Directed movements in probabilistic time geography

This article studies probabilistic time geography for space–time prisms, that is, for situations where observers know the location of an agent at one time and then again at another time. In the intervening period, the agent would have moved freely, according to its time budget. The article demonstrates that the probability of finding the agent somewhere in the space–time prism is not equally distributed, so any attempt of a quantitative time geographic analysis must consider the actual probability distribution. This article develops, implements, and demonstrates this distribution. A preceding article introduced probabilistic time geography for space–time cones. With cones and prisms, the elementary space–time volumes of time geography are provided.

[1]  Hongbo Yu,et al.  A GIS-based time-geographic approach of studying individual activities and interactions in a hybrid physical–virtual space , 2009 .

[2]  Stephan Winter,et al.  Towards a probabilistic time geography , 2009, GIS.

[3]  Uniuersita di L'Aquila An Algebraic Model for Spatial Objects with Indeterminate Boundaries , 2012 .

[4]  Max J. Egenhofer,et al.  Modeling Moving Objects over Multiple Granularities , 2002, Annals of Mathematics and Artificial Intelligence.

[5]  Anthony G. Cohn,et al.  The ‘Egg-Yolk’ Representation of Regions with Indeterminate Boundaries , 2020 .

[6]  Kai Nagel,et al.  Large-Scale Multi-Agent Simulations for Transportation Applications , 2004, J. Intell. Transp. Syst..

[7]  Tijs Neutens,et al.  Human Interaction Spaces under Uncertainty , 2007 .

[8]  Anthony G. Cohn,et al.  A Spatial Logic based on Regions and Connection , 1992, KR.

[9]  M. Egenhofer Categorizing Binary Topological Relations Between Regions, Lines, and Points in Geographic Databases , 1998 .

[10]  W. Tobler A Computer Movie Simulating Urban Growth in the Detroit Region , 1970 .

[11]  M. Kwan Gis methods in time‐geographic research: geocomputation and geovisualization of human activity patterns , 2004 .

[12]  D. Helbing,et al.  Self-organizing pedestrian movement; Environment and Planning B , 2001 .

[13]  Tracy Camp,et al.  A survey of mobility models for ad hoc network research , 2002, Wirel. Commun. Mob. Comput..

[14]  Torsten Hägerstraand WHAT ABOUT PEOPLE IN REGIONAL SCIENCE , 1970 .

[15]  Pip Forer,et al.  Movement beyond the snapshot - Dynamic analysis of geospatial lifelines , 2007, Comput. Environ. Urban Syst..

[16]  A. M. Edwards,et al.  Revisiting Lévy flight search patterns of wandering albatrosses, bumblebees and deer , 2007, Nature.

[17]  G. Pólya Über eine Aufgabe der Wahrscheinlichkeitsrechnung betreffend die Irrfahrt im Straßennetz , 1921 .

[18]  A. Rubinstein Modeling Bounded Rationality , 1998 .

[19]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .

[20]  Michael Batty,et al.  Agent-based pedestrian modelling , 2003 .

[21]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[22]  Tijs Neutens,et al.  Space–time opportunities for multiple agents: a constraint‐based approach , 2007, Int. J. Geogr. Inf. Sci..

[23]  Stephan Winter,et al.  Hierarchical Topological Reasoning with Vague Regions , 2002 .

[24]  Max J. Egenhofer,et al.  Reasoning about Binary Topological Relations , 1991, SSD.

[25]  T. Hägerstrand What about people in Regional Science? , 1970 .

[26]  Dirk Helbing,et al.  Modelling the evolution of human trail systems , 1997, Nature.

[27]  Harvey J. Miller,et al.  Modelling accessibility using space-time prism concepts within geographical information systems , 1991, Int. J. Geogr. Inf. Sci..

[28]  Ralf Hartmut Güting,et al.  Moving Objects Databases , 2005 .

[29]  Albert-László Barabási,et al.  Understanding individual human mobility patterns , 2008, Nature.

[30]  Dirk Helbing,et al.  Self-Organizing Pedestrian Movement , 2001 .

[31]  P. Bovy,et al.  ROUTE CHOICE: WAYFINDING IN TRANSPORT NETWORKS , 1990 .

[32]  P. A. Prince,et al.  Lévy flight search patterns of wandering albatrosses , 1996, Nature.