1. Introduction

Accessibility indicators measure the ease with which opportunities, such as jobs, can be reached by a traveler from a particular location (Levinson and et al. 2020). This vignette shows how to calculate and visualize accessibility in R using the r5r package using a reproducible example. In this example, we will be using a sample data set for the city of Porto Alegre (Brazil) included in r5r.

There are two ways to calculate / visualize accessibility using r5r. The quick and easy option is using the r5r::accessibility() function. The other alternative requires one to first calculate a travel time matrix, and then to use the {accessibility} package. This is a more flexible options because the {accessibility} package provides a wider range of options of accessibility metrics. We will cover both approaches in this vignette.

Before we start, we need to increase Java memory + load a few libraries, and to build routable transport network.

2. Build routable transport network with setup_r5()

options(java.parameters = "-Xmx2G")

library(r5r)
library(accessibility)
library(sf)
library(data.table)
library(ggplot2)
library(interp)
library(h3jsr)
library(dplyr)

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

r5r_core <- setup_r5(data_path)

3. Accessibility: quick and easy approach

There are different types of accessibility metrics. One of the simplest ones is the cumulative-opportunity metric, which counts the number of opportunities accessible from each location considering a maximum travel time cutoff. This is what we’ll be calculating in this vignette using the parameter decay_function = "step".

In this example, we will be calculating the number of schools and public healthcare facilities accessible by public transport within a travel time of up to 20 minutes. The sample data provided contains information on the spatial distribution of schools in Porto Alegre in the points$schools column, and healthcare facilities in the points$healthcare column.

With the code below we compute the number of schools and healthcare accessible considering median of multiple travel time estimates departing every minute over a 60-minute time window, between 2pm and 3pm. The accessibility() function can calculate access to multiple opportunities in a single call, which is much more efficient and convenient than producing a travel time matrix of the study area and manually computing accessibility.

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

# routing inputs
mode <- c("WALK", "TRANSIT")
max_walk_time <- 30      # in minutes
travel_time_cutoff <- 20 # in minutes
time_window <- 60        # in minutes
departure_datetime <- as.POSIXct("13-05-2019 14:00:00",
                                 format = "%d-%m-%Y %H:%M:%S")

# calculate accessibility
access1 <- r5r::accessibility(r5r_core,
                        origins = points,
                        destinations = points,
                        mode = mode,
                        opportunities_colnames = c("schools", "healthcare"),
                        decay_function = "step",
                        cutoffs = travel_time_cutoff,
                        departure_datetime = departure_datetime,
                        max_walk_time = max_walk_time,
                        time_window = time_window,
                        progress = FALSE)

head(access1)

Mind you that the r5r::accessibility() also allow users to calculate gravity-based accessibility metrics, which can be calculated by setting the decay_function to one of the following: "exponential" "fixed_exponential", "linear" or "logistic". Nonetheless, there are several other types of accessibility metrics not implemented in R5, including floating catchment area metrics, travel cost to closest N opportunities, time interval based cumulative opportunity, etc. This is where the {accessibility} package comes in.

4. Accessibility: flexible approach

The {accessibility} package provides a much more flexible approach to calculate accessibility estimates. A key input here is a travel time matrix, which we calculate using r5r:

# calculate travel time matrix
ttm <- r5r::travel_time_matrix(r5r_core,
                        origins = points,
                        destinations = points,
                        mode = mode,
                        departure_datetime = departure_datetime,
                        max_walk_time = max_walk_time,
                        time_window = time_window,
                        progress = FALSE)
head(ttm)

Now to calculate a traditional cumulative opportunity metric like we did above, we just need to call the accessibility::cumulative_cutoff() function, and pass our travel time matrix and land use data as input:

# calculate accessibility
access_edu <- accessibility::cumulative_cutoff(travel_matrix = ttm, 
                                        land_use_data = points,
                                        opportunity = 'schools',
                                        travel_cost = 'travel_time_p50',
                                        cutoff = 20)

access_health <- accessibility::cumulative_cutoff(travel_matrix = ttm, 
                                        land_use_data = points,
                                        opportunity = 'healthcare',
                                        travel_cost = 'travel_time_p50',
                                        cutoff = 20)
head(access_edu)
head(access_health)

5. Map Accessibility

The final step is mapping the accessibility results calculated earlier. We can use at least two different approaches to map our accessibility estimates.

# retrieve polygons of H3 spatial grid
grid <- h3jsr::cell_to_polygon(points$id, simple = FALSE)

# merge accessibility estimates
access_sf <- left_join(grid, access1, by = c('h3_address'='id'))

# plot
ggplot() +
  geom_sf(data = access_sf, aes(fill = accessibility), color= NA) +
  scale_fill_viridis_c(direction = -1, option = 'B') +
  labs(fill = "Number of\nfacilities within\n20 minutes") +
  theme_minimal() +
  theme(axis.title = element_blank()) +
  facet_wrap(~opportunity) +
  theme_void()

# interpolate estimates to get spatially smooth result
access_schools <- access1 %>% 
  filter(opportunity == "schools") %>%
  inner_join(points, by='id') %>%
  with(interp::interp(lon, lat, accessibility)) %>%
  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() %>%
  mutate(opportunity = "schools")

access_health <- access1 %>% 
  filter(opportunity == "healthcare") %>%
  inner_join(points, by='id') %>%
  with(interp::interp(lon, lat, accessibility)) %>%
  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() %>%
  mutate(opportunity = "healthcare")

access.interp <- rbind(access_schools, access_health)

# 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_sf(data = street_net$edges, color = "gray55", size=0.01, alpha = 0.7) +
  geom_contour_filled(aes(x=x, y=y, z=acc), alpha=.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, datum = NA) + 
  labs(fill = "Number of\nfacilities within\n20 minutes") +
  theme_void() +
  facet_wrap(~opportunity)

r5r::stop_r5(r5r_core)
rJava::.jgc(R.gc = TRUE)