Moving Walkways, Escalators, and Elevators

TL;DR

This paper models transportation facilities like escalators and walkways using a geometric approach, providing algorithms to optimally locate them to minimize maximum travel times between points.

Contribution

It introduces a simple geometric model for transportation facilities and develops algorithms to determine their optimal placement based on travel time minimization.

Findings

Algorithms for optimal facility placement are provided.

The model can represent various transportation modes like escalators and tunnels.

Optimal placement reduces maximum travel time between points.

Abstract

We study a simple geometric model of transportation facility that consists of two points between which the travel speed is high. This elementary definition can model shuttle services, tunnels, bridges, teleportation devices, escalators or moving walkways. The travel time between a pair of points is defined as a time distance, in such a way that a customer uses the transportation facility only if it is helpful. We give algorithms for finding the optimal location of such a transportation facility, where optimality is defined with respect to the maximum travel time between two points in a given set.