link analysis method based on logit–weibit hybrid model

Liu

Chen

et al. 2017

J. Mod. Transport.

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Select link analysis provides information of where traffic comes from and goes to at selected links. This disaggregate information has wide applications in practice. The state-of-the-art planning software packages often adopt the user equilibrium (UE) model for select link analysis. However, empirical studies have repeatedly revealed that the stochastic user equilibrium model more accurately predicts observed mean and variance of choices than the UE model. This paper proposes an alternative select link analysis method by making use of the recently developed logit-weibit hybrid model, to alleviate the drawbacks of both logit and weibit models while keeping a closed-form route choice probability expression. To enhance the applicability in large-scale networks, Bell's stochastic loading method originally developed for logit model is adapted to the hybrid model. The features of the proposed method are twofold: (1) unique O-D-specific link flow pattern and more plausible behavioral realism attributed to the hybrid route choice model and (2) applicability in large-scale networks due to the link-based stochastic loading method. An illustrative network example and a case study in a large-scale network are conducted to demonstrate the efficiency and effectiveness of the proposed select link analysis method as well as applications of O-D-specific link flow information. A visualization method is also proposed to enhance the understanding of O-D-specific link flow originally in the form of a matrix.

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“…This is a convenient way of rewriting the expected generalised costs because it becomes immediately clear that the deterministic model results as a limiting case when θ → ∞ (Akamatsu, 1997). For given route costs f r + c r (N r ), the variety discount 1 θ ln Nr N always decreases expected generalised costs, because choice probabilities N r /N are always smaller than 1, leading to a negative ln-term.…”

Section: Homogeneous Preferencesmentioning

confidence: 99%

Probabilistic Choice and Congestion Pricing with Heterogeneous Travellers and Price-Sensitive Demand

et al. 2014

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in AbstractThis paper deals with first-best and second-best congestion pricing of a stylised two-link network with probabilistic route choice of travellers. Travellers may have heterogeneous values of travel times and may differ in their idiosyncratic route preferences. We derive firstbest and second-best tolls taking into account how the overall network demand responds to generalized costs including the tolls that are levied. We show that with homogeneous values of times the welfare losses of second-best pricing, of one link only, may be smaller if route choice is probabilistic. Furthermore, we show that with heterogeneous values of times, common second-best tolls and group-differentiated tolls can be very close when route choice is governed by random utility maximisation, leading to low welfare losses from the inability to differentiate tolls.

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Decomposition of Path Choice Entropy in General Transport Networks

Cited by 83 publications

References 25 publications

Randomized Shortest-Path Problems: Two Related Models

Randomized Shortest-Path Problems: Two Related Models

A select link analysis method based on logit–weibit hybrid model

Probabilistic Choice and Congestion Pricing with Heterogeneous Travellers and Price-Sensitive Demand

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