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Towards a Percolation Model of Accessibility
HAYNES, Kingsley (firstname.lastname@example.org), Director, The Institute of Public Policy, STOUGH, Roger, (email@example.com), and KULKARNI, Rajendra, (firstname.lastname@example.org), George Mason University, ATTN: MS 3C6, Fairfax, VA 22030-4444
Key Words: accessibility, site, bond percolation
Transportation networks are characterized by two complementary functions: accessibility to economic activities and mobility to carry out these activities. One of the ways to measure accessibility is the number of opportunities available to a user of a transportation network. But for users to carry out economic activities, i.e., exercise mobility, they have to at least have conceptual or perceived links to the activities. Given this, we ask what is the process that leads to the development of these perceived links? We present an analytical approach based on percolation theory to explain the evolution of perceived links to economic activities. A subjective accessibility measure, i.e., a network of perceived links, is developed based on economic opportunities and individuals' income levels in a transport region. For this research a perceived link to an opportunity exists if the user's income is above some threshold. Accessibility to opportunities may be viewed as analogous to the sites and bonds percolation model where sites are opportunities and bonds are conceptual links. In the context of percolation theory, the complex network of sites and bonds is viewed as subject to the critical phenomenon of phase transitions. This paper describes and applies, through numerical analysis, i.e., computer simulation, an application of the sites and bonds percolation model to accessibility. The paper provides an original approach to the investigation of the evolution of perceived links in a transport network and the related mobility of network users.