Simulating visit probability distributions within planar space-time prisms

The space-time prism is key concept in time geography and moving objects databases; it demarcates all locations that a mobile object can occupy given anchor locations and times and a maximum velocity for travel. Although the prism’s spatial and temporal extent is widely applied as a measure of accessibility and object locational uncertainty, until recently little attention has been paid to the properties of the prism interior such as the probabilities of the object visiting different locations within the prism. Better understanding of the visit probability distribution within the prism can improve theoretical understanding as well as refine the prism as a practical measure of space-time accessibility and object uncertainty. This paper presents two methods for modeling the distribution of visit probabilities within planar space-time prisms: (1) a directed Random Walk method for discrete space and time, and (2) a truncated Brownian Bridges method for continuous space and time. We illustrate these methods and demonstrate the effect of prism and mobility parameters on the visit probability distributions within the prism.