Nima and Ben will share some of the experiences of modelling Manchester’s Metrolink network while building a real-life application – Tramchester.

1. Ben Earlam
[@BenEarlam]
Nima Montazeri
[@Nimamon]
[Presented By]
Route Finding in Time Dependent Graphs
[Located]

2. What are we going to cover?
Introduction
Why Graph?
About The
Data
Time Independent Model
Time-dependent Model
Demo
Q&A

3. How it all started?
Experiment
& Learn
Real world
problem
5 Week tech lab
Produce working
software
Small team

4. Manchester

5. The Focus…
Travel & Transport (Manchester)
Open Data
Open Source
Metrolink System (25 Million Journeys p/a)
Tech: Not Only SQL
• Neo4J
Experiment with Graph database as way of
modeling a travel network
Everything in the Cloud (AWS)

6. Tram Network

7. Why Graph database?
5
2
3
2
5
3
2
2
Map © Transport for Greater Manchester 2013

8. Tram Data…
Tabular Data in text file (General Transit Feed Specification)
250 Cities publish GTFS data
http://www.gtfs-data-exchange.com/agency/mta-new-york-citytransit/
Stops
Stop_id
Stop
Times
Trip_id
Trips
Service_id
Route_id
Routes
Calendar

9. Earliest Arrival Time Problem
Earliest Arrival Time (EAT) attempts to find the path through a
network from source to destination, such that given a start time T
we arrive at the destination at the earliest possible time after T.

10. Starting point…
G1
G2
2
2
F1
7
[goes_to]
A2
3
3
[goes_to]
B1
[platform]
[platform]
A1
F2
C1
4
7
B2
4
C2

11. Iterations
1
2
3
4

12. Time Independent
3
B
[goes_to]
R1
C
C
D
[Depart]
[board]
A
4
[Depart]
[board]
[goes_to]
R1
B
[Depart]
[board]
R1
A
R2
B
5
[goes_to]
R2
D

13. Applying the timetable
Paths
Timetable
Invalid Paths
Valid Paths

14. Different Graph at each point in time…

15. Different Graph at each point in time…
Example: A -> E
A
B
D
C
E
9:30 AM / Friday
F

16. Different Graph at each point in time…
Example: A -> E
A
B
D
C
E
9:30 AM / Saturday
F

17. Different Graph at each point in time…
Example: A -> E
A
B
D
C
E
10:00 AM / Saturday
F

18. Modeling Time
Time Expanded Model
• Model temporal events as Nodes –
– Arrivals
– Department
– Transfers
• Duration as edge weight, use Dijkstra to find EAT
Time Dependent Model
• Model temporal data as properties
• Model all distinct routes with 2 Node types –
 Station
 Station Route
• Use modified Dijsktra to perform Travel Time Function
during traversal

19. Time Dependent Model
3
[board]
[goes_to]
[goes_to]
R1
C
B
[Depart]
A
4
R1
B
[Depart]
[board]
R1
A
C

20. Modeling Time…
Up to 900 Trams…
A
[T2]
[T3]
[T4]
[T5]
[T6]
[T7]
[T8]
[T9]
[T2]
[T3]
[T4]
[T5]
R1
B
[board]
09:40
09:50
10:10
10:20
10:30
10:40
10:50
11:00
[Depart]
[board]
R1
A
[T1] 09:33
300 Nodes
100K Relations
300K Properties
B
09:43
09:53
10:13
10:23
[T7] 10:43
[T8] 10:53
[T9] 11:03
R1
C
[Depart]
[T1] 09:30
C

21. Modeling Time…
"Time is a dimension in which events can be ordered from
the past through the present into the future.” - Wikipedia

22. Modeling Time…
10:15
A
[T2]
[T3]
[T4]
[T5]
[T6]
[T7]
[T8]
[T9]
[T2]
[T3]
[T4]
[T5]
R1
B
[board]
09:40
09:50
10:10
10:20
10:30
10:40
10:50
11:00
[Depart]
[board]
R1
A
[T1] 09:33
B
09:43
09:53
10:13
10:23
[T7] 10:43
[T8] 10:53
[T9] 11:03
R1
C
[Depart]
[T1] 09:30
C

23. Traversal Framework
Traversal Framework
Evaluator
Path Expander
Branch Selector

24. Path Expander
The traversal framework use PathExpanders to discover
the relationships that should be followed from a
particular path to further branches in the traversal.
public class TripPathExpander implements PathExpander<GraphState>
{
public Iterable<Relationship> expand(…) {
}
}

25. The App
• http://www.tramchester.co.uk/

26. Any Questions?
Follow us on Twitter: @tramchester

27. Traversal Framework
Declarative Java API
It enables the user to specify a set of constraints that limit the parts
of the graph the traversal is allowed to visit
Can specify which relationship types to follow, and in which
direction (effectively specifying relationship filters)
Can specify a user-defined path evaluator that is triggered with each
node encountered

28. A nice problem to have…

29. Stop
Trip
Arr.
Dept.
1
12:00
12:01
B
1
12:05
12:05
C
1
12:10
C
2
12:11
D
2
12:16
C
3
12:20
D
3
12:26
A
Example - Time Dependent Model
T1 Arr.12:00 Dept.12:01
R1
B
T1 Arr.12:05 Dept.12:05
T2 Arr.12:10 Dept.12:21
T3 Arr.12:20 Dept.12:26
B
R1
C
R1
D
C
[Depart]
[Depart]
[board]
A
12:21
[board]
[board]
[Depart]
[board]
R1
A
12:11
D

30. Spatial Indexes
A
B
C
D
P