The Time Space Diagram Revisited

1 Widely used in the design and analysis of transportation systems, time-space diagrams were devel2 oped in an era of data scarcity, when it was necessary to obtain data by means of driver logs, human 3 observers or aerial photographs. In this paper we show how time-space diagrams still remain rel4 evant today, in an era of data abundance. We present an application that efficiently encodes the 5 trajectories of bus GPS data in a time-space cube and uses simple geometric methods to calculate 6 and visualize the headways and separation of buses on a bus route. We discuss these methods in 7 detail and explore how they can be used as the basis of a software package to monitor performance 8 measures for a variety of applications. 9 TRB 2014 Annual Meeting Paper revised from original submittal. Anwar, Zeng and Arisona 2 INTRODUCTION 1 Time-space diagrams are commonly used to solve a wide variety of transportation problems. Typ2 ically, we use the variable x to denote the distance traveled along a guideway from some arbitrary 3 reference point, and another variable t to denote the time elapsed from an arbitrary instant (1). 4 By studying how the position of a vehicle changes over time, we can better understand the perfor5 mance characteristics of the transportation system under analysis. 6 The biggest challenge in using a time-space diagram is collecting sufficiently accurate data 7 to build one (2). Time-space diagrams came into prominence in the 1950s and 1960s when trans8 portation engineering was in its infancy. Back then, data collection was tedious and expensive. 9 Today, it is standard practice for transport operators to know where all their vehicles are at all 10 times. For example, bus operators routinely use bus location data to inform passengers when the 11 next bus is arriving while taxi operators use real time taxi GPS data in their booking systems. 12 All this data is location based, and contains at the bare minimum a position (latitude and 13 longitude) and time stamp. In this paper, we propose using such data to build time-space diagrams 14 for use in the analysis and visualization of transportation operations. The main contributions of 15 this paper are: 16 • a way to efficiently store vehicle trajectories as line segments in 3D space for fast retrieval 17 • simple geometric methods inspired by the time-space diagram that apply intersection 18 tests with these line segments to find vehicle headways and spacing, 19 • a visualization and analysis tool that can allow transit operators and regulators to better 20 understand network performance and behavior, 21 • a brief discussion on how any transportation system with big data capability can use time 22 space diagrams to monitor service levels, network capacity and delays 23