Anchor uncertainty and space-time prisms on road networks

Abstract

Space-time prisms capture all possible locations of a moving person or object between two known locations and times given the maximum travel velocities in the environment. These known locations or 'anchor points' can represent observed locations or mandatory locations because of scheduling constraints. The classic space-time prism as well as more recent analytical and computational versions in planar space and networks assume that these anchor points are perfectly known or fixed. In reality, observations of anchor points can have error, or the scheduling constraints may have some degree of pliability. This article generalizes the concept of anchor points to anchor regions: these are bounded, possibly disconnected, subsets of space-time containing all possible locations for the anchor points, with each location labelled with an anchor probability. We develop two algorithms for calculating network-based space-time prisms based on these probabilistic anchor regions. The first algorithm calculates the envelope of all space-time prisms having an anchor point within a particular anchor region. The second algorithm calculates, for any space-time point, the probability that a space-time prism with given anchor regions contains that particular point. Both algorithms are implemented in Mathematica to visualize travel possibilities in case the anchor points of a space-time prism are uncertain. We also discuss the complexity of the procedures, their use in analysing uncertainty or flexibility in network-based prisms and future research directions

A GIS toolkit for measuring and mapping space–time accessibility from a place-based perspective

“…These have been characterised by an unrealistic modelling of the travel environment as they ignore the transportation network (Kwan and Hong 1998). This shortcoming has been addressed later in both theoretical (Neutens et al 2007, Miller and Bridwell 2009, Kuijpers et al 2010) and empirical work (Kwan and Hong 1998, Kwan 1998, Kim and Kwan 2003, Kwan and Weber 2003, Neutens et al 2010b, Neutens et al 2010c). …”

An Adaptive Sampling Approach for Trajectories Based on the Concept of Error Ellipses

“…Error ellipses are closely related to the concept of space-time prisms whereby all possible locations that a person can be in is depicted based on starting location, travel velocity and time taken (KUIJPERS et al 2010). Although space-time prisms are widely used, KOBAYASHI et al (2011) note that they classically assume the starting location and time factor are precisely known, which is not always the case.…”

The relationship between opening hours and accessibility of public service delivery

“…Relying on these time-geographical concepts, various so-called space-time accessibility measures (STAMs) have been proposed that incorporate the performance of the transport network (Miller, 1991;Kwan, 1998;Neutens et al, 2008b;Miller and Bridwell, 2009;Kuijpers et al, 2010). Spurred on by the developments in geographical information systems (GIS) and the availability of disaggregate travel data, the use of network-based STAMs has developed rapidly in the past decade.…”