Calculates the number of opportunities accessible under a given specified travel cost cutoff.

This function is generic over any kind of numeric travel cost, such as distance, time and money.

  group_by = character(0),
  active = TRUE,
  fill_missing_ids = TRUE



A data frame. The travel matrix describing the costs (i.e. travel time, distance, monetary cost, etc.) between the origins and destinations in the study area. Must contain the columns from_id, to_id and any others specified in travel_cost.


A data frame. The distribution of opportunities within the study area cells. Must contain the columns id and any others specified in opportunity.


A string. The name of the column in land_use_data with the number of opportunities/resources/services to be considered when calculating accessibility levels.


A character vector. The name of the columns in travel_matrix with the travel costs between origins and destinations to be considered in the calculation.


Either a numeric vector or a list of numeric vectors, one for each cost specified in travel_cost. The travel cost cutoffs to consider when calculating accessibility levels. If a list, the function finds every single possible cutoff combination and use them to calculate accessibility (e.g. if one specifies that travel time cutoffs should be 30 and 60 minutes and that monetary cost cutoffs should be 5 and 10 dollars, the output includes accessibility estimates limited at 30 min & 5 dollars, 30 min & 10 dollars, 60 min & 5 dollars and 60 min & 10 dollars). In these cases, cost constraints are considered simultaneously - i.e. only trips that take 30 minutes or less AND 5 dollars or less to be completed, for example, are included in the accessibility output. The cutoff parameter is not included in the final output if the input includes only a single cutoff for a single travel cost.


A character vector. When not character(0) (the default), indicates the travel_matrix columns that should be used to group the accessibility estimates by. For example, if travel_matrix includes a departure time column, that specifies the departure time of each entry in the data frame, passing "departure_time" to this parameter results in accessibility estimates grouped by origin and by departure time.


A logical. Whether to calculate active accessibility (the of opportunities that can be reached from a given origin, the default) or passive accessibility (by how many people each destination can be reached).


A logical. Calculating cumulative accessibility may result in missing ids if the they cannot reach any of the destinations within the specified travel cost cutoff. For example, using a travel time cutoff of 20 minutes, when estimating the accessibility of origin A that can only reach destinations with more than 40 minutes results in id A not being included in the output. When TRUE (the default), the function identifies which origins would be left out and fills their respective accessibility values with 0, which incurs in a performance penalty.


A data frame containing the accessibility estimates for each origin/destination (depending if active is TRUE or FALSE) in the travel matrix.

See also

Other cumulative access: cumulative_interval()


data_dir <- system.file("extdata", package = "accessibility")
travel_matrix <- readRDS(file.path(data_dir, "travel_matrix.rds"))
land_use_data <- readRDS(file.path(data_dir, "land_use_data.rds"))

# active accessibility: number of schools accessible from each origin
df <- cumulative_cutoff(
  travel_matrix = travel_matrix,
  land_use_data = land_use_data,
  cutoff = 30,
  opportunity = "schools",
  travel_cost = "travel_time"
#>                 id schools
#> 1: 89a881a5a2bffff       1
#> 2: 89a881a5a2fffff      10
#> 3: 89a881a5a67ffff       1
#> 4: 89a881a5a6bffff       0
#> 5: 89a881a5a6fffff       0
#> 6: 89a881a5b03ffff      14

df <- cumulative_cutoff(
  travel_matrix = travel_matrix,
  land_use_data = land_use_data,
  cutoff = c(30, 60),
  opportunity = "schools",
  travel_cost = "travel_time"
#>                 id travel_time schools
#> 1: 89a881a5a2bffff          30       1
#> 2: 89a881a5a2bffff          60      76
#> 3: 89a881a5a2fffff          30      10
#> 4: 89a881a5a2fffff          60      91
#> 5: 89a881a5a67ffff          30       1
#> 6: 89a881a5a67ffff          60      82

# passive accessibility: number of people that can reach each destination
df <- cumulative_cutoff(
  travel_matrix = travel_matrix,
  land_use_data = land_use_data,
  cutoff = 30,
  opportunity = "population",
  travel_cost = "travel_time",
  active = FALSE
#>                 id population
#> 1: 89a881a5a2bffff      11053
#> 2: 89a881a5a2fffff      31903
#> 3: 89a881a5a67ffff      12488
#> 4: 89a881a5a6bffff      14474
#> 5: 89a881a5a6fffff      15053
#> 6: 89a881a5b03ffff      69582

# using multiple travel costs
pareto_frontier <- readRDS(file.path(data_dir, "pareto_frontier.rds"))

df <- cumulative_cutoff(
  land_use_data = land_use_data,
  opportunity = "jobs",
  travel_cost = c("travel_time", "monetary_cost"),
  cutoff = list(c(20, 30), c(0, 5, 10))