lagrangian xgraphs: a logical data-model for spatio-temporal network data acknowledgement: venkata...

Lagrangian Xgraphs: A logical data-model for Spatio-temporal Network Data

Acknowledgement:

Venkata Gunturi, Shashi Shekhar

University of Minnesota, Minneapolis

Outline of the Talk

What is Spatio-temporal Network (STN) data?

Value addition potential of STN data

Problem Definition

Challenges

Limitations of Related Work

Proposed Lagrangian Xgraphs

Concluding Remarks

What is Spatial-temporal Network (STN) Data?

STN data is result of interactions (across time) of entity(s) with a network embedded in space.

Large number of urban sensors produce a variety of datasets. E.g., GPS navigation devices, Loop detector data, Social media etc.

Some are mobile, some are stationary, All of them capture diverse characteristics of a network in a urban

scenario

Sample STN datasets over Transportation Network Temporally detailed roadmaps. Traffic signal and coordination data. GPS tracks annotated with engine measurement data.

Motivation: Collective wisdom from these datasets could support valuable use-cases, e.g., eco-routing

From Traditional Roadmaps

Source: Google Maps

Dinky town RoadmapCorresponding Digital Representation

Intersection between 5th Ave SE and 4th St

Intersection between 5th Ave SE and 5th St

5th Ave SE edge

Attributes of 5th Ave SE road segment between N4 and N7

N7 N4

To Temporally Detailed (TD) Roadmaps

Contains typical travel-time under traffic equilibrium conditions

Per minute speed/travel time values 100 million road segments in US NAVTEQ’s highly compressed

weekly speed profile data

Source: ESRI and NAVTEQ

GPS traces

Sources: Mobile devices

Smart phones, in car/truck GPS devices, GPS collars Coupled with engine measurements

VGI Commuter preferred routes under non-equilibrium conditions

Estimate traffic signal delays? Ramp meters Coordinated signals Left turn delays

Waiting at signals

Outline of the Talk



Problem Definition

Challenges



Concluding Remarks

McKinsey Conjecture and Preliminary Evidence

U.P.S. Embraces High-Tech Delivery Methods (July 12, 2007) By “The research at U.P.S. is paying off. ……..— saving roughly three million gallons of fuel in good part by mapping routes that minimize left turns.”

Outline of the Talk



Problem Definition

Challenges



Concluding Remarks

Input– A collection of Spatio-temporal Network datasets– Use case queries (e.g. compare candidate routes)

Output– A unified logical model across these datasets

Objective– Travel related concepts are expressed upfront – Suitable for common routing algorithms e.g. Dijsktra’s, A*

PROBLEM DEFINITION

PROBLEM ILLUSTRATION: AT CONCEPTUAL LEVEL

Logical Model for STN datasets over Transportation Network Usually entities like Roads, Signals, Streets are modeled using lines

strings and polygons. Queried through OGIS operators

Not suitable for comparing candidate routes.

Modeling as Spatial/Spatio-temporal networks?

GPS DATA Delay DataTD roadmaps

Outline of the Talk



Problem Definition

Challenges



Concluding Remarks

CHALLENGES OF “SEQUENCE OF” RELATION

Logical Model for STN datasets over Transportation Network Current spatial/spatio-temporal models work for M=2 What if M>2? e.g. GPS traces and Traffic signal coordination

What if M >2?

Outline of the Talk



Problem Definition

Challenges



Concluding Remarks

After waiting at SG1, SG2 and SG3 become wait-free! Non-local interactions (SG1 not a neighbor of SG2)Typical delay measured over S-B-C-E-D will have wait only at SG1Not true for journeys starting after intersection B or intersection C

Limitations of Related Work: Non-decomposable Properties of N-ary relations

Holistic Property: Properties measured over a larger instance loose their semantic meaning

when broken down into properties of small instances

Sample N-ary relation: Typical delay experienced in series of coordination signals

Typical Representational model used by current network databases, e.g., Oracle spatial, ArcGIS etc.

Query: What is the typical travel-time experienced on Hiawatha Ave (between S and D)?Result: Between 21mins – 25mins 30secs

Current related work not suitable for representing holistic properties which cannot be decomposed

Cannot represent signal coordination upfront!

Limitations of Related Work: Non-decomposable Properties of N-ary Relations

Outline of the Talk



Problem Definition

Challenges



Concluding Remarks

Proposed Approach: Lagrangian Xgraphs

Summary of proposed approach

Holistic properties are modeled as series of overlapping “sub-journeys”

Each “sub-journey” is contains one non-local interaction

Suitable for non-decomposable properties of N-ary relations.

3mins

8mins

5mins

5mins

Travel Related Concepts: Lagrangian vs Eulerian frame of reference

Eulerian Frame: Perspective of a fixed observe, e.g., traffic observatory

What is cost of following routes at 5:00pm• I-35W• Hiawatha Route

Legend: A-I-D: UMN-I35W-Airport A-H-D: UMN-Hiawatha-Airport

Digital Road Map

Path Cost from Traveler Pers.

Cost at 5:00pmFixed Obs.

A-I-D 27 mins 20 minsA-H-D 25 mins 25 mins


Digital Road Map

Travel Related Concepts: Lagrangian vs Eulerian frame of reference

Lagrangian Frame: Perspective of a traveler travelling through the network




A-I-D 11+ 20 minsA-H-D ?? 25 mins


Digital Road Map

Lagrangian Frame: Perspective of a traveler travelling through the network

Travel Related Concepts: Lagrangian & Eulerian frame of reference




A-I-D 11+16 =27 20 minsA-H-D ?? 25 mins


Digital Road Map


5:00PM Snapshot

A-I-D 27 mins 20 minsA-H-D 25 mins 25 mins


Travel Related Concepts: Lagrangian & Eulerian frame of reference

Distance inferred from a GPS track can be decomposed into distances along individual road segments

Travel Related Concepts: Decomposable vs Holistic Properties

Decomposable: Property measured over a larger instance can be broken down into properties of small instances

Travel Related Concepts: Decomposable vs Holistic Properties

What about travel-time inferred from a GPS track?

Time spent on a segment depends on the initial velocity attained before entering the segment!

Holistic Property: Properties measured over a larger instance loose their semantic meaning when broken down into properties of small instances

Taxonomy of Travel Related Concepts Captured in STN Datasets

All STN datasets capture data along two dimensions.

TD roadmaps

Signal Delay Data

GPS DATA

Traveler’s Frame of Reference For Comparing Candidate Routes

Candidate routes are evaluated from the perspective of a person moving through the transportation network.

What is shortest path between A and D for t=1 ? A-B-D or A-C-D

A-C-D is shorter for t=1 : Lagrangian Frame needs to be upfront

Langrangian Xgraph: Formal Definition Lagrangian Xgraph: {Xnodes, Xedges}

Xnodes: Underlying entities at specific space-time coordinates.

– Xv1, Xv2, Xv3…

Xedges: Express a Lagrangian relation (i.e.,’as-traveled’ or ‘typical- experience-in-travel’) relationship among a group a Xnodes

– Xei = {Xvs, Xv1, Xv2, Xv3…, Xvk, Xvd1, Xvd2,..,Xvdj}

First and Last set of Xnodes in an Xedge are marked separately

Xedges are classified based on these TD roadmaps Shoot Xedges

GPS Traces Shoot and Stem Xedges

Trafffic Signal Delays Bush and Flower

Xedges

Get, Set and Join operators (only Xedges) For Xndoes and Xedges

Sample Langrangian Xgraph for Signal Coordination (1/2)

Xnodes: Underlying road segments between two road intersections at specific departure-times.

Xedges: Express a ‘as-traveled’ or ‘typical-experience-in-travel’ relationship among a group a Xnodes

3mins

8mins

5mins

Xnode ED6:Road segment ED for departure-time 7:03am at E

Xedge SB0 and (ED32, ED33, ED34, ED 35) as first and last Xnodes: – An Xedge representing: “If one leaves at S at 7:00am he/she can start

traversing segment E-D at times 7:16, 7:16:30, 7:17, or 7:17:30”

Sample Langrangian Xgraph for Signal Coordination (2/2)

Outline of the Talk



Problem Definition

Challenges



Concluding Remarks

Conclusion

Increased proliferation of sensors

– Spatio-temporal datasets capturing diverse phenomena on a transportation network

Collectively they can add significant value to societal use-cases.

However, they pose modeling challenges due to holistic nature of properties captured in these datasets.


– can model both decomposable and holistic properties

lagrangian xgraphs: a logical data-model for spatio-temporal network data acknowledgement: venkata...

Documents

logical datamodel

engine measurement data

loop detector data

ave se road segment

gps collarscoupled

ave se edge attributes

variety of datasets

eco routing