Using the time_window parameter

In r5r: Rapid Realistic Routing with 'R5'

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  eval = identical(tolower(Sys.getenv("NOT_CRAN")), "true"),
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1. Introduction

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 [@stepniak2019impact]. 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) [@pereiramtup2019; @levinson2020manual].

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 [@conway2018accounting; @stewart2022half].

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.

2. How the time_window works and how to interpret the results.

As mentioned above, when time_window is set, R⁵ computes multiple travel times / accessibility estimates starting at the specified departure_datetime and within the time_window selected by the user. By default, r5r will generate one estimate per minute. Nonetheless, users can set a number to the draws_per_minute parameter that will change the number of Monte Carlo draws to perform per time window minute. The default value of draws_per_minute is 5, which mean 300 draws in a 60 minutes time window, for example. For a detailed discussion on the effect of number of draws on result stability, see Stewart et al [-@stewart2022half].

In this case, there isn't a single estimate of travel time / accessibility, but a distribution of several estimates that reflect the travel time / accessibility uncertainties in the specified time window. To get our heads around so many estimates, we can use the percentiles parameter to specify the percentiles of the distribution we are interested in. For example, if we select the 25th travel time percentile and the results show that the travel time estimate between A and B is 15 minutes, this means that 25% of all trips taken between these points within the specified time window are shorter than 15 minutes.

Let's see a couple concrete examples now.

3. Demonstration of time_window.

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 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 = 30,
                          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 = 20,
                          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)

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.

References

r5r documentation built on Aug. 8, 2023, 9:07 a.m.