M. Florian. Nonlinear cost network models in transportation analysis. Mathematical Programming Study, 26:167--196, 1986.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... the entire tra#c pattern (rather than merely on the flow using that edge) to include di#erent types (or modes ) of tra#c, to allow elastic (rather than fixed) tra#c rates, and so on; research on these more general models have focused on establishing existence and uniqueness of tra#c equilibria [1, 26, 32, 45, 46, 47, 66, 67, 68, 84, 85, 102, 129, 173, 192], on designing algorithms to compute an equilibrium [1, 11, 18, 45, 46, 65, 66, 67, 68, 69, 78, 115, 118, 129, 134, 135, 187, 192] and on sensitivity analysis [45, 49, 83, 190] For an introduction to this literature, we recommend the survey of Florian and Hearn [68] and the book of She# [169] ....

.... of tra#c, to allow elastic (rather than fixed) tra#c rates, and so on; research on these more general models have focused on establishing existence and uniqueness of tra#c equilibria [1, 26, 32, 45, 46, 47, 66, 67, 68, 84, 85, 102, 129, 173, 192] on designing algorithms to compute an equilibrium [1, 11, 18, 45, 46, 65, 66, 67, 68, 69, 78, 115, 118, 129, 134, 135, 187, 192], and on sensitivity analysis [45, 49, 83, 190] For an introduction to this literature, we recommend the survey of Florian and Hearn [68] and the book of She# [169] More recently, Nesterov [131] see also Nesterov and De Palma [132] has proposed an interesting alternative to (rather than a ....

M. Florian. Nonlinear cost network models in transportation analysis. Mathematical Programming Study, 26:167--196, 1986.

....program (see also Section 2) gave existence and uniqueness results for traffic equilibria. Dafermos and Sparrow [7] were perhaps the first authors interested in computing the equilibrium efficiently, and many subsequent papers gave increasingly efficient methods for computing equilibria (see [10] for a survey) others have extended these results to more sophisticated models (see for example [1, 6, 10, 13, 21, 22, 27, 29, 30] In the past several decades, much of the work on this model has been inspired by a paradox first discovered by Braess [4] and later reported by Murchland [20] ....

.... and Sparrow [7] were perhaps the first authors interested in computing the equilibrium efficiently, and many subsequent papers gave increasingly efficient methods for computing equilibria (see [10] for a survey) others have extended these results to more sophisticated models (see for example [1, 6, 10, 13, 21, 22, 27, 29, 30]) In the past several decades, much of the work on this model has been inspired by a paradox first discovered by Braess [4] and later reported by Murchland [20] The essence of Braess s Paradox is captured by the example shown in Figure 1, where the edges are labeled with their latency ....

M. Florian. Nonlinear cost network models in transportation analysis. Mathematical Programming Study, 26:167--196, 1986.

....variational inequality: hF (X) 1 ff oeG; x Gamma yi 0 8y 2 Omega : 25) Note that, in the above, the state variable ff divides G, instead of multiplying it. The reader is referred to Marcotte and Zhu [11] for further details. In the standard traffic assignment model (see Florian [6]) under a strict monotonicity assumption, only the uniqueness of the total arc flow vector is guaranteed, since the decomposition of arc flows into commodity flows is not unique, in general. A key feature of the multiclass formulation of the traffic assignement model is that, under Condition A, ....

Florian, M., Nonlinear cost network models in transportation analysis, Mathematical Programming Study 26 (1986) 167--196.

....(O D) pair i 2 I on a path in the set P i , the set of paths connecting O D pair i. The cost experienced by a person using path p is given by C p : R nP R where nP denotes the cardinality of the set of paths P = i2I P i . In the most general version of this problem (for a review, see [12, 14]) path costs can be a function of the entire vector of path flows and the number of people traveling between O D pair i, and the demand function D i : R n I R is a function of the vector of (minimum) O D travel costs, min r2P j C r (F ) j 2 I) In this case, an equilibrium is typically ....

M. Florian, "Nonlinear Cost Network Models in Transportation Analysis," Mathematical Programming Study 26, 167--196 (1986).

....reviews by its explicit intention to identify candidates for medium scale applications. The categorisation used is not the only relevant classification. Referring to the figure in the introduction another classification is related to the treatment of congestion. In the characterisation used by Florian (1986) the models are classed into three groups; network equilibrium approaches, gravity entropy models and combined distribution assignment models. Most equilibrium based methods have not been applied to networks of sizes relevant in practical planning situations. 3.1. Traffic modelling based ....

M. Florian (1986), Nonlinear cost network models in transportation analysis, Mathematical programming study, 26.

....path is the minimum possible amongst all paths joining the same O D pair. Based on this principle, transportation planning models have been studied extensively and efficient algorithms have been devised for solving these traffic equilibria problems in last two decades, see Magnanti [7] or Florian [3]. In practice, the choice of paths based on a single criterion by all road users may not be reasonable. Minimum delay paths are sometimes not the cheapest ones to travel on. Take for example, freeways where tolls are collected. Some road users may choose an alternative road which incurs longer ....

....after a set of flows rather than a single flow. Given 2 . Let F (z) p (h) Gamma u i ( p 2 P i ; i 2 I; X p2P i h p Gamma d i ; i 2 I) z = h; u( If the vector cost is positive, then the parametric complementarity problem (2. 10) is equivalent to solving (see Florian [3]) F (z) T z = 0; F (z) 0; z = 0: Furthermore, if the vector cost is positive, 2.10) is also equivalent to the following parametric variational inequality problem VI( Find z = 0; s:t: F (z) T (y Gamma z) 0; 8y = 0: Since there exist several well known techniques for ....

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M. Florian, "Nonlinear cost network models in transportation analysis," Mathematical Programming 26 (1986) 167-196.

....of a mixed complementarity problem, a specialization of the variational inequality. Many papers have discussed the formulation and solution of user equilibrium problems using complementarity and variational inequality models, as well as the applications of these problems to urban planning; see [18, 19, 21, 30, 40]. The first two sections of the paper show how the user equilibrium problem is cast as a mixed complementarity problem (MCP) formulated within the GAMS modeling language, and solved using the PATH algorithm. Some examples of problems formulated using these tools are described in [6] There are ....

M. Florian. Nonlinear cost network models in transportation analysis. Mathematical Programming Study, 26:167--196, 1986.

....number of articles have been devoted to Jacobi and Gauss Seidel approaches. Cyclic decomposition methods for [TAP] are presented in e.g. 20, 21, 22, 16, 27, 73, 82, 88] In combination with simplicial decomposition column generation (see [47, 51] such algorithms have also been presented in [39, 55, 72, 74, 36, 34]. Jacobi Gauss Seidel methods have also been applied to the problem of optimal routing in computer communication networks (a problem with the same structure as [TAP] often in combination with Newton type approaches. We would like to stress that most applications of Jacobi or Gauss Seidel ....

Florian, M. (1986), Nonlinear cost network models in transportation analysis. Mathematical Programming Study 26, pp. 167-196.

....and that they all solve shortest route problems more often than the algorithms outlined in the preceding paragraph. For large scale problems, this will probably make these algorithms less efficient, due to the complexity of shortest route algorithms. For further reading, we refer to Florian [58] and Patriksson. 55] Column generation methods have also been extended to variational inequality and nonlinear complementarity formulations of the asymmetric traffic assignment problem. The algorithm of Bertsekas and Gafni [59] is a Newton type linearization method, based on diagonal ....

M. Florian, "Nonlinear cost network models in transportation analysis," Mathematical Programming Study 26, pp. 167-196 (1986).

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Florian, M., "Nonlinear cost network models on transportation analysis", Mathematical Programming Study 26 (1986) 167-196.

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M. Florian. Nonlinear cost network models in transportation analysis. Mathematical Programming Study, 26:167--196, 1986.

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M. Florian. Nonlinear cost network models in transportation analysis. Mathematical Programming Study, 26:167--196, 1986.

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M. Florian. Nonlinear cost network models in transportation analysis. Mathematical Programming Study, 26:167--196, 1986.

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Florian, M., Nonlinear cost network models in transportation analysis, Mathematical Programming Study, Vol. 26, pp. 167-196, 1986.

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M. Florian, "Nonlinear Cost Network Models in Transportation Analysis, " Mathematical Programming Study 26 (1986) 167--196.

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