Traffic assignment problem for a general network

Dafermos, Stella; Sparrow, F.T.

doi:10.6028/jres.073b.010

Cited by 485 publications

(365 citation statements)

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“…It is well known ( [2], [8], [15]; see also [4], especially Proposition 3.1) that, for homogeneous networks with differentiable latency functions l e , one can use the marginal costs 3f e l e (f e ) as b e in Theorem 1 to achieve the following classical result: Theorem 3. If functions l e are differentiable, thenf is an equilibrium for the selfish routing game with T P (f ) := e∈P (l e (f e ) +f e l e (f e )).…”

Section: Comparison To the Original Latenciesmentioning

confidence: 99%

“…This technique has been studied by the traffic community for a long time (cf. [5] and the references therein), especially in the context of marginal costs (see, for example, [2], [8], [15]). Each selfish user of class i using path P will experience the following path cost: path cost(P ) := latency(P ) + a(i) · taxation(P ).…”

Section: Introductionmentioning

confidence: 99%

“…In the homogeneous case, marginal costs have been shown (cf. [2], [8], [15]) to be optimal taxes. In the heterogeneous case, the existence and calculation of such optimal taxes were shown for the single source-destination pair case by Cole et a.…”

Section: Introductionmentioning

confidence: 99%

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The Efficiency of Optimal Taxes

Karakostas

Kolliopoulos

2005

Combinatorial and Algorithmic Aspects of Networking

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Abstract. It is well known that the selfish behavior of users in a network can be regulated through the imposition of the so-called optimal taxes on the network edges. Any traffic equilibrium reached by the selfish users who are conscious of both the travel latencies and the taxes will minimize the social cost, i.e., will minimize the total latency. Optimal taxes incur desirable behavior from the society point of view but they cause disutility to the network users since the users' total cost is in general increased [4]. Excessive disutility due to taxation may be undesirable from the societal perspective as well. In this work we examine the efficiency of taxation as a mechanism for achieving the desired goal of minimizing the social cost. We show that for large classes of latency functions the total disutility due to taxation that is caused to the users and/or the system is bounded with respect to the social optimum. In addition, we show that if the social cost takes into account both the total latency and the total taxation in the network, the coordination ratio for certain latency functions is better than the coordination ratio when taxation is not used.

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Section: Comparison To the Original Latenciesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The Efficiency of Optimal Taxes

Karakostas

Kolliopoulos

2005

Combinatorial and Algorithmic Aspects of Networking

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“…The elegance of this computational procedure in the context of variational inequality (11) lies in that it allows one to utilize algorithms for the solution of the uncapacitated systemoptimization problem (for which numerous algorithms exist in the transportation science literature) with straightforward update procedures at each iteration to obtain the link capacities and the Lagrange multipliers. To solve the former problem we utilize in Section 3 the well-known equilibration algorithm (system-optimization version) of Dafermos and Sparrow (1969), which has been widely applied (see also, e.g., Nagurney (1999Nagurney ( , 2006). Recall that the modified projection method (cf.…”

Section: Theoremmentioning

confidence: 99%

“…The quadratic programming problem in product flows corresponds to the classical system -optimization problem (cf. Dafermos and Sparrow (1969) and Nagurney (1999)), for which numerous efficient algorithms exist since transportation network problems are widely solved in practice. The solutions to the link capacity subproblems, as well as the Lagrange multiplier subproblems, in turn, can be obtained via closed form expressions, since the underlying feasible sets are very simple.…”

Section: Theorem 4: Convergencementioning

confidence: 99%

Sustainable supply chain network design: a multicriteria perspective

Nagurney

2010

International Journal of Sustainable Engineering

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In this paper we develop a rigorous modeling and analytical framework for the design of sustainable supply chain networks. We consider a firm that is engaged in determining the capacities of its various supply chain activities, that is, the manufacturing, storage, and distribution of the product to the demand locations. The firm is faced with both capital costs associated with constructing the link capacities as well as the links' operational costs. Moreover, the firm is aware of the emissions generated associated with the alternative manufacturing plants, storage facilities, and modes of transportation/shipment, which may have different levels of emissions due, for example, to distinct technologies of, respectively, production, storage, and transportation. The firm is assumed to be a multicriteria decisionmaker who seeks to not only minimize the total costs associated with design/construction and operation, but also to minimize the emissions generated, with an appropriate weight, which reflects the price of the emissions, associated with the various supply chain network activities. We provide both the network optimization modeling framework and an algorithm, which is then applied to compute solutions to a spectrum of numerical sustainable supply chain design examples in order to illustrate our approach.

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Dynamic multi-sector, multi-instrument financial networks with futures: Modeling and computation

Nagurney

Siokos

1999

Networks

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In this paper, we develop a dynamic model of financial behavior in the case of multiple sectors and multiple instruments in the presence of financial futures, which demonstrates the evolution of the underlying networks through time. The dynamic model is formulated as a projected dynamical system whose set of stationary points coincides with the set of solutions to a variational inequality problem. We identify the network structure of the individual sectors' portfolio optimization problems out of equilibrium and then prove that the equilibrium solution can be reformulated as the solution to a network optimization problem, in which the network represents a merger of the individual networks. We subsequently provide a discrete time algorithm for the solution of the continuous time financial model, which exploits the network structure, and provide convergence results. The model and algorithm are then illustrated through numerical examples. © 1999 John Wiley & Sons, Inc. Networks 33: 93–108, 1999

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Traffic assignment problem for a general network

Cited by 485 publications

References 0 publications

The Efficiency of Optimal Taxes

The Efficiency of Optimal Taxes

Sustainable supply chain network design: a multicriteria perspective

Dynamic multi-sector, multi-instrument financial networks with futures: Modeling and computation

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