Analyzing collective accessibility using average space-time prisms

New publication:  Lee, J. and Miller, H.J. (2019) “Analyzing collective accessibility using average space-time prisms,” Transportation Research Part D: Transport and Environment, 69, 250-264.

Abstract:  The space-time prism (STP) is the envelope of all possible travel paths in space and time between two anchor locations and times, measuring accessibility for an individual given a designated travel and activity episode. Although the STP provides a powerful measure of individual accessibility, transportation researchers often need to analyze accessibility at collective-levels for planning and policy analysis. Deriving a representative STP of a set of individual STPs would provide a general idea of how collective members’ accessibility is performing. However, there is no analytical time geographic method to calculate a collective-level representative STP that is consistent with individual STPs. To fill this gap, this research develops the concept of average space-time prism (ASTP). The ASTP is a representative STP of a group of individual STPs with respect to size, shape, and location. We develop methods for calculating an ASTP using analytical time geography and elliptic Fourier shape analysis techniques. The ASTP provides a geometric and visual summary of collective accessibility: it can be used to generate representative STPs for aggregate geographic units such as neighborhoods and cities based on individual-level data. A possible application of the ASTP is the spatial equity analysis of accessibility. The ASTP can be located at individuals’ anchor locations and overlaid with opportunities, enabling in-situ comparisons between individual versus collective accessibility and accessibility equity analysis considering geographic contexts. We illustrate this ASTP’s capability when measuring the impacts of new transit service on healthcare access equity in a neighborhood in Columbus, Ohio, USA.

Harvey Miller uses new mobility data to understand cities and transportation

I was interviewed by Prof. David Staley for the Ohio State University Voices of Excellence from Arts and Sciences podcast: we talk about GIS, sustainable transportation, mobility data and time geography.

Check it out:

Harvey Miller uses new mobility data to understand cities and transportation

New publication: Accessibility with time and resource constraints

Mahmoudi, M., Song, Y., Miller, H.J. and Zhou, X.  (2019) “Accessibility with time and resource constraints: Computing hyper-prisms for sustainable transportation planning,” Computers, Environment and Urban Systems, 73, 171-183


Accessibility is the ease of obtaining desired destinations, activities, or services in an environment. A common accessibility measure in basic and applied transportation science is the space-time prism (STP) and the network-time prisms (NTPs): these are the envelopes of all possible paths between two locations and times in planar space and transportation networks, respectively. STPs and NTPs focus on time as the scarce resource limiting accessibility. However, other resource constraints can constrain space-time accessibility, such as limits or “budgets” for energy, emissions, or monetary expenses. This paper extends NTPs to include other resource constraints in addition to time. Network-based resource hyper-prisms (RHPs) incorporate other resource constraints into NTP, capturing the trade-offs between time and other resources in determining space-time accessibility. We conceptualize RHPs as a constrained optimization problem and develop a forward and backward resource-dependent time-dependent dynamic programming to determine the boundaries of a RHP given time and other resource budgets. We illustrate our approach using the Chicago sketch network (with 933 nodes and 2967 links) for the use case of an individual with an internal combustion engine vehicle and a carbon emission budget and using portions of Washington, D.C. and Baltimore networks (with 12,145 nodes and 30,697 links) for the use case of siting electric vehicle charging stations to maximize regional accessibility.


Resource hyper-prisms; Space-time prisms; Accessibility; Sustainable transportation; Dynamic programming