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 event are going to be used. These locations are within this area https://www.openstreetmap.org#map=15/-34.5847/-58.3970

• 266939565 Mercato Centrale

• 2531656518 Stazione di Santa Maria Novella

• 5020458299 Palazzo dei Congressi

• 6483155124 Hotel Albani

• 1798374718 Cattedrale di Santa Maria del Fiore

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 (266939565, 2531656518, 5020458299, 6483155124, 1798374718)
ORDER BY osm_id;

   osm_id   |  id   
------------+-------
  266939565 |   956
 1798374718 |  6354
 2531656518 |  7039
 5020458299 | 11186
 6483155124 | 21407
(5 rows)

• 266939565 Mercato Centrale (956)

• 2531656518 Stazione di Santa Maria Novella (7039)

• 5020458299 Palazzo dei Congressi (11186)

• 6483155124 Hotel Albani (21407)

• 1798374718 Cattedrale di Santa Maria del Fiore (6354)

The corresponding id are shown in the following image, and a sample route from “Palazzo dei Congressi” to “Cattedrale di Santa Maria del Fiore”.

2.1.1. Exercise 1: Single pedestrian routing

Problem:

• Walking from “Mercato Centrale” to the “Palazzo dei Congressi”.

Solution:

• The pedestrian wants to go from vertex 956 to vertex 11186 (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
    ',
 956,
 11186,
    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 “Mercato Centrale” and “Stazione di Santa Maria Novella” to the “Palazzo dei Congressi”.

Solution:

• The pedestrians are departing at vertices 956 and 7039 (line 9).

• All pedestrians want to go to vertex 11186 (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[956,7039],
11186,
directed := false);

Exercise: 2 (Chapter: Pedestrian)

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

Problem:

• Walking from the “Palazzo dei Congressi” to the “Mercato Centrale” and “Stazione di Santa Maria Novella” (in seconds).

Solution:

• All pedestrians are departing from vertex 11186 (line 9).

• Pedestrians want to go to locations 956 and 7039 (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
    ',
11186,
ARRAY[956,7039],
directed := false);

Exercise: 3 (Chapter: Pedestrian)

2.1.4. Exercise 4: Many Pedestrians going to different destinations

Problem:

• Walking from Mercato Centrale and Stazione di Santa Maria Novella to the “Hotel Albani” and “Cattedrale di Santa Maria del Fiore” (in minutes).

Solution:

• The pedestrians depart from 956 and 7039 (line 9).

• The pedestrians want to go to destinations 21407 and 6354 (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[956, 7039],
ARRAY[21407, 6354],
directed := false);

Exercise: 4 (Chapter: Pedestrian)

Note

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

• Going to vertex 21407:

  • from 956 takes 8.84.. minutes (seq = 35)

  • from 7039 takes 5.84.. minutes (seq = 74)

• Going to vertex 6354:

  • from 956 takes 7.44.. minutes (seq = 7)

  • from 7039 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 “Hotel Albani” or “Cattedrale di Santa Maria del Fiore” (get only the cost in minutes).

Solution:

• The pedestrians depart from 956 and 7039 (line 10).

• The pedestrians want to go to destinations 21407 and 6354 (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[956, 7039],
ARRAY[21407, 6354],
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 “Hotel Albani” or “Cattedrale di Santa Maria del Fiore” (summarize cost in minutes).

Solution:

• The pedestrians depart from 956 and 7039 (line 10).

• The pedestrians want to go to destinations 21407 and 6354 (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[956, 7039],
    ARRAY[21407, 6354],
    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 “Stazione di Santa Maria Novella” than from the “Mercato Centrale”.