The variance location problem on a network with continuously distributed demand

Most location problems on networks consider discrete nodal demand. However, for many problems, demands are better represented by continuous functions along the edges, in addition to nodal demands. Several papers consider the optimal location problem of one or more facilities when demands are continuously distributed along the network, and the objective function dealt with is the median one. Nevertheless, in location of public services it is desirable to use an equity criterion. One of the latter is variance of distance distribution which has been studied only for discrete nodal demands. In this paper the variance problem has been generalized to the case where one allows the demand to arise discretely on the nodes as well as continuously along the edges. Properties and behaviour of the objective function are studied. Likewise we present an exact algorithm for solving this problem in a network, which reduces the complexity of the exhaustive procedure.Spanish Research Council (DGICYT

Discrete Choices under Social Influence: Generic Properties

We consider a model of socially interacting individuals that make a binary choice in a context of positive additive endogenous externalities. It encompasses as particular cases several models from the sociology and economics literature. We extend previous results to the case of a general distribution of idiosyncratic preferences, called here Idiosyncratic Willingnesses to Pay (IWP). Positive additive externalities yield a family of inverse demand curves that include the classical downward sloping ones but also new ones with non constant convexity. When j, the ratio of the social influence strength to the standard deviation of the IWP distribution, is small enough, the inverse demand is a classical monotonic (decreasing) function of the adoption rate. Even if the IWP distribution is mono-modal, there is a critical value of j above which the inverse demand is non monotonic, decreasing for small and high adoption rates, but increasing within some intermediate range. Depending on the price there are thus either one or two equilibria. Beyond this first result, we exhibit the generic properties of the boundaries limiting the regions where the system presents different types of equilibria (unique or multiple). These properties are shown to depend only on qualitative features of the IWP distribution: modality (number of maxima), smoothness and type of support (compact or infinite). The main results are summarized as phase diagrams in the space of the model parameters, on which the regions of multiple equilibria are precisely delimited.Comment: 42 pages, 15 figure

Examining trade-offs between social, psychological, and energy potential of urban form

Urban planners are often challenged with the task of developing design solutions which must meet multiple, and often contradictory, criteria. In this paper, we investigated the trade-offs between social, psychological, and energy potential of the fundamental elements of urban form: the street network and the building massing. Since formal methods to evaluate urban form from the psychological and social point of view are not readily available, we developed a methodological framework to quantify these criteria as the first contribution in this paper. To evaluate the psychological potential, we conducted a three-tiered empirical study starting from real world environments and then abstracting them to virtual environments. In each context, the implicit (physiological) response and explicit (subjective) response of pedestrians were measured. To quantify the social potential, we developed a street network centrality-based measure of social accessibility. For the energy potential, we created an energy model to analyze the impact of pure geometric form on the energy demand of the building stock. The second contribution of this work is a method to identify distinct clusters of urban form and, for each, explore the trade-offs between the select design criteria. We applied this method to two case studies identifying nine types of urban form and their respective potential trade-offs, which are directly applicable for the assessment of strategic decisions regarding urban form during the early planning stages