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Road networks

Data

The source of geospatial data on road networks is OpenStreetMap (OSM) (© OpenStreetMap contributors), downloadable via OSMnx.

N-Min-CT contains the OSMnx-fetched road networks for walking, cycling and driving as of June 15, 2025.

Altering the networks

The OSM-based road network can be altered by adding or removing road segments.

Adding the segments

- consists of four steps:

  1. activate the Add segment button
  2. initiate drawing by clicking twice on the left mouse button
  3. add one or more breakpoints with a single click of the left mouse button
  4. finalize the drawing by clicking twice on the left mouse button

Travel Radius within Time (TRT) is then recomputed, with the added segment, and shown on the map.

For the new segment to have any effect on TRT, it must have at least one spatial intersection with the existing road net network, i.e. isolated segments are not accounted for.

Adding new road segments involves several geospatial manipulations, understanding which is the key to correctly interpreting the results obtained. The figure below illustrates these manipulations as four essential steps.

addsegments

In the first quadrant, there are three lines drawn by the user which are meant to represent a new connected road network. To connect these distinct segments, additional two network nodes (a.k.a. vertices) are put (by the software) at their intersections, the originally three segments are hence split into seven (second quadrant). Through the next steps, the software integrates this new network into the existing one. The third quadrant illustrates how the new road network (solid lines) is further split by adding nodes at its intersection with the existing network (dashed lines). Finally, the reverse operation, where the segments of the existing network (dashed lines) are split by the new network (solid lines) is carried out in the fourth quadrant.

The result is a road network where the lines drawn by the user are first connected between themselves and then to the existing (OSM) network at every intersection. This implies commuter's freedom to move across all the segments involved at their intersection points. Such freedom, however, is sometimes not desirable, e.g. when the new segment is meant to represent a tunnel or a bridge. To achieve that, one could remove all the crossing segments of an existing network except those representing the entrance/exit to/from the tunnel/bridge.

Deleting the segments

- is done as follows:

  1. activate the Del segment button
  2. hover over the road segment intended for deletion until highlighted
  3. click on the segment

TRT is then recomputed, without the selected segment, and shown on the map.

Deleting the existing road segments can represent many actions, e.g. introducing the physical barriers on the road, closing it for certain vehicle types, or actually removing it... As far as the TRT is concerned, it only means that the segment is no longer participating in the assessment of the shortest paths.

Networks for public transport and TRT assessment with mixed travel modes are to be added to N-Min-CT in the future.

Assessing TRT

In N-Min-CT, Travel Radius within Time (TRT) is solved by taking a set of inputs and using a sequence of steps discussed below.

Inputs

  1. Road network for a certain commuting mode, either walk, cycle or drive
  2. Travel origin's geospatial coordinates, given as Origin: λ=longitude, φ=latitude
  3. Maximum travel time N (minutes)
  4. User-requested modifications of the original road network, i.e. road segments to delete/add or none

Algorithm

  1. Find the nearest (by haversine distance) network node to the selected origin. This nearest node becomes a new origin
  2. From the new origin, find the shortest (by combined length of road segments) paths to all other network nodes. This is known as a Single-Source Shortest Path (SSSP) problem

  3. Estimate the time needed to reach all other network nodes from the origin through the shortest path. Commuting speed is assumed constant and takes the following values, depending on the transportation mode:

    • walking: 4.2 km/h
    • cycling: 10 km/h
    • driving: 40 km/h

    No other factors that may affect the commuter's speed are considered here. For more accurate TRT assessment, future development of N-Min-CT will account for some of such factors, e.g. elevation profile, seasonal differences, characteristics of a commuter etc.

  4. Filter out the network nodes not achievable within the time limit

  5. Build a concave hull around the achievable network nodes