generating time dependencies in road networks - sea 2011 · generating time dependencies in road...

KARLSRUHE INSTITUTE OF TECHNOLOGY – INSTITUTE OF THEORETICAL INFORMATICS

Generating Time Dependencies in Road NetworksSEA 2011

Sascha Meinert, Dorothea Wagner | May 7th, 2011

KIT – University of the State of Baden-Wuerttemberg and

National Laboratory of the Helmholtz Association

www.kit.edu

Motivation

Available static road networksDIMACS Challenge (Europe, commercial: PTV)

Tiger/Line (USA, government)

OSM (Planet, collaborative)

Artificially generated [Bauer et al., AAIM’10]

Available time-dependent road networksthere is no such real-world data set available to the public!

(artificial data [Delling et al., WEA’08])

Goal:Generate meaningful time-dependency information of continental-sizeroad networks in a daily scenario.

Motivation Analysis of Confidential Data Algorithms Experiments Conclusion

Sascha Meinert, Dorothea Wagner – Generating Time Dependencies in Road Networks May 7th, 2011 2/18

Motivation

Outline

1 Motivation

2 Analysis of Confidential Data

3 Algorithms

4 Experiments

5 Conclusion

Road Network

Graph Modelnodes: crossings, bends, ends

coordinates. . .

edges: pieces of roadsroad category (urban, highway, expressway, . . . )lengthtravel speedspeed limitcapacitydirected. . .time-dependency information

Road Network

coordinates. . .

Road Network

coordinates. . .

Time-Dependency Information

Piecewise Linear Functionsencode the speed reduction

96 supporting points, eachcovers 15 minutes of a day

intermediate points areinterpolated linearly

assigned to affected edges

Dataset of Germany:nodes: ∼ 4 million

edges: ∼ 11 million

time-dependent edges:∼ 7%

piecewise linear functions:∼ 400

0 20 40 60 80

Supporting points

0 20 40 60 80

Supporting points

0 20 40 60 80

Supporting points

Profiles for Tuesday - Thursday

Supporting points

0 20 40 60 80

Compressed Profiles using K-Means

0 20 40 60 80

morningafternoonfull-timecamel

Supporting points

Profile Types

full-time (FUL):almost constant decreaseoccurs mainly within towns

morning (MOR):decrease peak in the morningoccurs mainly on roads into towns

afternoon (AFT):decrease peak in the afternoonoccurs mainly on roads out of towns

camel (CAM):decrease peaks in the morning and the afternoonoccurs on roads out of / into towns without seperated lanes

Conclusion of the Data Analysis

1 Traffic between towns and their region of influence cause delays2 According to the location of the edge a certain profile type is attached3 Profiles have similar curve progressions and are well compressible4 Graph model indicates similar profiles on paths (e.g. bends /

crossings)

Generic Approach

Preprocessing split the set of nodes into two disjoint sets

Urban attach profile type FUL to certain paths

Rural attach profile types MOR/AFT to certain paths

Filtering fit global statistical properties (remove profiles)Postprocessing create the profiles for affected edges:

(AFT ∧ !MOR)→ AFT(!AFT ∧MOR)→ MOR(AFT ∧MOR)→ CAM(FUL ∧ !AFT ∧ !MOR)→ FUL

Generic Approach

Algorithm I: Affected-By-Category

1 BFS: union urban nodes byroad category

2 get boundary nodes (BN)3 all BN pairs shortest paths:

attach FUL profile type4 dampeningBFSM/A(BN):

M: MOR profile typeA: AFT profile type

+ flexible commuters

– harsh BN profile change

– road category may change

Urban area

Algorithm II: Affected-By-Region

1 BFS:union urban nodesregion of influenceouter ring nodes (ORN)

2 all BN pairs shortest paths3 Dijkstra:

ORN→ RNDUA: MORRNDUA → ORN: AFT

+ individual behaviour

+ no harsh BN profile changes

– long distance commuters

Urban area

Area of influence

Urban area

Area of influence

Outer ring nodes

Urban area

Area of influence

Outer ring nodes

Urban area

Area of influence

Outer ring nodes

Urban area

Area of influence

Outer ring nodes

Urban area

Area of influence

Outer ring nodes

Urban area

Algorithm III: Affected-By-Level

1 compute bounding boxes2 assign 1/area(BBox)3 split node set into HL/LL4 limitDijkstra for LL

find HL in search spaceSP to random(HL)assign MOR/AFT �

5 limitDijkstra for HLfind similar HLcompute SPassign FUL �

+ coordinates only

– many edges affected

+ coordinates only

High level area

Low level area 0.1

+ coordinates only

High level area

Low level area 0.1

+ coordinates only

High level area

Low level area 0.1

+ coordinates only

High level area

Low level area 0.1

+ coordinates only

High level area

Low level area 0.1

+ coordinates only

High level area

Low level area 0.1

+ coordinates only

High level area

Low level area 0.1

+ coordinates only

High level area

Low level area 0.1

+ coordinates only

Global Statistical Properties

Category PTV Category Region Level I Level IInotset 93.00% 92.60% 90.73% 92.13% 80.55%camel 2.73% 2.19% 1.53% 3.60% 9.33%morning 1.21% 1.22% 3.40% 2.44% 5.30%afternoon 1.53% 1.22% 3.40% 1.30% 3.30%full-time 1.50% 2.74% 0.92% 0.50% 1.52%time (min) - 55 72 21 26

Local Statistical Properties

Assigned profile types along the shortest paths of 10, 000 randomshortest path queries:

Graph full-time evening camel morning∑

TDE not-setPTV 6.14 26.49 28.36 18.79 79.78 188.99Category 8.16 35.36 7.73 40.18 91.43 177.33Region 1.09 32.28 31.63 33.60 98.60 170.16Level I 2.23 4.80 17.66 13.15 37.84 230.93Level II 5.89 10.07 41.03 31.93 88.92 179.85

Shortest Path Behaviour

Algorithmic properties of 23, 000 time-dependent Dijkstra queries:

Graph sNodes touEdges tdEdges errors rel-av rel-maxPTV 364722 436399 27608.2 - - -Category 364700 436362 32684.0 22.77% 0.39% 5.88%Region 364705 436364 37852.8 26.07% 0.45% 5.88%Level I 364721 436400 29787.9 22.62% 0.43% 5.95%Level II 364725 436407 73641.3 21.88% 0.56% 9.70%

Conclusion

Summaryanalyzed a commercial time-dependent road network

presented algorithms to artificially generate time-dependent data inroad networks of continental size that either admit coordinate orcategory information

showed their usefulness experimentally

Outlookincorperate speed-up techniques

use better filtering techniques

improve post processing

evaluate time-dependent speed-up techniques

Conclusion

Summaryanalyzed a commercial time-dependent road network

presented algorithms to artificially generate time-dependent data inroad networks of continental size that either admit coordinate orcategory information

showed their usefulness experimentally

Outlookincorperate speed-up techniques

use better filtering techniques

improve post processing

evaluate time-dependent speed-up techniques

Time-Dependency Overlay of Karlsruhe

Thank you for your attention!

generating time dependencies in road networks - sea 2011 · generating time dependencies in road...

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