time dependent transportation network models petko bakalov, erik hoel, wee-liang heng #...

Time Dependent Transportation Network Models

Petko Bakalov, Erik Hoel, Wee-Liang Heng# Environmental Systems Research Institute (ESRI)

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Outline

Review of network dataset model Time dependent data Time dependent analysis. Incorporating time data into the network model

Internal representation Build process.

Experimental Results

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Network Model: Definition

A mechanism for defining and managing a connectivity information for features in a geodatabase.

Feature is graphic representation of a real-world object Line (e.g. freeways and railways) Point (e.g. railway stations)

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The connectivity information is explicitly represented with network elements that are found in a single associated logical network (graph).

Three types of

network elements Junctions Edges Turns

The Underlying Logical Network

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The Underlying Logical Network

Line Feature

* FID* Geometry

Point Feature

* FID* Geometry

Edge

* ID

Junction

* ID* Attributes

Turn

* ID

* Attributes

* Attributes

1 1

0..n

* 0..n

2

* *

1..n 1..n

Conn. Graph

Feature Space - stores features which have geometry

Connectivity graph – contains connectivity information about the features in the feature space

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Network Attributes

Network attributes are properties of the network elements that control traversability Cost. Certain attributes

are used to measure and model impedances, such as travel time

Descriptors. Those are attributes that describe characteristics of the network or its elements.

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Defining and Maintaining

Building – a process of establishment of connectivity where the connectivity graph is derived from the features As edits are made to the features in a network

model, the logical network becomes stale. Need to keep track of the modifications

Employ the dirty area management concept. When a feature is modified it creates dirty area

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Build Algorithms

Initial build of a logical network Simply a special case of a rebuild over a dirty

region that encompasses the entire network Existing logical network is empty.

Incremental Rebuilding Rebuilding region is a subset of the dirty region. When we rebuild the entire dirty region, the

resulting logical network is completely correct.

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Build Algorithm

First step: compute the set of connectivity nodes for the entire network.

Extracted through connectivity analysisline endpoint

interstate(indivisble)

street(divisible)

mid-span vertex

interstate tunnel

street bridge

Interstate group:

Street group:

Interstate--Street interconnect:

transition pointstreetsconnect

streetsconnect

interstatesconnect

I1 I2

S1

B1

T1

(0,0)

I3

S2

S3

S4P1

interstateconnects to

street

Connectivity Nodes(X,Y) Point FCID, FID Line FCIDs, FIDs, %'s along

(0,0) T1 I1/100%; I2/0%(0,0) B1 S1/33%(1,0) P1 I2/100%; S4/0%(2,0) S4/100%

(-1,0) I1/0%; I3/100%

(-1,1) I3/0%(0,1) S1/0%

(-1,-1) S2/0%(0,-1) S2/50%; S1/67%(1,-1) S2/100%(-1,-2) S3/0%(0,-2) S3/50%; S1/100%(1,-2) S3/100%

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Step 1: Connectivity Analysis

Extract the geometry of all features in the network dataset.

Sort the vertex information in the table by coordinate values so that the coincident vertexes are grouped together

Analyze each group of coincident vertexes according to the connectivity model

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Step 2: Junction creation

Create junction elements and populate vertex information table from the extracted connectivity nodes

1.For each connectivity node2. Create a logical junction element and set its x and y coordinate

weight values3. If there is a point feature participating in the connectivity node4. Associate the junction element with the point feature5. For each line vertex participating in the connectivity node6. Add a record to the vertex information table, tagged

with the junction element

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Example

Connectivity Nodes(X,Y) Point FCID, FID Line FCIDs, FIDs, %'s along

(0,0) T1 I1/100%; I2/0%(0,0) B1 S1/33%(1,0) P1 I2/100%; S4/0%(2,0) S4/100%

(-1,0) I1/0%; I3/100%

(-1,1) I3/0%(0,1) S1/0%

(-1,-1) S2/0%(0,-1) S2/50%; S1/67%(1,-1) S2/100%(-1,-2) S3/0%(0,-2) S3/50%; S1/100%(1,-2) S3/100%

j1 j2

j3 j6=P1 j7

j8 j9 j10

j11 j12 j13

j4=T1

j5=B1

Streets

S1

67%

j3

Vertex Information TableLine FCID Line FID Relative Position Junction EID

StreetsI3

0%j1Interstate

I1100%

j9

Interstate

I1

0%j2

Streets S250%

j4

Streets S1

100%

j10

Streets

S4100%

j11

0%Interstate I3 j3InterstateInterstate I2 0% j4

33% j5Interstate I2 j6

j60%Streets S4 100% j7

0% j8S2

j9Streets S1Streets S2 100%Streets S3 0%

j12Streets S3 50%Streets S1 100% j12

j13Streets S3 100%

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Create edge elements from vertex information table

1. Sort the vertex information table using the line FCID as primary key, line FID as secondary key, and relative position as tertiary key

2. For each adjacent pair of records in the sorted table

3. If the pair involves the same line feature

4. Create a logical edge element between the junction

elements specified by the two records

Step 3: Edge creation

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Example

e11

e1

e9

e2

e10 e8

e4

e3

e5

e6 e7

j1 j2

j3 j6=P1 j7

j8 j9j10

j11 j12j13

j4=T1

j5=B1

Streets

S1

67%

j3

Sorted Vertex Information TableLine FCID Line FID Relative Position Junction EIDStreets

I3

0%

j1Interstate

I1

100%

j9

InterstateI1

0%

j2

Streets S250%

j4

Streets S1

100%

j10Streets

S4

100%

j11

0%

Interstate I3 j3

InterstateInterstate I2 0% j4

33% j5

Interstate I2 j6

j60%Streets S4 100% j7

0% j8S2

j9Streets S1

Streets S2 100%Streets S3 0%

j12Streets S3 50%

Streets S1 100% j12

j13Streets S3 100%

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Outline

Review of network dataset model Time dependent data Time dependent analysis. Incorporating time data into the network model

Internal representation Build process.

Experimental Results

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Time Dependent Data

Historical Speeds: based on the idea that travel speeds follow a week-long pattern. The traffic speeds are given to us in time slices

e.g. 15 min durations. Current travel times can deviate considerably.

Dynamic Traffic Speeds: The model client has to connect to the data providers over the Internet, download the live travel speeds Real Live Predictive

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Time Dependent Data

Time-Dependent Turn Restrictions: Data vendors also provide addendums to their turn tables that specify the time of the day when turn restrictions are in effect Left turn is restricted from 4 to 6 pm Right turn is restricted on weekdays only.

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Outline

Review of network dataset model Time dependent data Time dependent analysis. Incorporating time data into the network model

Internal representation Build process.

Experimental Results

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Time Dependent Analysis

Clients query for the attribute value of a network element by specifying a current time, and the attribute implementation retrieve the appropriate value.

To perform network analysis that is dependent on the time-of day, the historic and dynamic traffic speeds have to be converted to actual travel times.

Obey the FIFO Principle for Time-Dependent Travel Times

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FIFO Principle

For two departure times from the beginning of an edge, the earlier departure cannot arrive after the later departure.

e1

3-4 pm: 15 mph (4 mins per mile)4-5 pm: 30 mph (2 mins per mile)

3:56

3 miles at 15 mph

4:08

e1

4:00

3 miles at 30 mph

4:06

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FIFO Principle

Account for crossing time-slice boundaries while traversing an edge.

e1

3:56

2 miles at 30 mph

4:04

1 mile at 15 mph

4:00

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Outline

Review of network dataset model Time dependent data Time dependent analysis. Incorporating time data into the network model

Internal representation Build process.

Experimental Results

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Internal Representation

Huge volume of data: For each applicable street, there is a set of speed values for various time-slices across the week, e.g., 672 values for a week.

To resolve the data volume issue, we exploit the fact that the historic speeds are inherently imprecise, and can be well approximated by a small set of representative daily profiles.

The values in the profiles are relative (ranging from 0.0 to 1.0).

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Example

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Build

There are three additional data processing steps in the above network building example needed to support the population of traffic data. Extract free flow, weekday and weekend speeds

from the data sources and map to profile. Create list of edge records. Resolve historic join. “Merge” the sorted list of

regular edge tuples from step.

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System Architecture

NetworkBuild Engine

Traffic Windows Service

Solver

Time-DependentTraffic

Evaluator

Network Dataset

NavTeq Inrix

TMC Translator

In-MemoryDynamic TMC Mapping

TMC

106P057

EID Direction

e4 FT

106N057 e4 TF

….. ….. …..

….. ….. …..

EdgeFID

…..

99

…..

EdgeFCID

…..

1

…..

ObjectID

…..

301

…..

Streets_DynamicTMCs

EdgeFromPos

…..

0.6

…..

EdgeToPos

…..

1.0

…..

TMC

…..

106P057

…..

991302 1.0 0.6 106N057

TF_FreeflowSpeed

Streets (FeatureClassID 1)

…..

…..

…..

…..

35

…..

…..FT_

FreeflowSpeed

…..

30

…..

Length

…..

…..

…..

Shape

…..

…..

…..

ObjectID

…..

99

…..

NetworkDataset

Geodatabase

Dynamic TMC Mapping Table

TMC

106P057

EID Direction

e4 FT

106N057 e4 TF

….. ….. …..

….. ….. …..

In-Memory Cacheof Dynamic Speeds

StartTime

08:15

EndTime

08:30

Data

EID Direction

e4 FT

e4 TF

….. …..

Speed

35

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…..

….. ….. …..

1. Create

network dataset

Create

2. Build

network dataset

3. Install and configure traffic

Windows service (accounts for NavTeq and Inrix; reference to network dataset)

4. Start traffic Windows service

4a. Instantiate TMC

translator and initialize it with reference to network dataset

4b. TMC

translator copies dynamic TMC mapping table

into local memory

5. At 5-minute intervals, traffic

Windows service pulls dynamic feeds from data providers and digests the feeds

5a. Update local

FileGDB with digested feeds

5b. Use

TMC translator to convert

digested feed into BLOB

format

6. Solver requests refresh

of dynamic speeds

6a. Network dataset reads BLOB from

FileGDB and de-serializes it into in-memory cache

7a. Solver

requests dynamic speed

7c. Evaluator

returns dynamic speed

7b. Evaluator

reads dynamic speed from cache

Integrating Dynamic Traffic Data into Network Datasets

File Geodatabase

TimeSlices Table

StartTime

08:00

EndTime

08:15

TableName

DataTable1

08:15 08:30 DataTable2

BlobData

TMC

106P057

106N057

…..

Speed

45

43

…..

DataTable1

….. …..

TMC

106P057

106N057

…..

Speed

35

41

…..

DataTable2

….. …..

Traffic Server

Client Machine

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Outline

Review of network dataset model Time dependent data Time dependent analysis. Incorporating time data into the network model

Internal representation Build process.

Experimental Results

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Experimental Results

 Edges Junctions Size

North America73.5 million 27.2 million 23.7 GB

Europe141.5 million 55.5 million 51.8 GB

Latin America25.1 million 8.4 million 6.9 GB

Table 1 Test Datasets

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Experimental Results

Table 2 Performance Results – North America

Table 3 Performance Results- Europe

  Average 90th percentile

Local 3 stop routes ~680 ms ~965 ms

Nationwide 3 stops routes 3.5 seconds 5.5 seconds

  Average 90th percentile

Local 3 stop routes ~712 ms ~1034 msNationwide 3 stops routes 4.4 seconds 6.7 seconds

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Questions ???