Using the time_window parameter

The problem

Travel time and accessibility estimates require a departure time, and they can differ significantly across departure times because public transport service levels vary across the day (Stepniak et al. 2019). Even leaving at 10:00am instead of 10:04am can change results considerably, depending on when vehicles arrive and how well transfers are coordinated. This relates to the modifiable temporal unit problem (MTUP) (Pereira 2019; Levinson and et al. 2020).

The uncertainty is greater when GTFS feeds have a frequencies.txt table, because exact vehicle departure times are unknown (Conway et al. 2018; Stewart and Byrd 2022).

The solution

A common strategy is to compute estimates for multiple departure times over a time window and take the average or median. Repeating the routing for each departure is slow, though.

In r5r, functions such as travel_time_matrix() and accessibility() have a time_window parameter that does this in a single call. This vignette shows how to use it and interpret the results.

3.1 Build routable transport network with build_network()

We use the São Paulo (Brazil) sample data included in r5r.

# increase Java memory
options(java.parameters = "-Xmx2G")

# load libraries
library(r5r)
library(sf)
library(data.table)
library(ggplot2)
library(dplyr)

# build a routable transport network with r5r
data_path <- system.file("extdata/spo", package = "r5r")
r5r_network <- build_network(data_path)

# routing inputs
mode <- c('walk', 'transit')
max_walk_time <- 30 # minutes
max_trip_duration <- 90 # minutes

# load origin/destination points
points <- fread(file.path(data_path, "spo_hexgrid.csv"))

# departure datetime
departure_datetime = as.POSIXct("13-05-2019 14:00:00", 
                                format = "%d-%m-%Y %H:%M:%S")

3.2 Accessibility with time_window.

Number of schools reachable from each location within 45 minutes (decay_function = "step", cutoffs = 45), for departures between 2pm and 3pm (time_window = 60):

# estimate accessibility
acc <- r5r::accessibility(
  r5r_network,   
  origins = points,
  destinations = points, 
  opportunities_colnames = 'schools',
  mode = mode,
  max_walk_time = max_walk_time,
  decay_function = "step",
  cutoffs = 45,
  departure_datetime = departure_datetime,
  progress = FALSE,
  time_window = 60,
  percentiles = c(10, 20, 50, 70, 80)
  )

head(acc, n = 10)

The output is in long format, one row per origin and percentile, so the first 5 rows refer to the same origin. The 10th percentile counts the schools reachable in at least 10% of departures, the 50th those reachable in at least half of them; so accessibility never increases as the percentile rises. An accessibility of 0 means no school is reachable within 45 minutes.

The plot shows, for each origin (sorted by median), the range of accessibility between the 10th and 80th percentiles, with the median as a dot:

# summarize
df <- acc[, .(min_acc = min(accessibility),
              median = accessibility[which(percentile == 50)],
              max_acc = max(accessibility)), by = id]

# plot
ggplot(data=df) +
  geom_linerange(color='gray', alpha=.5, aes(x = reorder(id, median) , 
                      y=median, ymin=min_acc, ymax=max_acc)) +
  geom_point(color='#0570b0', size=.5, aes(x = reorder(id, median), y=median)) +
  labs(y='N. of schools accessible\nby public transport', x='Origins sorted by accessibility',
       title="Accessibility uncertainty between 2pm and 3pm",
       subtitle = 'Upper limit 10% and lower limit 80% of the times') +
  theme_classic() +
  theme(axis.text.x=element_blank(),
        axis.ticks.x=element_blank())

3.3 Travel time matrix with time_window.

All-to-all travel times for departures between 2pm and 3pm:

# estimate travel time matrix
ttm <- travel_time_matrix(
  r5r_network,   
  origins = points,
  destinations = points,    
  mode = mode,
  max_walk_time = max_walk_time,
  max_trip_duration = max_trip_duration,
  departure_datetime = departure_datetime,
  progress = TRUE,
  time_window = 60,
  percentiles = c(10, 20, 50, 70, 80)
  )

head(ttm, n = 10)

Each travel_time_pXX column gives the travel time within which XX% of the trips departing between 2pm and 3pm are completed: travel_time_p10 for the fastest 10%, travel_time_p50 the median, and so on. An NA means fewer than XX% of the trips arrive within max_trip_duration (90 minutes). A wider time_window can include departures with worse service, so it can produce more NAs in the higher percentiles.

3.4 Expanded travel time matrix with time_window.

With time_window, expanded_travel_time_matrix() returns the fastest route departing at each minute of the window, instead of percentiles. It can be very memory intensive for large data sets and time windows.

ettm <- r5r::expanded_travel_time_matrix(
  r5r_network,
  origins = points[1:30,],
  destinations = points[31:61,],    
  mode = mode,
  max_walk_time = max_walk_time,
  max_trip_duration = max_trip_duration,
  departure_datetime = departure_datetime,
  progress = FALSE,
  time_window = 20
  )

head(ettm, n = 10)

3.5 Detailed itineraries with time_window.

detailed_itineraries() returns itineraries rather than travel time or accessibility percentiles. With time_window, it returns the fastest itinerary: the shortest travel time measured from its own departure, so it may depart and arrive later than others (use time_window = 1 for the earliest arrival). With shortest_path = FALSE, it also returns sub-optimal alternatives.

With the default shortest_path = TRUE and no fare_structure, it routes one departure at each minute of time_window, as travel_time_matrix() does with schedule-based GTFS; ties between equally fast itineraries go to the earliest departure.

With shortest_path = FALSE or a fare_structure, it uses the McRaptor algorithm with one draw per minute (see Section 2): consecutive departures are 30 to 90 seconds apart, so a 10-minute time_window simulates about 10 departures. Each departure is routed separately, and with the default suboptimal_minutes = 0 only the itineraries arriving earliest are kept for each departure, even if a slower one has fewer transfers.

obs. detailed_itineraries() cannot route public transport trips on frequency-based GTFS feeds; use gtfstools::frequencies_to_stop_times() to create a suitable feed.

Cleaning up after usage

Stop the network and run Java’s garbage collector to free the memory it used:

r5r::stop_r5(r5r_network)
rJava::.jgc(R.gc = TRUE)

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