Trade-offs between travel time and monetary cost

1. Introduction

Routing models usually find either the fastest or the cheapest route. Accounting for both time and monetary cost at once is hard, because minimizing trip duration and minimizing cost are competing objectives (Conway and Stewart 2019). To address this problem, r5r’s pareto_frontier() returns the most efficient combinations of travel time and monetary cost between origin/destination pairs. This vignette shows, with a reproducible example, how to use it and interpret its results.

2. What the pareto_frontier means.

Imagine a trip from A to B with several route alternatives (figure below):

  • Walking is the cheapest option but takes 50 minutes.
  • Bus + subway is the fastest: 15 minutes for R$ 8.
  • In between:
    • a single bus: R$ 3, 35 min;
    • two buses with one transfer: R$ 5, 29 min;
    • walking to the subway: R$ 6, 20 min.

These options form the Pareto frontier of routes from A to B: no route is both faster and cheaper than any route on the frontier. On the frontier, a trip cannot be made faster without costing more, nor cheaper without taking longer.


The frontier shows the time-cost trade-offs that public transport passengers face. It also supports cumulative-opportunity accessibility metrics with both time and cost cutoffs (e.g. the number of jobs reachable within 40 minutes and R$ 5) (Conway and Stewart 2019). Let’s see a couple concrete examples showing how r5r can calculate the Pareto frontier for multiple origins.

3. Demonstration of pareto_frontier().

3.1 Build routable transport network with build_network()

We use the Porto Alegre (Brazil) sample data included in r5r.

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

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

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

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

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

3.2 Set up the fare structure

R5 computes the monetary cost of each route from the fare rules of the public transport system. In Porto Alegre:

  • A bus ticket costs R$ 4.80.
  • A second bus ride adds R$ 2.40; subsequent bus rides cost the full R$ 4.80.
  • A train ticket costs R$ 4.50, with unlimited train rides as long as the passenger does not leave the stations.
  • The integrated bus + train fare has a 10% discount, totalling R$ 8.37.

A fare structure with these rules ships with r5r, so we simply read it. The fare structure vignette shows how to build one step by step.

fare_structure <- r5r::read_fare_structure(file.path(data_path, "fares/fares_poa.zip"))

3.3 Calculating a pareto_frontier().

We compute the Pareto frontier from all origins to all destinations with these monetary cost cutoffs:

  • R$ 1.00: walking only
  • R$ 4.50: a train trip
  • R$ 4.80: a single bus trip
  • R$ 7.20: bus + bus
  • R$ 8.37: bus + train
departure_datetime <- as.POSIXct("13-05-2019 14:00:00",
                                 format = "%d-%m-%Y %H:%M:%S")

prtf <- pareto_frontier(
  r5r_network,
  origins = points,
  destinations = points,
  mode = c("WALK", "TRANSIT"),
  departure_datetime = departure_datetime,
  fare_structure = fare_structure,
  fare_cutoffs = c(1, 4.5, 4.8, 7.20, 8.37),
  progress = TRUE
  )

head(prtf)

For illustration, the Pareto frontiers between the Farrapos train station and (a) the Praia de Belas shopping mall and (b) the Moinhos hospital:

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.

References

Conway, Matthew Wigginton, and Anson F. Stewart. 2019. “Getting Charlie Off the MTA: A Multiobjective Optimization Method to Account for Cost Constraints in Public Transit Accessibility Metrics.” International Journal of Geographical Information Science 33 (9): 1759–87. https://doi.org/10.1080/13658816.2019.1605075.