One metric used throughout this organisation is travel times relative to equivalent times taken by motorcars. This repository documents procedures used to calibrate estimates of motorcar travel times to empirical data.
The empirical data are from Uber movement, with these analyses calibrating against data from Santiago, Chile. The data used are the “All Data” version for the first quarter of 2020, grouped by “Hour of Day”. The download tab on the website linked to above also includes a link to the “Geo Boundaries”, which are also required. Both of these data should be saved to a local directory.
The Uber movement data extend over a far greater boundary than the
“Santiago” boundary returned by Nominatim. The OSM network data were
therefore obtained here from the complete Chile pbf file downloaded
from Geofabrik, and then processed with osmium-tools by:
- Trimming to bbox of (-71.363,-33.851,-70.377,-33.113)
- Constructing separate keyword-filtered subsets with keywords of: “highway”, “restriction”, “access”, “bicycle”, “foot”, “motorcar”, “motor_vehicle”, “vehicle”, “toll”.
- Converting all of these single
pbffiles toosm(XML) format. - Reading in each via
osmdata::osmdata_sc(), and combining all data into singleosmdata_scobject.
The calibration proceeds in two steps:
- Calibration of waiting times both at traffic lights, and to turn across oncoming traffic. The effects of these parameters was examined in a 2020 Scientific Data paper, “Longitudinal spatial dataset on travel times and distances by different travel modes in Helsinki Region, which implemented a complicated parametrisation of waiting times at various types of intersections “based on previous research.”
- Calibration of estimated times to measures of network centrality. These effects were examined in a 2014 Nature Communications paper, “Predicting commuter flows in spatial networks using a radiation model based on temporal ranges, which started with a “base” model able to predict observed travel times with an r-squared correlation coefficient of 0.639. This was then increased through inclusion of the effects of centrality, using a simple threshold model, to 0.752.
These two types of calibration are successively applied here.
Waiting times were examined through two parameters:
- The effective waiting time at traffic lights; and
- The effective waiting time to turn across oncoming traffic.
Street networks were weighted for time-based routing using specific values of these two parameters, and travel times estimated for all 320,666 observed origins and destinations in the Uber Movement data. The minimal-error model corresponded to an R-squared correlation of 0.782 for an effective waiting time at traffic lights of 8 seconds in morning peak hour traffic (7-10 am), or 9 seconds in afternoon traffic (3-7 pm). Corresponding effective waiting times to turn across oncoming traffic were only 2 or 1 seconds, respectively, although these made very little difference to model results compared with the effects of traffic lights.
The preceding waiting times were then used to calculate time-based metrics of centrality, and to adjust observed travel times by centrality. These adjustments made, however, very little difference, and increasing travel times along more central portions of the network increased agreement with observed values at most by only a few hundredths of a percent or less. The best model was to logarithmically transform centrality, divide by the maximum value, and increase travel times for the upper 30% of the centrality distribution by the corresponding values. Even this, however, only increased resultant r-squared values by just over 1%.
This repository documents and justifies the general procedure pursued here, to estimate vehicular travel times through using the following time penalties:
- Wait at traffic lights = 9 seconds
- Wait to turn across oncoming traffic = 1 second
No additional adjustments for network centrality are implemented. The estimated times are then slightly faster than the observed times, with a median ratio of log-times of 0.94.
