Accessibility with time and resource constraints: Computing hyper-prisms for sustainable transportation planning

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.