Calculating and visualizing Accessibility

Rafael H. M. Pereira, Marcus Saraiva, Daniel Herszenhut, Carlos Kaue Braga, Matthew Wigginton Conway

2021-04-15

Abstract

This vignette shows how to calculate and visualize accessibility in R using the r5r package.

Introduction

Accessibility metrics measure the ease with which opportunities, such as jobs, can be reached by a traveler from a particular location (Levinson and et al. 2020). One of the simplest forms of accessibility metrics is the cumulative-opportunities, which counts all of the opportunities accessible from each location in less than a cutoff time. Using a travel time matrix and information on the number of opportunities available at each location, we can calculate and map accessibility. This vignette shows how to do that in R using the r5r package.

In this reproducible example, we will be using a sample data set for the city of Porto Alegre (Brazil) included in r5r. We can compute accessibility in 5 quick steps:

  1. Increase Java memory and load libraries
  2. Build routable transport network
  3. Calculate travel times
  4. Calculate Accessibility
  5. Map Accessibility

1. Increase Java memory and load libraries

Before we start, we need to increase the memory available to Java and load the packages used in this vignette

options(java.parameters = "-Xmx2G")

library(r5r)
library(sf)
library(data.table)
library(ggplot2)
library(akima)
library(dplyr)

2. Build routable transport network with setup_r5()

To build a routable transport network with r5r and load it into memory, the user needs to call setup_r5 with the path to the directory where OpenStreetMap and GTFS data are stored.

# system.file returns the directory with example data inside the r5r package
# set data path to directory containing your own data if not using the examples
data_path <- system.file("extdata/poa", package = "r5r")

r5r_core <- setup_r5(data_path, verbose = FALSE)

3. Calculate travel times

In this example, we will be calculating the travel times by public transport between all city blocks in the city of Porto Alegre. With the code below we compute multiple travel time estimates departing every minute over a 60-minute time window, between 2pm and 3pm.

# read all points in the city
points <- fread(file.path(data_path, "poa_hexgrid.csv"))

# routing inputs
mode <- c("WALK", "TRANSIT")
max_walk_dist <- 1000 # in meters
max_trip_duration <- 60 # in minutes
departure_datetime <- as.POSIXct("13-05-2019 14:00:00",
                                 format = "%d-%m-%Y %H:%M:%S")

time_window <- 60 # in minutes
percentiles <- 50

# calculate travel time matrix
ttm <- travel_time_matrix(r5r_core,
                          origins = points,
                          destinations = points,
                          mode = mode,
                          departure_datetime = departure_datetime,
                          max_walk_dist = max_walk_dist,
                          max_trip_duration = max_trip_duration,
                          time_window = time_window,
                          percentiles = percentiles,
                          verbose = FALSE)

head(ttm)
#>             fromId            toId travel_time 
#> 1: 89a901291abffff 89a901291abffff           2 
#> 2: 89a901291abffff 89a901295b7ffff          45 
#> 3: 89a901291abffff 89a9012809bffff          49 
#> 4: 89a901291abffff 89a901285cfffff          38 
#> 5: 89a901291abffff 89a90129977ffff          52 
#> 6: 89a901291abffff 89a90128e27ffff          48

4. Calculate Accessibility

Once we have the travel time matrix at hand, calculating accessibility is simple. The sample data provided contains information on the spatial distribution of schools in Porto Alegre, which we will use to compute the number of schools accessible by public transport in less than 20 minutes.

# merge schools information to travel time matrix
ttm[points, on=c('toId' ='id'), schools := i.schools]

# calculate number of schools accessible
access <- ttm[travel_time <= 20, .(acc = sum(schools)), by=fromId]

5. Map Accessibility

The final step is mapping the accessibility results calculated earlier. The code below demonstrates how to do that, with some extra steps to produce a prettier map.

# interpolate estimates to get spatially smooth result
access.interp <- access %>%
  inner_join(points, by=c('fromId'='id')) %>%
  with(interp(lon, lat, acc)) %>%
                        with(cbind(acc=as.vector(z),  # Column-major order
                                   x=rep(x, times=length(y)),
                                   y=rep(y, each=length(x)))) %>% as.data.frame() %>% na.omit()

# find results' bounding box to crop the map
bb_x <- c(min(access.interp$x), max(access.interp$x))
bb_y <- c(min(access.interp$y), max(access.interp$y))

# extract OSM network, to plot over map
street_net <- street_network_to_sf(r5r_core)

# plot
ggplot(na.omit(access.interp)) +
  geom_contour_filled(aes(x=x, y=y, z=acc), alpha=.8) +
  geom_sf(data = street_net$edges, color = "gray55", size=0.1, alpha = 0.7) +
  scale_fill_viridis_d(direction = -1, option = 'B') +
  scale_x_continuous(expand=c(0,0)) +
  scale_y_continuous(expand=c(0,0)) +
  coord_sf(xlim = bb_x, ylim = bb_y) + 
  labs(fill = "Schools within\n20 minutes\n(median travel time)") +
  theme_minimal() +
  theme(axis.title = element_blank())

If you have any suggestions or want to report an error, please visit the package GitHub page.

References

Levinson, David, and et al. 2020. “Transport Access Manual: A Guide for Measuring Connection Between People and Places,” January. https://ses.library.usyd.edu.au/handle/2123/23733.