Measures and the Law of the Iterated Logarithm

Let m be a unidimensional measure with dimension d. A natural question is to ask if the measure m is comparable with the Hausdorff measure (or the packing measure) in dimension d. We give an answer (which is in general negative) to this question in several situations (self-similar measures, quasi-Bernoulli measures). More precisely we obtain fine comparisons between the mesure m and generalized Hausdorff type (or packing type) measures. The Law of the Iterated Logarithm or estimations of the L^q-spectrum in a neighborhood of q=1 are the tools to obtain such results.Comment: 18 page

Bimodal traffic regulation system: A multi-agent approach

International audienceThe development of surface public transportation networks is a major issue in terms of ecology, economy and society. Their quality in terms of punctuality and passengers services (regularity between buses) should be improved in order to improve their attractiveness. To do so, cities often use regulation systems at intersections that grant priority to buses. The problem is that each transportation mode has its own characteristics and a dedicated decision support system. Therefore, most of them hardly take into account both public transport vehicles such as buses and private vehicle traffic. This paper proposes a multi-agent model that supports bimodal regulation and preserves monomodal regulation. The objective is to improve global traffic, to reduce bus delays and to improve bus regularity in congested areas of the network. In our approach, traffic regulation is obtained thanks to communication, collaboration and negotiation between heterogeneous agents. We tested our strategy on a complex network of nine junctions. The results of the simulation are presented

Shared Autonomous Vehicles Implementation for a Disrupted Public Transport Network

The paper proposes the management of bus disruption (e.g. fleet failure) and maintain a resilient transportation system through a synergy between shared autonomous vehicles and the existing public transport system based on the organizational structure and demand characteristics. The methodology is applied to the region of Rennes (France) and its surroundings

Estimating Travel Time Distribution under different Traffic conditions

Increasing mobility and congestion result in an increase in travel time variability and in a decrease in reliability. Reliability becomes an important performance measure for transportation facilities. A variety of performance measures have been proposed to quantify it. Many of these indicators are based on percentiles of travel time. The knowledge of the distribution of travel time is needed to properly estimate these values. Congestion distorts the distribution and particular statistical distributions are needed. Different distributions have been proposed in the literature. In a previous paper, we presented a comparison of six statistical distributions used to model travel time. These six distributions are the Lognormal, Gamma, Burr, Weibull, a mixture of two Normal distributions and a mixture of two Gamma distributions. In this paper a probabilistic modeling of travel time which takes into account the levels-of-service is given. Levels of service are identified, then travel time distributions are modeled by level of service. This result in a very good fit between the empirical and modeled distributions Moreover, the adjustment was improved, thanks to the calibration of 'Bureau of Public Roads' functions, linking the travel time to the traffic flow by level of service. The superiority of the Singh-Maddala distribution appears in many cases. This has been validated, thanks to travel time data from the same site at another period. However the parameters of the distributions vary from one year to another, due to changes in infrastructure. The transferability of the approach, not performed, will be based on travel time data on another site

A Data-driven Approach for Estimating the Fundamental Diagram

The fundamental diagram links average speed to density or traffic flow. An analytic form of this diagram, with its comprehensive and predictive power, is required in a number of problems. This paper argues, however, that, in some assessment studies, such a form is an unnecessary constraint resulting in a loss of accuracy. A non-analytical fundamental diagram which best fits the empirical data and respects the relationships between traffic variables is developed in this paper. In order to obtain an unbiased fundamental diagram, separating congested and non-congested observations is necessary. When defining congestion in parallel with a safety constraint, the density separating congestion and non-congestion appears as a decreasing function of the flow and not as a single critical density value. This function is here identified and used. Two calibration techniques - a shortest path algorithm and a quadratic optimization with linear constraints - are presented, tested, compared and validated