Optimizing Proportionally Fair Prices

We demonstrate the non-uniqueness of Proportionally Fair prices, and show that the model of [1] falls into the category of models which can be generaliz- ed to allow optimization of the link prices, with a view toward profit maximization. However, through this framework, we also show that the total revenue that can be obtained through Proportional Fairness pricing on a network is unique

A Convergent Algorithm for the Multimodal Traffic Equilibrium Problem

The multimodal traffic equilibrium problem is in described in general by non-monotone, asymmetric, variational inequality problem. We show that in spite of the non-monotonicity of the cost operator, the problem may admit a different weaker property, which describes the hierarchical nature of the travel cost interactions. This property permits a natural decomposition approach, not otherwise available, which admits provably convergent algorithms- . We present one such algorithm, easily implementable using a solver for the single-class traffic equilibrium problem, and a convergence proof. This represents the first provably convergent method for solving the non-monot- one, asymmetric, traffic equilibrium problem

Stability of Transportation Networks Under Adaptive Routing Policies

AbstractGrowing concerns regarding urban congestion, and the recent explosion of mobile devices able to provide real-time information to traffic users have motivated increasing reliance on real-time route guidance for the online management of traffic networks. However, while the theory of traffic equilibria is very well-known, much fewer results exist on the stability of such equilibria, especially in the context of adaptive routing policy. In this work, we consider the problem of characterizing the stability properties of traffic equilibria in the context of online adaptive route choice induced by GPS-based decision making. We first extend the recent framework of “Markovian Traffic Equilibria” (MTE), in which users update their route choice at each intersection of the road network based on traffic conditions, to the case of non-equilibrium conditions, while preserving consistency with known existence and uniqueness results on MTE. We then exhibit sufficient conditions on the network topology and the latency functions for those MTEs to be stable in the sense of Lyapunov for a single destination problem. For various more restricted classes of network topologies motivated by the observed properties of travel patterns in the Singapore network, under certain assumptions we prove local exponential stability of the MTE, and derive analytical results on the sensitivity of the characteristic time of convergence on network and traffic parameters. The results proposed in this work are illustrated and validated on synthetic toy problems as well as on the full Singapore road network with real demand and traffic data, and the applicability of our results for online road network analysis, pricing and control is discussed

An Optimal Smart Market for the Pricing of Telecommunications Services

In [7], Mackie-Mason and Varian suggested the creation of a Smart market for the pricing of Internet services, based on the idea of having a Vickrey-ty- pe auction, at the packet level, at each node of the network. While this idea has attracted the attention of numerous researchers, in telecommunication- s and in economics, no optimization model has to date been proposed that captures this behavior. In this paper, we present such a mathematical model. We provide techniques for solving the model through an equivalent linear transformation, and present some numerical experience on sample networks

Optimal Location of Intermodal Freight Hubs

Projet ADOPTAttempts at reducing the externalities of freight transport in Europe are generally focused on the incorporation of a more significant use of rail into freight itineraries. One new scenario for increasing the share of rail in intermodal transport involves the development of a dedicated subnetwork of freight rail lines. Within this European Union project, the use of hub-and-spoke type networks, in combination with fixed-length shuttle services for freight, are under discussion. We present this innovative project and the proposed optimization model. The problem is cast as a nonlinear concave-cost hub location problem. A linearization procedure along with two efficient variable-reduction heuristics are proposed for its resolution, making use of recent results on polyhedral properties of this class of problems. Computational experience is provided on the European network of potential hub terminals