A Markovian measure for evaluating accessibility to urban opportunities

Accessibility is a fundamental notion in urban planning and its related fields. While accessibility is dynamic and varies during different time moments, most of the accessibility metrics are static and do not take this variation into account. In doing so, to address the questions of (1) how accessible urban opportunities are in different time moments and (2) how accessibility value of a person to a certain place changes regarding his/her spatiotemporal restrictions in time instants, this article—by using semi-Markovian and Brownian Bridge stochastic processes—offers a probabilistic time-dependent accessibility model that blends the magnitude of opportunities magnitude with the probability of individuals visiting. To show the model's applicability, it was applied on a hypothetical case, along with two common accessibility metrics, and the outputs were compared. Then the proposed model was implemented in a study area for measuring temporal accessibility in two real policies made for daily markets in Isfahan, Iran. The first policy that presented the model application for analytical purposes was "market exclusion and area expansion," and the second policy that depicted the model implementation for normative usage was "new market location." Results of the model execution on the hypothetical cases indicated there was a significant difference between the outputs of the common metrics and the ones of the proposed model. In addition, in the study area, the first policy generated higher total accessibility value in comparison with the second policy when market 2 was excluded and the area for market 8 was doubled.