Route Finding in Time Dependent Graphs

Ben Earlam [@BenEarlam]

Nima Montazeri [@Nimamon]

[Presented By]

[Located]

What are we going to cover?

Introduction

Why Graph?

About The Data

Time Independent Model

Q & ADemo

Time-dependent Model

How it all started?

5 Week tech lab

Experiment &

Learn

Real world problem

Produce working software Small team

Manchester

The Focus…

Travel & Transport (Manchester)Open DataOpen SourceMetrolink System (25 Million Journeys p/a)

Tech: Not Only SQL• Neo4JExperiment with Graph database as way of modeling a travel networkEverything in the Cloud (AWS)

Tram Network

Why Graph database?

3

35

52

2

2

2

Map © Transport for Greater Manchester 2013

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-city-transit/

StopsStop

TimesTrips Calenda

r

Routes

Stop_id Trip_id Service_id

Route_id

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.

Starting point…

A1

A2

B1

B2

3

3

C1

C2

4

4

G2

F2

2

G1

F1

2

[goes_to]

[platform]

[platform]

[goes_to]

7

7

Iterations

1 2

3 4

Time Independent

A C

R1A

R1B

R1C

B

[board]

[Depart]

[Depart]

[goes_to] [goes_to]

3 4

[board]

R2D

D

R2B

[board]

[Depart]

5

[goes_to]

Applying the timetable

Paths Timetable

Invalid Paths Valid Paths

Different Graph at each point in time…

Different Graph at each point in time…

A

B

CD

E

F9:30 AM / Friday

Example: A -> E

Different Graph at each point in time…

A

B

CD

E

F9:30 AM / Saturday

Example: A -> E

Different Graph at each point in time…

Different Graph at each point in time…

A

B

CD

E

F10:00 AM / Saturday

Example: A -> E

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

Time Dependent Model

A C

R1A

R1B

R1C

B

[board]

[board]

[Depart]

[Depart]

[goes_to] [goes_to]

3 4

Modeling Time…

A C

R1A

R1B

R1C

B

[board]

[board]

[Depart]

[Depart]

[T1] 09:30

[T2] 09:40[T3] 09:50[T4] 10:10[T5] 10:20[T6] 10:30[T7] 10:40[T8] 10:50[T9] 11:00

[T1] 09:33

[T2] 09:43[T3] 09:53[T4] 10:13[T5] 10:23

[T7] 10:43[T8] 10:53[T9] 11:03

Up to 900 Trams…

300 Nodes100K Relations300K Properties

Modeling Time…

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

Modeling Time…

A C

R1A

R1B

R1C

B

[board]

[board]

[Depart]

[Depart]

[T1] 09:30

[T2] 09:40[T3] 09:50[T4] 10:10[T5] 10:20[T6] 10:30[T7] 10:40[T8] 10:50[T9] 11:00

[T1] 09:33

[T2] 09:43[T3] 09:53[T4] 10:13[T5] 10:23

[T7] 10:43[T8] 10:53[T9] 11:03

10:15

Traversal Framework

Traversal Framework

Evaluator

Branch Selector

Path Expander

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(…) {

}

}

The App

• http://www.tramchester.co.uk/

Any Questions?

Follow us on Twitter: @tramchester

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

A nice problem to have…

Example - Time Dependent ModelStop Trip Arr. Dept

.

A 1 12:00

12:01

B 1 12:05

12:05

C 1 12:10

C 2 12:11

12:11

D 2 12:16

C 3 12:20

12:21

D 3 12:26

A

C

R1A

R1B

R1C

B

[board]

[board]

[Depart]

[Depart]

T1 Arr.12:00 Dept.12:01

T1 Arr.12:05 Dept.12:05

[board]

D

R1D [

Depart]

[board]

T2 Arr.12:10 Dept.12:21T3 Arr.12:20 Dept.12:26

Spatial Indexes

C

B

A

D

P