Using the time_window parameter

The problem

To calculate the travel time from A to B, or to calculate the accessibility level at a given location, one has to select a departure time. However, travel time and accessibility estimates can differ significantly at different departure times because of how public transport service levels vary across the day (Stepniak et al. 2019). Even a small difference, say leaving at 10:00am or 10:04am might importantly change travel time and accessibility estimates depending on when a person departs relative to when a public transport vehicle arrives, and how well transfers are coordinated given a service timetable. This is a very common issue related to the modifiable temporal unit problem (MTUP) (Pereira 2019; Levinson and et al. 2020).

This problem gets even more complicated when public transport GTFS feeds have a frequencies.txt table. In these cases, we cannot know the exact departure time of vehicles, what creates greater uncertainty for our travel time and accessibility estimates (Conway, Byrd, and van Eggermond 2018; Stewart and Byrd 2022).

The solution

A common strategy to overcome this problem is to calculate travel times and accessibilities at multiple departure times sampled over a time window, and then take the average or median value. Now you may ask, but how many departure times should I use? You might also be thinking that doing multiple repeated routing analysis can be cumbersome and take a lot of time. Right?

Here is where r5r comes in. Both the travel_time_matrix()and accessibility() functions have a parameter called time_window. When this parameter is set, R⁵ will automatically compute multiple travel times / accessibility estimates considering multiple departures per minute within the time_window selected by the user.

This vignette shows a reproducible example to explain how one can use the time_window and interpret the results.

3.1 Build routable transport network with setup_r5()

First, let’s build the network and create the routing inputs. In this example we’ll be using the a sample data set for the city of São Paulo (Brazil) 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_core <- setup_r5(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")

ps. Please keep in mind that the Monte Carlo draws in time_window only affects the results when the GTFS feeds contain a frequencies.txt table.

3.2 Accessibility with time_window.

In this example we calculate the number of schools accessible from each location within a 60-minute time window departing between 2pm and 3pm. In this example we’ll be using a cumulative accessibility metric decay_function = "step" with a max time threshold of 45 minutes cutoffs = 45.

# estimate accessibility
acc <- r5r::accessibility(r5r_core = r5r_core,   
                          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)

This output is in long format, so the first 5 rows show the result for the same origin. In this case, we see that in only 10% of the trips departing from that origin between 2pm and 3pm a person would be able to access up to 111 schools. Meanwhile, 50% of the times she would only access 79 schools. By contrast, the accessibility from the other origin shown in the output above is 0, meaning there are no schools accessible from that location given the max travel time of 45 minutes.

We can use a plot like the one below to visualize this uncertainty in how accessibility levels might vary between 2pm and 3pm depending on the departure time within that 60-minute time window.

# 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.

Now let’s calculate all-to-all travel time estimates within a 60-minute time window departing between 2pm and 3pm and see how the output looks like.

# estimate travel time matrix
ttm <- travel_time_matrix(r5r_core = r5r_core,   
                          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)

Now let’s look at the 2nd row of the output above. This output tell us that only 10% of the trips between 2pm and 3pm for that origin-destination pair took 39 minutes or less. Meanwhile, 50% of those trips took up tp 45 minutes and 80% of them were 48-minute long or shorter.

The last row in the result above has a few NAs. This tell us that at least 50% of all simulated trips between 2pm and 3pm for that origin-destination pair could not be completed because they took longer than the max_trip_duration we have set (90 minutes).

3.4 Expanded travel time matrix with time_window.

Finally, we can also use the time_window in the expanded_travel_time_matrix() function. In this case, though, when the user sets a time_window value, the expanded_travel_time_matrix() will return the fastest route alternative departing each minute within the specified time window. Please note this function can be very memory intensive for large data sets and time windows.

ettm <- r5r::expanded_travel_time_matrix(r5r_core = r5r_core,   
                                    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.

In the detailed_itineraries() function, the number of Monte Carlo draws per minute is hardcoded to 1. This means that the function simulates only one departure per minute within the time_window. So if you set a time_window of 10 minutes, it would simulate 10 departures, one in each minute. This is largely because the time_window behaves slightly differently here.

See, functions like travel_time_matrix() or accessibility(), for example, return estimates of travel times or accessibility. In these cases, when we use the time_window parameter, these functions output selected percentiles of those values generated based on the distribution of all estimates that result from the multiple trip simulations.

The detailed_itineraries(), on the other hand, does not return travel times or accessibility estimates. It returns alternatives of trip journeys. In this case, when we use the time_window parameter, the function will return the optimal trip itinerary found within the time window. It can also return the optimal route along with multiple sub-optimal journey alternatives found within the time window if the the user sets shortest_path = FALSE.

obs. Mind you that detailed_itineraries() cannot be computed for public transport trips if the the network uses a frequencies-based GTFS feed. In these cases, we suggest using gtfstools::frequencies_to_stop_times() to create a suitable feed.

Cleaning up after usage

r5r objects are still allocated to any amount of memory previously set after they are done with their calculations. In order to remove an existing r5r object and reallocate the memory it had been using, we use the stop_r5 function followed by a call to Java’s garbage collector, as follows:

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

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