Calculates the average or median number of opportunities that can be reached considering multiple maximum travel cost thresholds within a given travel cost interval specified by the user. The time interval cumulative accessibility measures was originally proposed by Tomasiello et al. (2023) .

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

  interval_increment = 1,
  summary_function = stats::median,
  group_by = character(0),
  active = 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 string. The name of the column in travel_matrix with the travel cost between origins and destinations.


A numeric vector of length 2. Indicates the start and end points of the interval of travel cost thresholds to be used. The first entry must be lower than the second.


A numeric. How many travel cost units separate the cutoffs used to calculate the accessibility estimates which will be used to calculate the summary estimate within the specified interval. Should be thought as the resolution of the distribution of travel costs within the interval. Defaults to 1.


A function. This function is used to summarize a distribution of accessibility estimates within a travel cost interval as a single value. Can be any function that takes an arbitrary number of numeric values as as input and returns a single number as output. Defaults to stats::median().


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


Tomasiello DB, Herszenhut D, Oliveira JLA, Braga CKV, Pereira RHM (2023). “A Time Interval Metric for Cumulative Opportunity Accessibility.” Applied Geography, 157, 103007. ISSN 0143-6228, doi:10.1016/j.apgeog.2023.103007 .

See also

Other cumulative access: cumulative_cutoff()


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"))

df <- cumulative_interval(
  travel_matrix = travel_matrix,
  land_use_data = land_use_data,
  interval = c(20, 30),
  opportunity = "schools",
  travel_cost = "travel_time"
#>                 id schools
#>             <char>   <int>
#> 1: 89a88cdb57bffff       0
#> 2: 89a88cdb597ffff      14
#> 3: 89a88cdb5b3ffff      17
#> 4: 89a88cdb5cfffff       4
#> 5: 89a88cd909bffff       6
#> 6: 89a88cd90b7ffff      12

df <- cumulative_interval(
  travel_matrix = travel_matrix,
  land_use_data = land_use_data,
  interval = c(40, 80),
  opportunity = "jobs",
  travel_cost = "travel_time"
#>                 id   jobs
#>             <char>  <int>
#> 1: 89a88cdb57bffff 435782
#> 2: 89a88cdb597ffff 409191
#> 3: 89a88cdb5b3ffff 423974
#> 4: 89a88cdb5cfffff 460740
#> 5: 89a88cd909bffff 437645
#> 6: 89a88cd90b7ffff 449585