Statistical Laws in Urban Mobility from microscopic GPS data in the area of Florence

📝 Abstract

The application of Statistical Physics to social systems is mainly related to the search for macroscopic laws, that can be derived from experimental data averaged in time or space,assuming the system in a steady state. One of the major goals would be to find a connection between the statistical laws to the microscopic properties: for example to understand the nature of the microscopic interactions or to point out the existence of interaction networks. The probability theory suggests the existence of few classes of stationary distributions in the thermodynamics limit, so that the question is if a statistical physics approach could be able to enroll the complex nature of the social systems. We have analyzed a large GPS data base for single vehicle mobility in the Florence urban area, obtaining statistical laws for path lengths, for activity downtimes and for activity degrees. We show also that simple generic assumptions on the microscopic behavior could explain the existence of stationary macroscopic laws, with an universal function describing the distribution. Our conclusion is that understanding the system complexity requires dynamical data-base for the microscopic evolution, that allow to solve both small space and time scales in order to study the transients.

💡 Analysis

The application of Statistical Physics to social systems is mainly related to the search for macroscopic laws, that can be derived from experimental data averaged in time or space,assuming the system in a steady state. One of the major goals would be to find a connection between the statistical laws to the microscopic properties: for example to understand the nature of the microscopic interactions or to point out the existence of interaction networks. The probability theory suggests the existence of few classes of stationary distributions in the thermodynamics limit, so that the question is if a statistical physics approach could be able to enroll the complex nature of the social systems. We have analyzed a large GPS data base for single vehicle mobility in the Florence urban area, obtaining statistical laws for path lengths, for activity downtimes and for activity degrees. We show also that simple generic assumptions on the microscopic behavior could explain the existence of stationary macroscopic laws, with an universal function describing the distribution. Our conclusion is that understanding the system complexity requires dynamical data-base for the microscopic evolution, that allow to solve both small space and time scales in order to study the transients.

📄 Content

Statistical Laws in Urban Mobility from microscopic GPS data in the area of Florence Armando Bazzani , Bruno Giorgini , Sandro Rambaldi , Riccardo Gallotti and Luca Giovannini Physics of the City Laboratory, Physics Department and C.I.G. University of Bologna, Italy, INFN, sezione di Bologna, Italy e-mail: bazzani@bo.infn.it Abstract: The application of Statistical Physics to social systems is mainly related to the search for macroscopic laws, that can be derived from exper- imental data averaged in time or space,assuming the system in a steady state. One of the major goals would be to find a connection between the statistical laws to the microscopic properties: for example to understand the nature of the microscopic interactions or to point out the existence of interaction networks. The probability theory suggests the existence of few classes of stationary distributions in the thermodynamics limit, so that the question is if a statistical physics approach could be able to enroll the complex nature of the social systems. We have analyzed a large GPS data base for single vehicle mobility in the Florence urban area, obtaining statistical laws for path lengths, for activity downtimes and for activity degrees. We show also that simple generic assumptions on the microscopic behavior could explain the existence of stationary macroscopic laws, with an universal function describing the distribution. Our conclusion is that understanding the system complexity requires dynamical data-base for the microscopic evolution, that allow to solve both small space and time scales in order to study the transients. Keywords and phrases: Urban Mobility, GPS data, Probability Distri- butions, Statistical Physics.

1. Introduction Any statistical analysis of real systems is based on the Ergodic Principle for the microscopic dynamics, that implies the relaxation towards steady states and the independence property of elementary components. Even if the existence of mi- croscopic interactions is necessary for the system to evolve toward a statistical equilibrium, in this state any particle moves independently from the others and all the particles are statistically equivalent (any particle may be representative for the whole). The thermodynamics laws that are derived from a statistical me- chanics approach, concern some macroscopic observables of the system, evolving adiabatically with respect the microscopic relaxation time (i.e. we can consider the whole system in a almost equilibrium state), so that the effects of single par- ticle dynamics are conveniently described by means of stochastic processes. As 1 imsart-generic ver. 2009/08/13 file: stat_law.tex date: October 23, 2018 arXiv:0912.4371v1 [physics.soc-ph] 22 Dec 2009 A. Bazzani et al./Statistical Laws in Urban Mobility 2 a consequence, there should exist a natural separation among macroscopic and microscopic space-time scales. Indeed space and time scales are expected to be strictly correlated: to understand small scale phenomena we need to solve short time scales and viceversa. Nevertheless the statistical mechanics has a great success in describing evolution of macroscopic systems and there is a strong effort to generalize the results for a non-equilibrium thermodynamics and for application to complex systems[1]. The statistical properties of social systems have been recently considered under a different point of view due to the possi- bility of recording large microscopic data sets[2, 3]. The main problem is what are the macroscopic effects of cognitive behavior for ”social particles”. Indeed the cognitive behavior would imply the existence of strong bidirectional inter- actions among the dynamics at different space and time scales of the system[4]. Emergence and self-organization characterize the macroscopic states, but the question is which macroscopic observables (if they exist) may enrol the complex nature of the system. These variables may also play an important role in the study of phase transitions and in the control parameters definition. In Italy GPS data on individual vehicle paths are currently recorded for insur- ance reasons over a sample ≃2% of the whole private vehicle population[5, 6]. This data set gives the opportunity to study the individual mobility demand in urban contexts. The GPS data set contains the geographical coordinates, the time, the instantaneous velocity and the path length of individual trajectories at positions whose relative distance is of order 1 ÷ 2 km. Special signals are recorded when the engine is switched on and off. We remark that the data refer mainly to the private transportation mobility and that, due to privacy legal problems, we do not have any knowledge on the social features of individuals in the sample. In this paper we analyze the statistical distributions of the path lengths of indi- vidual trajectories, of the activity downtime and the distribution of the monthly activity degree. Our aim is to point out the main macroscopic featu

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