2. Pedestrian Routing

pgRouting was first called pgDijkstra, because it implemented only shortest path search with Dijkstra algorithm. Later other functions were added and the library was renamed to pgRouting.

2.1. pgr_dijkstra

Dijkstra algorithm was the first algorithm implemented in pgRouting. It doesn’t require other attributes than id, source and target ID and cost and reverse_cost.

You can specify when to consider the graph as directed or undirected.

Signature Summary

pgr_dijkstra(Edges SQL, start_vid,  end_vid  [, directed])
pgr_dijkstra(Edges SQL, start_vid,  end_vids [, directed])
pgr_dijkstra(Edges SQL, start_vids, end_vid  [, directed])
pgr_dijkstra(Edges SQL, start_vids, end_vids [, directed])
pgr_dijkstra(Edges SQL, Combinations SQL [, directed])

RETURNS SET OF (seq, path_seq [, start_vid] [, end_vid], node, edge, cost, agg_cost)
    OR EMPTY SET

Description of the parameters can be found in pgr_dijkstra.

Note

• Many pgRouting functions have sql::text as one of their arguments. While this may look confusing at first, it makes the functions very flexible as the user can pass a SELECT statement as function argument as long as the returned result contains the required number of attributes and the correct attribute names.

• Most of pgRouting implemented algorithms do not require the geometry.

• The pgRouting functions do not return a geometry, but only an ordered list of nodes or edges.

Identifiers for the Queries

The assignment of the vertices identifiers on the source and target columns may be different, the following exercises will use the results of this query. For the workshop, some locations near of the FOSS4G Argentina event are going to be used. These locations are within this area https://www.openstreetmap.org#map=15/-34.5847/-58.3970

• 192903446 Plaza Intendente Alvear

• 4289340366 Hard Rock Café

• 2153015792 Facultad de Derecho

• 6357258588 Centro de Convenciones Buenos Aires

• 196017392 Palacio Duhau-Park Hyatt Buenos Aires

Connect to the database, if not connected:

psql city_routing

Get the vertex identifiers

SELECT osm_id, id FROM ways_vertices_pgr
WHERE osm_id IN (192903446, 4289340366, 2153015792, 6357258588, 196017392)
ORDER BY osm_id;

   osm_id   |  id   
------------+-------
  192903446 |  1993
  196017392 |  2197
 2153015792 |  6646
 4289340366 |  9129
 6357258588 | 15011
(5 rows)

• 192903446 Plaza Intendente Alvear (1993)

• 4289340366 Hard Rock Café (9129)

• 2153015792 Facultad de Derecho (6646)

• 6357258588 Centro de Convenciones Buenos Aires (15011)

• 196017392 Palacio Duhau-Park Hyatt Buenos Aires (2197)

The corresponding id are shown in the following image, and a sample route from “Facultad de Derecho” to “Palacio Duhau-Park Hyatt Buenos Aires”.

2.1.1. Exercise 1: Single pedestrian routing

Problem:

• Walking from “Plaza Intendente Alvear” to the “Facultad de Derecho”.

Solution:

• The pedestrian wants to go from vertex 1993 to vertex 6646 (lines 9 and 10).

• The pedestrian’s cost is in terms of length. In this case length (line 6), which was calculated by osm2pgrouting, is in unit degrees.

• From a pedestrian perspective the graph is undirected (line 11), that is, the pedestrian can move in both directions on all segments.

SELECT * FROM pgr_dijkstra(
    '
      SELECT gid AS id,
        source,
        target,
        length AS cost
      FROM ways
    ',
 1993,
 6646,
    directed := false);

Exercise: 1 (Chapter: Pedestrian)

Note

• The returned cost attribute represents the cost specified in the inner SQL query (edges_sql::text argument). In this example cost is length in unit “degrees”. Cost may be time, distance or any combination of both or any other attributes or a custom formula.

• node and edge results may vary depending on the assignment of the identifiers to the vertices given by osm2pgrouting.

2.1.2. Exercise 2: Many Pedestrians going to the same destination

Problem:

• Walking from the “Plaza Intendente Alvear” and “Hard Rock Café” to the “Facultad de Derecho”.

Solution:

• The pedestrians are departing at vertices 1993 and 9129 (line 9).

• All pedestrians want to go to vertex 6646 (line 10).

• The cost to be in meters using attribute length_m (line 6).

SELECT * FROM pgr_dijkstra(
    '
      SELECT gid AS id,
        source,
        target,
        length_m AS cost
      FROM ways
    ',
ARRAY[1993,9129],
6646,
directed := false);

Exercise: 2 (Chapter: Pedestrian)

2.1.3. Exercise 3: Many Pedestrians departing from the same location

Problem:

• Walking from the “Facultad de Derecho” to the “Plaza Intendente Alvear” and “Hard Rock Café” (in seconds).

Solution:

• All pedestrians are departing from vertex 6646 (line 9).

• Pedestrians want to go to locations 1993 and 9129 (line 10).

• The cost to be in seconds, with a walking speed s = 1.3 m/s and t = d/s (line 6).

SELECT * FROM pgr_dijkstra(
    '
      SELECT gid AS id,
        source,
        target,
        length_m / 1.3 AS cost
      FROM ways
    ',
6646,
ARRAY[1993,9129],
directed := false);

Exercise: 3 (Chapter: Pedestrian)

2.1.4. Exercise 4: Many Pedestrians going to different destinations

Problem:

• Walking from the hotels to the “Centro de Convenciones Buenos Aires” and “Palacio Duhau-Park Hyatt Buenos Aires” (in minutes).

Solution:

• The pedestrians depart from 1993 and 9129 (line 9).

• The pedestrians want to go to destinations 15011 and 2197 (line 10).

• The cost to be in minutes, with a walking speed s = 1.3 m/s and t = d/s (line 6).

• Result adds the costs per destination.

SELECT * FROM pgr_dijkstra(
    '
      SELECT gid AS id,
       source,
       target,
       length_m / 1.3 / 60 AS cost
      FROM ways
    ',
ARRAY[1993, 9129],
ARRAY[15011, 2197],
directed := false);

Exercise: 4 (Chapter: Pedestrian)

Note

Inspecting the results, looking for totals (edge = -1):

• Going to vertex 15011:

  • from 1993 takes 8.84.. minutes (seq = 35)

  • from 9129 takes 5.84.. minutes (seq = 74)

• Going to vertex 2197:

  • from 1993 takes 7.44.. minutes (seq = 7)

  • from 9129 takes 12.06.. minutes (seq = 55)

2.2. pgr_dijkstraCost

When the main goal is to calculate the total cost, without “inspecting” the pgr_dijkstra results, using pgr_dijkstraCost returns a more compact result.

Signature Summary

pgr_dijkstraCost(edges_sql, start_vid,  end_vid  [, directed])
pgr_dijkstraCost(edges_sql, start_vid,  end_vids [, directed])
pgr_dijkstraCost(edges_sql, start_vids, end_vid  [, directed])
pgr_dijkstraCost(edges_sql, start_vids, end_vids [, directed])
pgr_dijkstraCost(edges_sql, combinations_sql   [, directed])

RETURNS SET OF (start_vid, end_vid, agg_cost)
    OR EMPTY SET

Description of the parameters can be found in pgr_dijkstraCost

2.2.1. Exercise 5: Many Pedestrians going to different destinations returning aggregate costs

Problem:

• Walking from the hotels to the “Centro de Convenciones Buenos Aires” or “Palacio Duhau-Park Hyatt Buenos Aires” (get only the cost in minutes).

Solution:

• The pedestrians depart from 1993 and 9129 (line 10).

• The pedestrians want to go to destinations 15011 and 2197 (line 11).

• The cost to be in minutes, with a walking speed s = 1.3 m/s and t = d/s (line 7).

• Result as aggregated costs.

SELECT *
FROM pgr_dijkstraCost(
    '
      SELECT gid AS id,
       source,
       target,
       length_m  / 1.3 / 60 AS cost
      FROM ways
    ',
ARRAY[1993, 9129],
ARRAY[15011, 2197],
directed := false);

Exercise: 5 (Chapter: Pedestrian)

Compare with Exercise 4: Many Pedestrians going to different destinations ‘s note.

2.2.2. Exercise 6: Many Pedestrians going to different destinations summarizing the total costs per departure

Problem:

• Walking from the hotels to the “Centro de Convenciones Buenos Aires” or “Palacio Duhau-Park Hyatt Buenos Aires” (summarize cost in minutes).

Solution:

• The pedestrians depart from 1993 and 9129 (line 10).

• The pedestrians want to go to destinations 15011 and 2197 (line 11).

• The cost to be in minutes, with a walking speed s = 1.3 m/s and t = d/s (line 7).

• Result adds the costs per destination.

SELECT start_vid, sum(agg_cost)
FROM pgr_dijkstraCost(
    '
      SELECT gid AS id,
        source,
        target,
        length_m  / 1.3 / 60 AS cost
      FROM ways
    ',
    ARRAY[1993, 9129],
    ARRAY[15011, 2197],
    directed := false)
GROUP BY start_vid
ORDER BY start_vid;

Exercise: 6 (Chapter: Pedestrian)

Note

An interpretation of the result can be: In general, it is faster to depart from the “Hard Rock Café” than from the “Plaza Intendente Alvear”.