Variability of Travel Time,Congestion, and the Cost of Travel

The variability of travel time modifies the rush hour traffic and the cost of commuting. The bottleneck model of road congestion with fixed peak-load demand is augmented of an additive random delay. When individuals have (α-β-γ) preferences, there exists a unique Nash equilibrium. The variability of travel time leads to departure rates that are spread more evenly over the rush hour than when travel times are deterministic. This equilibrium mechanism mitigates both congestion and the cost of unreliability. This implies that “single-traveler models,” which treat congestion as an exogenous phenomenon, overestimate the value of reliability for the rush hour. The application with the uniform or with the exponential distribution helps appraise the overestimation.     

Modeling Multisite Activity from Occupational Surveys: Deducing the Number of Anesthesiologists from a Count of Anesthesiology Posts in France

Reliable data on the total number of physicians practicing in France cannot be obtained from national professional or administrative files which are not kept to date. From a public health standpoint, the total number of physicians' posts in establishments matters more than the actual total number of physicians, although the latter is necessary for demographic projections and to determine training needs. Shared work in the same post is sometimes encouraged to avoid closure of the post or even of the establishment. The relationship between the total number of posts in an occupation and the total number of individuals working in those posts depend on the duration of a reference period for the enumeration. An original model of this relationship is developed and applied to a count of anesthesiology posts in France with different values of the reference period. Instead of the usual question “How many anesthesiologists are currently working in your hospital?” the model suggests that the right question is “How many anesthesiologists have been working in your institute since the last 2.5 weeks?”. The total number of anesthesia and intensive care practitioners estimated by the model is 8,992 which is lower than the direct count of 9,741 posts.     

Rationality and Order-Dependent Sequential Rationality

We show that an individual using a choice function is sequentially rational and the decisions he makes are independent of the order of implementation of the rationales if and only if he is rational with the union of the rationales as a base binary relation. When he makes his decisions following a choice correspondence, the sufficiency part of this claim still holds, the necessity part of it does not.      

The Multi-scale Marked Area-interaction Point Process: A Model for the Spatial Pattern of Trees

Abstract.  The spatial pattern of trees in forests often combines different types of structure (regularity, clustering or randomness) at different scales. Taking species or size into account leads to marked patterns. The question addressed is to model such multi-scale marked patterns using a single process. Within the category of Markov processes, the area-interaction process has the advantage of being locally stable, whether it is attractive or repulsive. This process was originally defined as a one-scale non-marked process. We propose an extension as a multi-scale marked process. Three examples are presented to show the adequacy of this process to model tree patterns: 1. A pine pattern showing anisotropic regularity and clustering at different scales. 2. A bivariate (adult/juvenile) kimboto pattern in French Guiana, showing regularity for one type, clustering for the other and repulsion between the two. 3. A marked pattern in Gabon where the mark is tree diameter.